(PDF) Dynamic Programming for Aligning Sketch Maps

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Dynamic Programming for

Aligning Sketch Maps

Dissertation submitted in partial fulfillment of the requirements

for the Degree of Master of Science in Geospatial Technologies

February 24, 2020

_______________________________________

Violeta Ana Luz Sosa León

vsosaleo@uni-muenster.com

https://github.com/violetasdev

Supervised by:

Prof. Dr. Angela Schwering

Institute for Geoinformatics

University of Münster

Co-supervised by:

Dr. Malumbo Chipofya

Institute for Geoinformatics

University of Münster

and

Prof. Dr. Marco Painho

Nova Information Management School

Universidade Nova de Lisboa

__________________________________

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Declaration of Academic Integrity

I hereby confirm that this thesis on Dynamic Programming for Aligning

Sketch Maps is solely my own work and that I have used no sources or aids

other than the ones stated. All passages in my thesis for which other sources,

including electronic media, have been used, be it direct quotes or content

references, have been acknowledged as such and the sources cited.

February 24, 2020

___________________________________

I agree to have my thesis checked in order to rule out potential

similarities with other works and to have my thesis stored in a database for

this purpose.

February 24, 2020

___________________________________

iii

Acknowledgments

I am grateful to the joint program coordinated by Dr. Christoph Brox at

the University of Muenster, Prof. Dr. Joaquín Huerta at Jaume I University,

and my also supervisor, Prof. Dr. Marco Painho at the University Nova de

Lisboa for this opportunity to have one of the most significant experiences in

my academic, social, and professional aspects. I hope you can continue helping

more students in the future with the program from which I have been part.

A special thanks to my supervisors, Prof. Dr. Angela Schwering and

Dr. Malumbo Chipofya, from whom I have learned in a range of different

topics from theoretical to technical, in how to engage research and to manage

myself to improve continually. Your kind support and knowledge have made

possible this thesis to flourish and be an essential step in my future academic

and professional life. I am inspired and motivated to be more involved in the

Spatial Intelligence research field and continuing exploring the

interdisciplinarity approaches between spatial cognition and computer

science.

Finally, I would like to acknowledge my family, professors, and friends

in Mexico, Colombia, and Japan, and my new friends all over the world.

Thanks for your overwhelming care and support in this adventure, pushing

me out of my comfort zone to learn from every experience and giving me love,

courage, and advice when I most needed it.

 
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TABLE OF CONTENTS 
Chapter 1 INTRODUCTION ................................................................. 1.2 
1 Related work and motivation................................................... 1.2 
2 Research questions and objectives .......................................... 1.3 
3 General methodology ................................................................ 1.4 
4 Thesis outline .............................................................................. 1.5 
Chapter 2 BACKGROUND .................................................................... 2.6 
1 Sketch Maps ................................................................................ 2.6 
2 The graph matching problem ................................................... 2.7 
3 Qualitative Spatial Representation .......................................... 2.9 
3.1 Qualitative Spatial Calculi .................................................. 2.10 
3.2 Qualitative Constraint Networks ...................................... 2.11 
3.3 Local Compatibility Matrix ................................................ 2.12 
4 Link analysis ............................................................................. 2.13 
5 Reinforcement Learning Algorithms .................................... 2.13 
Chapter 3 METHODOLOGY ............................................................... 3.16 
1 Implementation workflow ...................................................... 3.16 
2 System setup ............................................................................. 3.18 
2.1 Python .................................................................................... 3.18 
2.2 SmartSkeMa framework ..................................................... 3.19 
2.3 Metric map generation ........................................................ 3.21 
2.4 Execution environment ....................................................... 3.21 
3 Input Datasets ........................................................................... 3.21 
3.1 Artificial dataset ................................................................... 3.23 
3.2 El Remanso............................................................................ 3.23 
3.3 Mailua Ranch ........................................................................ 3.25 

 
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4 Qualitative Analysis ................................................................ 3.26 
5 Score system.............................................................................. 3.27 
5.1 Page Rank .............................................................................. 3.27 
5.2 Spectral Solution Technique ............................................... 3.30 
5.3 Heuristic scores from LCM ................................................. 3.31 
6 Searching Algorithms .............................................................. 3.33 
6.1 Tabu Search ........................................................................... 3.33 
6.2 SARSA ................................................................................... 3.37 
7 Evaluation ................................................................................. 3.41 
Chapter 4 RESULTS AND DISCUSSION .......................................... 4.43 
1 Performance .............................................................................. 4.46 
1.1 Execution time ...................................................................... 4.46 
1.2 Precision and Recall ............................................................. 4.48 
2 Alignment Results.................................................................... 4.51 
3 Discussion ................................................................................. 4.53 
4 Limitations ................................................................................ 4.56 
Chapter 5 CONCLUSIONS .................................................................. 5.58 
1 Future Work .............................................................................. 5.60 
Chapter 6 REFERENCES ...................................................................... 6.61 
 
 
 
 
 
 

 
vi 
 
List of Tables 
Table 1 Spatial Calculi for Qualitative Representations ..................... 2.10 
Table 2 SmartSkeMa feature types ........................................................ 3.22 
Table 3 Artificial dataset features .......................................................... 3.23 
Table 4 El Remanso dataset features ..................................................... 3.25 
Table 5 Mailua Ranch dataset features ................................................. 3.26 
Table 6 Confusion Matrix ....................................................................... 3.41 
Table 7 Mailua Ranch Marsh feature attributes .................................. 4.44 
Table 8 Link Analysis sample results .................................................... 4.45 
Table 9 LCM(H1) score sample .............................................................. 4.46 
Table 10 Artificial SVG: Precision and Recall Results ........................ 4.49 
Table 11 El Remanso: Precision and Recall Results (H2) ................... 4.49 
Table 12 El Remanso: Precision and Recall Results (H1) ................... 4.50 
Table 13 Mailua Ranch: Precision and recall results ........................... 4.50 
Table 14 Artificial SVG: Alignment result sample .............................. 4.51 
Table 15 El Remanso: alignment result sample ................................... 4.52 
Table 16 Mailua Ranch: alignment result sample ............................... 4.52 
 
  
 
 
 
 
 
 

 
vii 
 
List of Figures 
Figure 1 Thesis challenges outline ........................................................... 1.4 
Figure 2 Methodology overview ............................................................. 1.5 
Figure 3 Graph: nodes, edges, and labels (M. Chipofya et al., 2017) .. 2.8 
Figure 4 Graph Matching techniques (Conte et al., 2016) .................... 2.8 
Figure 5 Graph labels and nodes (color) (M. Chipofya et al., 2017) . 2.12 
Figure 6 Framework implementation workflow ................................. 3.17 
Figure 7 Thesis implementation workflow .......................................... 3.18 
Figure 8 SmartSkeMa interface .............................................................. 3.19 
Figure 9 SmartSkeMa vectorization ...................................................... 3.20 
Figure 10 SmartSkeMa Geometry Editor user interface ..................... 3.20 
Figure 11 Artificial dataset SVG ............................................................ 3.23 
Figure 12 El Remanso neighborhood (Google Maps view) ............... 3.24 
Figure 13 El Remanso: sketch (left) and metric (right) maps ............ 3.24 
Figure 14 Mailua Ranch: sketch (left) and metric (right) maps ......... 3.25 
Figure 15 Transition probabilities for a graph G (Ceri et al., 2013) .. 3.28 
Figure 16 Link Analysis evaluation diagram ....................................... 3.29 
Figure 17 Diagram for the Spectral Solution Technique algorithm .. 3.31 
Figure 18 Heuristic scores calculation workflow ................................ 3.33 
Figure 19 Tabu Search workflow diagram ........................................... 3.34 
Figure 20 SARSA dynamic ..................................................................... 3.37 
Figure 21 Mailua Ranch vectorized sketch map .................................. 4.43 
Figure 22 Qualitative representation input maps ............................... 4.44 

 
viii 
 
Figure 23 Artificial SVG execution time ............................................... 4.47 
Figure 24 El Remanso execution time ................................................... 4.47 
Figure 25 Mailua ranch execution time ................................................ 4.48 
Figure 26 Tabu clustering alignment .................................................... 4.54 
Figure 27 SARSA(H2) clustering alignment ........................................ 4.55 
Figure 28 SARSA(H2) compared to SARSA(H1) alignment ............. 4.55

ix

List of Algorithms

Algorithm 1. Tabu Search ....................................................................... 3.35

Algorithm 2 SARSA Main ...................................................................... 3.40

Algorithm 3 SARSA Environment: Policy ........................................... 3.40

x

List of Acronyms

DPSM Dynamic Programming Sketch Maps Implementation

FP False Positive

FN False Negative

GIS Geographic Information System

LA Link Analysis

LCM Local Compatibility Matrix

LCM(H1) First heuristic score from the LCM

LCM(H2) Second heuristic score from the LCM

QMC Qualitative Constraint Map

QCN Qualitative Constraint Network

SST Spectral Solution Technique

TP True Positive

TN True Negative

1.1

Abstract

Sketch maps play an important role in communicating spatial

knowledge, particularly in applications interested in identifying

correspondences to metric maps for land tenure in rural communities. The

interpretation of a sketch map is linked to the users’ spatial reasoning and the

number of features included. Additionally, in order to make use of the

information provided by sketch maps, the integration with information

systems is needed but is convoluted. The process of identifying which element

in the base map is being represented in the sketch map involves the use of

correct descriptors and structures to manage them. In the past years, different

methods to give a solution to the sketch matching problem employs iterative

methods using static scores to create a subset of correspondences. In this thesis,

we propose an implementation for the automatic aligning of the sketch to

metric maps, based on dynamic programming techniques from reinforcement

learning. Our solution is distinctive from other approaches as it searches for

pair equivalences by exploring the environment of the search space and

learning from positive rewards derived from a custom scoring system. Scores

are used to evaluate the likeliness of a candidate pair to belong to the final

solution, and the results are back up in a state-value function to recover the

best subset states and recovering the highest scored combinations.

Reinforcement learning algorithms are dynamic and robust solutions for

finding the best solution in an ample search space. The proposed workflow

improves the outcoming spatial configuration for the aligned features

compared to previous approaches, specifically the Tabu Search.

Keywords: sketch map, metric map, dynamic programming, tabu search,

learning algorithm, link analysis, alignment.

1.2

CHAPTER 1 INTRODUCTION

1.1 RELATED WORK AND MOTIVATION

As humans, we communicate our perception of the elements

surrounding us by using different tools: book descriptions, paintings, and

more elaborated representations like maps in different types, including sketch

maps. Sketch maps contain a set of items displaying the author’s conception

of the space, providing spatial information useful for studying and

understanding the environment in which she lives (Malumbo Chipofya, Wang,

& Schwering, 2011). To be able to unveil the meaning behind a sketch map

without the author’s feedback, it is necessary to compare every structure to a

more structured representation of geographical elements, such as metric maps

(Klaus Broelemann, Jiang, & Schwering, 2016). By having them side-by-side, it

is possible to identify the abstraction created in the sketched map and relate it

to a specific item in the metric map. As the elements increase in the input map,

the association’s complexity with the metric map also grows, and therefore the

relationships included, requiring automatizing the aligning process.

The difficulties in this task include the definition of appropriate

representations of the problem space in order to structure the search for

correspondences (Wallgrün, Wolter, & Richter, 2010). Graphs are robust

information structures with gained popularity to represent formal structures

for displaying relations of different types such as spatial, geometrical, or

conceptual (Bunke, 2000). They are often used to examine the relationships

correspondence and consistency of the data structure implemented with an

exhaustive analysis of their distribution defined as a case of graph matching

problems, with different approaches according to the category in which the

graph representation belongs (Foggia, Percannella, & Vento, 2014). Diverse

techniques to solve the matching problem include the measure of distances,

composite graph similarities, string-based methods, and statistical graph

matching (Emmert-Streib, Dehmer, & Shi, 2016). One of the current

implementations for the sketch to the metric alignment problem, translated as

a graph matching problem with the implementation of Qualitative Constraint

1.3

Networks, analyzes specialized local structures to evaluate candidate pairs

while searching for correspondences (Malumbo Chipofya, Schwering, & Binor,

2013). The correspondence problem using LCM has arisen solutions with

exponential time complexity, which may not be a feasible solution for

significant scale problems (Malumbo Chipofya, 2018). In the recent years, the

artificial intelligence field has developed different techniques for giving

solutions to large scale tasks involved with graph nature problems in

computer vision, integrating algorithms that rely on patterns and deductions

from the accessible information (Foggia et al., 2014). By exploiting the

capabilities of Local Compatibility Matrices, newer algorithms for significant

scale problems, and other similarities measures studied for matching tasks in

other fields, how to improve the pair selection process by taking advantage of past

exploration in local compatibility matrices?

1.2 RESEARCH QUESTIONS AND OBJECTIVES

This research aims to implement and compare two searching

algorithms to identify the next optimal pair selection during the matching

process between a sketch and a metric map. The following research questions

are defined:

• How can the pair selection algorithm be modified to increase the number of

correctly matching objects for alignment between sketch and metric maps?

• How can the exploration in the pair selection algorithm be used to recover

critical information for the matching process between sketch and metric maps?

• Does the new pair selection algorithm improve the alignment solution?

In order to answer the previous research questions, the following

objectives are defined:

• Calculate a new selection score system for the matching process

• Retain feedback for future decision processes during the exploration in the

search algorithm

• Evaluate the matching results comparing the search algorithms implemented

to measure changes in performance

1.4

The open challenges identified from the sketch to metric map alignment

process are addressed with the stated research questions as displayed in

Figure 1:

1.3 GENERAL METHODOLOGY

The sketch to metric map alignment process workflow is divided into 5

modules: first of all, for the Input Processing, the sketch and metric map are

processed in the SmartSkeMa framework to translate the features from

geometries to a set of vectors by a computer vision segmentation process and

then identify the spatial relationships from the vectorized features are

organized in a graph like data structure, implementing Qualitative Constraint

Networks. Secondly, the Qualitative Analysis module analyzes the output from

the framework and assesses the compatibility of each feature in terms of

feature type and similarity. The next step in the workflow is the Score System,

which provides the measurements of Link Analysis ranking score, Spectral

Solution clustering solution, and the two Local Compatibility Matrices

Heuristic Scores H1 and H2 to evaluate the likeliness of a candidate pair to

belong to the alignment solution. Finally, in the Searching Algorithms

component, we implement two different algorithms to find correspondences

between candidate pairs: a metaheuristic approach named the Tabu Search

and a reinforcement learning algorithm, SARSA. We compare the provided

solutions in terms of their performance, precision, and recall. Figure 2

summarizes the processes outlined and their outputs.

RQ 1

Algorithm modification

Challenge 1

Lower computation expenses

Challenge 2

Decrease the omission of candidate

pairs

RQ 2

Use exploration for information

recovery

Challenge 1

Lower computation expenses

Challenge 3

Take into account local information

about during search

RQ 3

Does the new algorithm improve the

alignment solution

Challenge 2

Decrease the omission of candidate

pairs

Figure 1 Thesis challenges outline

1.5

Figure 2 Methodology overview

1.4 THESIS OUTLINE

The following sections are organized as follows:

• Chapter 2 describes the theoretical background introducing the

concepts employed in this thesis including the use of sketch maps, the

importance and past work for giving solution to the graph matching

problem, the spatial representation calculus and data structures

implemented to make use of them, and finally, a review to different

strategies for searching algorithms.

• In Chapter 3, the proposed methodology is outlined in detail,

describing the sketch and metric maps used as an input and the

assessment of the compatibility between features followed by the

definition of the scoring system for the pair selection, and finally, the

design and pseudo code for the Tabu and SARSA algorithms.

• Chapter 4 displays the results of the workflow described in Chapter 3

to automatically align sketch maps followed by the evaluation process

to measure the performance and quality of the solution in terms of

precision and recall for each search algorithm, discussion of the results,

as well as the findings and the encountered limitations.

• Finally, Chapter 5 includes the conclusions and future work.

2.6

CHAPTER 2 BACKGROUND

This section presents an outline of the concepts supporting this thesis

from the literature. Initially, we present Sketch Maps and a brief background

to the graph matching problem, introducing qualitative spatial

representations and the different qualitative calculi involved. Secondly, we

outline the theory of Link Analysis to identify the importance of vicinities in

local exploration, and finally, we portray strategies to solve searching

problems from the perspective of artificial intelligence.

2.1 SKETCH MAPS

Sketch maps are representations of the space surrounding an individual

decomposed into different spatial elements such as roads, buildings, and other

physical features describing the relationships between the scene elements

(Schwering & Wang, 2010). Moreover, every individual due to different

experiences give an interpretation of the objects and their relationships being

a topic of interest in research for map sketching in schools, governmental

projects, and academia.

The decoding of the information from a sketch (input) map to a metric

(output) map is an approach by projects such as the SmartSkeMa framework

delivering the scene spatial segmentation, qualitative representations, and

input/output alignment process (Schwering et al., 2014). Along with the

implementation, several analyses and techniques have been implemented to

give solutions to the alignment process resulting in theoretical implications

and findings such as Qualitative Constraint Matrices. On the other hand, the

its4land project is one of the real-world applications of this kind of framework.

By using sketch maps, communities in Kenya are able to participate in land

delimitation and appropriation, helping to the management of natural and

human-build resources.

To accurate relate subjective maps and metric maps, techniques for

assessing qualitative map alignment has been applied to find matches among

the input representation such as a sketched entity, and one or several entities

in a metric map using Local Compatibility Matrices (LCM) (M. C. Chipofya,

2.7

Schultz, & Schwering, 2016). The version of the implemented Tabu algorithm

aims to face challenges such as the omission of promissory matching

candidates and long execution times on large datasets. However, the dynamic

metaheuristics generated in Chipofya’s algorithm gave better performance

and accuracy versus standard compatibility matrices; leaving open the

research for the refinement during the iterative match-candidates selection

process since it rapidly leaves the matching process without candidates due to

the removal of not compatible local pairs at a particular stage. As the search

space grows, it may be helpful to identify how to associate potential additions

during the exploration in previous regions of the search space (Malumbo

Chipofya et al., 2013)

2.2 THE GRAPH MATCHING PROBLEM

The most significant benefit of graphs is that they can represent

structured data and have been used to undertake problems in data mining,

document analysis, and graphical pattern recognition, and bioinformatics

(Cook & Holder, 2006). A graph  is composed by:

• , a set of finite nodes

• , a set of edges where and edge , starts at node  and

ends at node 

•   is a function to assign nodes labels

• , is a function to assign edges labels

In Figure 3, color circles are nodes, and black lines are edges. The set of

strings are edges labels and represent a spatial

relationship between nodes. Further explanation about spatial relationships can

be found in Section 2.3.

2.8

Figure 3 Graph: nodes, edges, and labels (M. Chipofya et al., 2017)

Graph matching involves estimating the configuration similarity by

finding a correspondence between edges and nodes of a pair of graphs

fulfilling several constraints to find similar substructures on one graph into

the other (Conte, Foggia, Sansone, & Vento, 2004). The comparison between

graphs is classified into two main approaches, Exact to find isomorphic

relations or Inexact to asses an approximate solution, depending on how

elements are paired (Foggia et al., 2014). Exact graph matching is usually

restricted to a set of problems and have a binary solution: a match is true or

false, whereas Inexact or error-tolerant matching is capable of handling real-

world class distortions and providing an evaluate the level of similarity

between two graphs but is more expensive to compute (Cook & Holder, 2006;

Emmert-Streib et al., 2016).

Figure 4 Graph Matching techniques (Conte et al., 2016)

For solving the error-tolerant matching, one of the most used

formalizations to the use of the edges’ constraints is the weighted graph matching

in which the graphs are illustrated by the corresponding adjacency or similarity

matrices (Foggia et al., 2014) . Given two graphs with similarity matrices  and

, the compatibility between two edges  and  can be measure by a

function:

Graph

Matching

Inexact

Graph edit distance

Iterative Methods

Exact Isomorphism-based

measures

2.9

    

   

where  is a defined compatibility function. The correspondence

solution to this graph matching category includes algorithms designed to

compute an approximation of the Graph Edit Distance obtained from node-

editing actions (delete, insert) and constraints are still satisfied (Conte et al.,

2004), others are based on properties related to the eigenvectors of the

adjacency matrix referenced as Spectral Techniques, as well as Iterative Methods

on the other hand for studying repetitive arrangements derived from the

calculus of similarities scores (Cho, Lee, & Lee, 2010; Foggia et al., 2014). These

methods evaluate the node’s vicinity to assign correspondences during the

search, and their application is linked to the nature of the problem. Other

approaches include heuristic techniques for combinatorial situations, such as

tabu search, which are described in section 2.13 and 3.33.

2.3 QUALITATIVE SPATIAL REPRESENTATION

As Sketch Maps does not have a georeferenced system, it is necessary

to automatize the analysis of spatial relationships to identify the underlaying

correspondence between the elements represented (Wallgrün et al., 2010).

Furthermore, the system requires the appropriate constraints design to

establish correspondences to the desired dataset, such as a metric map

(Malumbo Chipofya et al., 2011). These constraints are derived from the

encoding process from physical experiences in which we applied our

reasoning in daily activities, generating knowledge to describe the

relationships between elements in the surrounding space (Štěpánková, 1992).

The spatial relations like adjacency or inclusion for elements such points, lines,

or regions are described by qualitative representations from the perspective of

direction, position, or the physics of space (Jan, Schwering, Schultz, &

Chipofya, 2015). Instead of numerical labels to define the structure of the

physical world, qualitative representations illustrate our perception from

specific conceptual distinctions (Freska, 1991). In order to calculate these

representations, different qualitative spatial calculi are applied to be organized

as constraints in a new graph and constructing a Qualitative Constraint

Network (QCN) (M. C. Chipofya et al., 2016). This leads to the idea that finding

2.10

correspondences between qualitative spatial relationships from a sketch map

to a metric map can be done through the match of the equivalent QCN for each

map (Malumbo Chipofya et al., 2013).

In the following subsections, we detailed the different spatial calculi

and QCN structures developed for giving a solution to the problem of finding

correspondences between a sketch and a metric map.

2.3.1 Qualitative Spatial Calculi

A qualitative calculus is defined as the set of algebraic structures to

describe qualitative reasoning between objects which constitute the domain of

the calculus (sharing the same type: line, points, or regions) by assigning a

relation (Malumbo Chipofya et al., 2013). Table 1 displays a subset of the

available spatial calculi involved in the graph matching problem for the

alignment in sketch maps derived from empirical studies (Malumbo Chipofya

et al., 2011; Jan et al., 2018):

Table 1 Spatial Calculi for Qualitative Representations

Calculi

Description

Example

RCC8

Eight topological relations

based on the primitive relation

 (Randell, Cui, & Cohn,

1992)

EC Externally Connected

RCC11-LPC

Eleven topological relations

between city blocks based on

the dim of the intersection of

boundaries (line or point

contact) (Jan et al., 2015).

ECp Externally connected by a point

Relative

Distance

Three relations based on

relative metric minimum

distance and clusters into three

groups (near, far, very far) for

polygonal features (Jan et al.,

2018)

Object D is far near to the cluster (1) and far from

the cluster (2)

2.11

Calculi

Description

Example



Nine relative orientation

relations to spatially express a

situation for a starting point

, reference point  and a

focus point  (Scivos &

Nebel, 2005)

Looking from  to ,  is to the left

Adjacency

Five relative orientation

relations (left_of, right_of,

front, back, and crosses). It

computes the spatial relation

between near-by objects (Jan et

al., 2018)

Object B is left_of object C

Region

starVars

Relative orientation relations

which divide the plane into

cone-based regions. With a

granularity factor  the

number of total relations is 

. Helps to describe the

orientation of one polygon

respecting other (Jan et al.,

2018; Lee, Renz, & Wolter,

2013)

A starVars object  with   and angle of

orientation 

Each one of these calculi is useful for delineating and analyze specific

arrangements regarding the world that we perceive in reality and construct

structures called constraint networks to communicate knowledge from a scene

(Ligozat, 2005). The next section contains the details about this structure.

2.3.2 Qualitative Constraint Networks

A Qualitative Constraint Network (QNC) is a complete graph in which

the edges are labeled from a qualitative calculus (for example, RCC11), which

describes the relation shared by the endpoints or nodes (Malumbo Chipofya

et al., 2013). For a finite set of nodes , a set of relations  and  a

projection which to each set of nodes , we assign an element  of 

called a constraint on the edge . In Figure 5, the nodes or pairs are

illustrated in color circles  and their corresponding label or constraints

( from the RCC8 calculus relation set 

2.12

Figure 5 Graph labels and nodes (color) (M. Chipofya et al., 2017)

There are three properties in qualitative reasoning to asses consistency

in a constraint network. A network is said to be (Ligozat, 2005):

1. Normalized: if the node  labeled by  and the node  is labeled

by  for all 

2. Atomic: if  has only one basic relation for each pair 

3. A-Closed: if for every triplet of nodes  exists 



Consistency is achieved if there is an appropriate structure along with

the constraints (Ligozat, 2013). In particular, if in a constraint network every

restriction is coherent then, it is said to be closed and stablishes the consistency

of a QCN with a spatial calculus , leading to the exercise of encountering

correspondences for a set of qualitative spatial representations as the solution

for the QCN matching problem (Malumbo Chipofya et al., 2013).

As it is a high order dimensionality problem, we need more specialized

structures to find matches efficiently (M. C. Chipofya et al., 2016). In the

following sections, we highlight the use of local compatibility matrices

constructed from the qualitative constraint networks.

2.3.3 Local Compatibility Matrix

A Local Compatibility Matrix (LCM) is a case of QCN derived from two

graphs qualitative analysis, offering a global representation for the

correspondence for a set of pairs during the match search for an input graph

(Malumbo Chipofya, 2018).

An LCM states the compatibility between a specified pair 

and  and every other pair. In the matrix, a row corresponds to the

input node , a column the target node  and, the cell, the largest label

2.13

common to both edges . Represent the compatibility between

every pair requires  LCMs (M. C. Chipofya et al., 2016).

Properties from LCM are derived from its geometry. The first one is the

possibility to sort rows and columns in a way that the cell with the same labels

forms rectangular submatrices. Secondly, for non-overlapping and equal

labels, these submatrices do not overlap each other (M. C. Chipofya et al., 2016).

Extracting information about the local compatibility in this structure requires

the computation of two heuristic scores, which is detailed in the System

Scoring subsection 3.5.3.

2.4 LINK ANALYSIS

Traditional methods to recover information about a graph structure are

focused on encountering a substructure to obtain a set of probabilities

distribution (Dehmer, 2008). Finding a solution to the graph matching

problem in computing engineering for pattern recognition, for example, has

derived methods ranging from the manipulation of the similarity matrix to the

redefinition of the graph class to obtain new similarity measures (Cour,

Srinivasan, & Shi, 2007; Dehmer, Emmert-Streib, & Kilian, 2006). One

approach is spectral techniques developed in computer vision, giving

consistent results in identifying the correspondence between features

analyzing the compatibility of the geometric constraints with the idea of

identifying clusters from highly related items to fulfill an approximate

solution contribute some insights to the current design of matching algorithms

(Leordeanu & Hebert, 2005).

2.5 REINFORCEMENT LEARNING ALGORITHMS

Diverse techniques for matching a variety of features, including multi-

polygons, have been developed in computer science (Bunke & Jiang, 2000). As

the search space increases, these techniques need to be able to handle

significant inputs of information and offer the possibility to find patterns

(Foggia et al., 2014). In this regard, learning algorithms offer a routine in which

is possible to improve the performance: it stores the data during the agent-

environment interaction, maximizing the weight of the backup information

2.14

with a set of received rewards in a Markov Decision Process, to organize and

structure the search and make appropriate decisions, based on the

environment arrangement (Sutton & Barto, 1999).

One of the keys configurations in reinforcement learning algorithms is

the pertinent generation of the action-value and the state-value functions. By

correctly identifying the conditions for selecting a feature in the case of the

correspondence problem, the optimal solution computation time may

improve, learning to associate potential aggregation with profitable regions of

the search space to mitigate the adverse effects of an exponential expansion of

the search space (Chipofya,2016). If the agent experiences future lower

rewards, it returns to a past state in which a better next step or selection exists.

Reinforcement learning techniques are an approach to make the best decision

from the exploration and identification of situations and their consequences

(Sutton & Barto, 1999).

For any Reinforcement Learning problem,

 are the steps in which the environment receives a state

 is the environment state at the step  such as  where  are all

the possible states

The agent then selects an action accordingly to its current state,  is an

action such as  where ) are all the actions available in the state

. As a result of this action, the agent receives a numerical reward, and the

agent advance to a new state. By doing so, the agent is pursuing a mapping,

formally called a policy, from states to probabilities of selecting each possible

action:

 Is a policy, a mapping from each state   and action   to

the probability  of selecting action  when the agent is in the state 

From this, by following the policy in a specific state, the expected state-

value is obtained in

 



  

2.15

Furthermore, by following a policy starting in a specific state and taking

a specific action, the expected action-value is obtained in

  



   

The goal is to have a good enough policy that maximizes the reward

reflected in the V and Q values. Producing an optimal approximation implies

to select the best value available, by backing up and comparing these results.

The concept of Dynamic Learning is visible in this approach: by iteratively

evaluate the best possible decision combination (policy) in a value function, it

is possible to find the best solution to the selection process.

3.16

CHAPTER 3 METHODOLOGY

This chapter focuses on the methods implemented to answers the

research questions. First, a description of the implementation workflow is

presented in section 3.1 to illustrate the connection between each module. The

system setup is described in section 3.2, followed by the description of the data

used to test the searching algorithms. Next, in Section 3.4, the scoring system

components are presented, giving details on how they are calculated. Finally,

section 3.5 describes the design and pseudocode for the Tabu and SARSA

searching algorithms, respectively.

3.1 IMPLEMENTATION WORKFLOW

The process of aligning one feature to another between a sketch and a

metric map requires the integration of the new implementation with the

SmartSkeMa functionalities. In the following sections, we refer to the

developed solution as the Dynamic Programming for Sketch Maps, DPSM.

First, to recognize the drawing, the metric and the sketch maps are uploaded

as inputs in the of the SmartSkeMa interface to be displayed and processed in

the backend (1. Input Processing). Following the Qualitative Segmentation, a

computer vision process that identifies the features in the sketch map (for

more information about this process, review Murcia, 2018), the data obtained

from the vectorization is used by the Qualitative Representation module to

derived the relation set values and return the Qualitative Set and the Similarity

Matrix, two inputs used in DPSM for assessing the compatibility and the

similarity between features (2. Qualitative Analysis). Once the data is received

from the mentioned modules, three different scores Link Analysis, Spectral

Solution, and Local Compatibility heuristics, are calculated and provided (3. Score

System). Next, the searching algorithms start the alignment process with the

scores as arguments (4. Searching Algorithms). A more detailed review of the

different modules is:

• Input processing: Using the SmartSkeMa’s project interface, the sketch and

metric maps are processed. SmartSkeMa will execute the Qualitative

Segmentation (recognize the sketch maps features).

3.17

• Qualitative Analysis: once SmartSkeMa vectorizes the image, it will run

the process of Qualitative Representation, giving as outputs the Similarity

Matrix and the Qualitative Constraints datasets. In the DPSM

implementation, we evaluate the compatibility between candidates’ pair

and temporary solutions.

• Scoring System: this module is useful to calculate different scores for each

candidate pair as a criterion to evaluate if it will be added to the current

solution. One of the tasks is to recreate the Local Compatibility Matrix for

each candidate pair and the current solution to calculate the LCM heuristic

score. It is also used to calculate the Link Analysis score for each pair

considered based on the similarity matrix. Finally, by using the LA score,

it will calculate the Spectral Solution to be considered as initial solutions

for the algorithms as it will show highly connected pairs inside the search

space.

• Searching algorithms: two different algorithms are implemented to give a

solution to the alignment problem: a Tabu search, from the non-learning

algorithms, and a SARSA algorithm from the reinforcement learning

algorithms. Both are fed with the output generated in the previously

mentioned modules given. As a result, a list of sketch and metric maps

features to be displayed in the SmartSkeMa interface.

Finally, the searching results will be evaluated by the performance

(execution time in seconds), precision, and recall. In this section, the concepts

will be explained in more detail. The implementation diagram is detailed in

Figure 6:

Figure 6 Framework implementation workflow

3.18

For each major component, every module is responsible for a set of

process and outputs that are going to be used in future functionalities; this

workflow is shown in Figure 7 with gray dotted lines for the modules used

from the SmartSkeMa framework:

Figure 7 Thesis implementation workflow

3.2 SYSTEM SETUP

For workflow implementation, it is necessary to integrate different

libraries and modules in a unique environment. For the system setup, the

following libraries were used from and in the SmartSkeMa framework.

3.2.1 Python

The proposed methodology is developed in Python. Python is an object-

oriented programming language with high-level data structures as it offers

diverse standard libraries from string processing to system interfaces, some of

which are specially design and optimized to handle large datasets (The Python

Software Foundation, 2009).

The main Python libraries implemented are:

• Numpy (v. 1.18.1): package dedicated to scientific computing with Python

offering tools for manipulating N-dimensional array datasets. We use the

matrix tools to store, manipulate and process data (NumPyCommunity,

2020)

• Intertools (v. 2.3): this module offers fast and memory-efficient tools to

iterate through data. As in our research, it is needed to search in large

datasets. This module helps to optimize the process in between during the

solution exploration (The Python Software Foundation, 2003b).

3.19

• Collections (v. 2.4): module implementing specially designed container

datatypes as alternatives to the Python’s standard built-in ones, with a

high-performance outcome in our case for storing and manipulating the

data in the implementation (The Python Software Foundation, 2003a)

• OpenAI Gym: a library with a collection of test problems called environments

to implement reinforcement-learning algorithms with a shared interface

(Brockman et al., 2016)

3.2.2 SmartSkeMa framework

The Smart Sketch Map system (SmartSkeMa) is an application to record

sketch-based information regarding land tenure in the frame of peri-urban and

rural territories displaying an integrated vision of the end user’s sketch map

and a cartographic dataset (M Chipofya, Jan, Schultz, & Schwering, 2017). An

overview of the interface is displayed in Figure 8 with the input sketch map in

the left and in the right side, the corresponding metric map.

Figure 8 SmartSkeMa interface

From the SmartSkeMa project, the main modules used are:

• Sketch recognition: for identifying distinctive elements in the sketch maps,

for instance, water bodies, houses or mountains, the module processes

shapes, and features’ representations by using a symbol recognizer to

extract visual representations and transforming them into vector

geometries (see Figure 9) to be stored in the system, using supervised

learning techniques, polygonal clustering methods (Ng & Han, 2002) and

3.20

image recognition methods (K. Broelemann, 2011; Klaus Broelemann &

Jiang, 2013)

z

Figure 9 SmartSkeMa vectorization

Through the interface, we provide the sketch and the metric map

files and run the Automatic Vectorization process, and additionally, we

provide more vectorized features using the Geometry Editor functionality.

The interface described is displayed in Figure 10:

Figure 10 SmartSkeMa Geometry Editor user interface

• Qualitative Representation: In the sketch to map alignment problem, every

item is defined as a node inside the qualitative map with a designated class

and the corresponding attribute values to identify them. Spatial relations

are used to describe the location of each item in the qualitative spatial

representation, becoming labels between each node in a graph matching

model, and only a set of qualitative calculus are combined with stabilizing

the distortions captured from the sketch map (M Chipofya et al., 2017).

As a result, the module generates the corresponding Qualified Map

for the sketch and the metric maps and the Similarity Matrices. Both datasets

are organized based on the candidate pairs; these are each possible

3.21

combination between an element in the sketch map that may correspond

to another element in the metric map. The Qualified Map dataset describes

the labels between each node in the graph representation of the sketch to

map association per relation set. On the other hand, the Similarity Matrix

contains binary information about the compatibility between each label for

every candidate pair.

3.2.3 Metric map generation

For the generation of the metric map’s dataset, the software QGIS in the

version 3.10 A Coruña is used to digitalize the areas’ features and export them

as a geoJSON file. QGIS is an open-source and multiplatform Geographic

Information System (GIS) application supporting raster, vector, and database

operations and functionalities for managing geographical information

(QGISORG, 2002).

3.2.4 Execution environment

All the procedures were executed on an Intel Core i7-75002U CPU at

2.70GHz, and 8GB DDR4 memory card with a 19GB dedicated virtual memory.

A set of environments with different Python configurations are created

through Anaconda, a scalable data science multi-platform environment

manager for packages and Python distributions, with an extensive collection

of open source modules to find, access and share (Anaconda, 2020). An

Anaconda environment executes a Python version 3.6.4 configuration along

with the packages required to run the SmartSkeMa framework. This version

of Python is selected according to TensorFlow’s version requirements for the

Qualitative Segmentation Module.

3.3 INPUT DATASETS

Sketch mapping is a drawing exercise on a large piece of paper that

allows recreating a global image of the people’s spatial distribution of their

territory (Štěpánková, 1992) The following sketch maps are spatial

representations with different complexity levels to test the proposed

algorithms. All of them have been generated by humans on different platforms,

with two of them with the same objective: describe an area of interest

3.22

according to the mental image of a space previously experienced. In the

following subsections, a detailed description of each one is provided.

The common relevant attributes in these representations include:

• smart_skema_type: type of feature according to the domain model

implemented in the SmartSkeMa framework, derived from the

workshops carried in the Maasai community in Kenya for the its4land

project (Karamesouti et al., 2018; Murcia, 2018). The features’ type

catalog is detailed in Table 2.

• name: a descriptive label for each feature for identifying purposes

• id: feature unique identifier for different processes inside SmartSkeMa

and the DPSM implementation.

Table 2 SmartSkeMa feature types

Feature type

Description

beacon

An object for specifying land boundary

boma

A small place where people rest

boundary

Clear delimitation of an area

house

Standard family living unit

marsh

Large wetland with plants. Associated to green

areas in the experiment

mountain

Represents a single mountain or chain of

mountains

olopololi

Area for agricultural activities. Associated to

bridges in the experiment

oltinka

Water collection site

river

Natural or human-made water currents

road

Human-made access with or without pavement

surface

school

Building with educational purposes

tree

An area containing one or more trees

water_tank

Water storing area for a collective usage

3.23

3.3.1 Artificial dataset

The artificial dataset is a set of different elements with a random

distribution. In Figure 11, the resulting sketch map is displayed. On the left

side is the sketch map representation, and on the right side, the objective

metric map to align.

Figure 11 Artificial dataset SVG

Each one of the map representations contains the features described in

Table 3:

Table 3 Artificial dataset features

Map type

Number of features

Type of features

Sketch

6

(2) Marsh

(1) River

(1) Olopololi

(1) Road

(2) Mountain

Metric

7

(2) Marsh

(1) River

(1) Olopololi

(1) Road

(2) Mountain

3.3.2 El Remanso

El Remanso is a small neighborhood located in Bogotá, Colombia, in a

residential area between the Fucha river (blue line) and the Primera de Mayo

Avenue (yellow line), as displayed in Figure 12. The community enjoys green

areas around the river, such as the Ciudad Montes Park, which has a small

lake (blue circle). People from the southwest side of the river can cross using a

3.24

bridge (purple line). Bogotá is known for the mountain chain in the east called

Eastern Hills, as they are visible from most of the citizens and serves as an

essential spatial reference element in the landscape (Pavony, 2000; Robson,

van Kerkhoff, & Cork, 2019)

Figure 12 El Remanso neighborhood (Google Maps view)

The sketch map represents the mental image of the main elements

recalled from the neighborhood, as shown in Figure 13:

Figure 13 El Remanso: sketch (left) and metric (right) maps

The metric map geoJSON file is created in QGIS A Coruña, and the

attributes are filled according to the SmartSkeMa guidelines. Each one of the

map representations contains the features described in Table 4:

3.25

Table 4 El Remanso dataset features

Map type

Number of features

Type of features

Sketch

13

(5) House

(2) Marsh

(1) Boma

(1) Olopololi

(2) Mountain

(1) River

(1) Road

Metric

15

(7) House

(2) Marsh

(1) Boma

(1) Olopololi

(2) Mountain

(1) River

(1) Road

3.3.3 Mailua Ranch

The Mailua Ranch is a sketch map data set collected in the Maasai

community located in Southern Kenya, in which the SmartSkeMa project

participates with other partner universities to provide tools in the land rights

for the area residents. The sketch map in Figure 14 was created by individuals

from the Maasai community in one of the field studies where additionally the

domain model was generated for the spatial components described including

classes for environmental characteristics, social units, activities, shapes,

housing, and farming (Karamesouti et al., 2018).

Figure 14 Mailua Ranch: sketch (left) and metric (right) maps

The sketch map object representations contain the features described in

Table 5:

3.26

Table 5 Mailua Ranch dataset features

Map type

Number of features

Type of features

Sketch

(geometry editor)

16

(1) School

(1) River

(2) Road

(3) Mountain

(1) Marsh

(3) Boma

(5) Olopololi

Sketch

(vectorization)

31

(1) School

(1) River

(2) Road

(4) Mountain

(5) Marsh

(8) Boma

(11) Olopololi

Metric

106

(1) School

(1) River

(2) Road

(3) Mountain

(3) Marsh

(n) Boma

(n) Olopololi

3.4 QUALITATIVE ANALYSIS

The sketch to map features alignment is approached as a graph

matching problem in which every map feature is defined as a node and each

relation label as an edge, as described in section 3.2.2. In the SmartSkeMa Input

Processing, the system generates the Similarity matrices and Qualitative

Constraint Map (QCM) and stores them to be used in the Qualitative analysis

module, responsible for providing the compatibility and the similarity

evaluation between two candidate pairs during the execution of the searching

algorithms.

A candidate pair p is a set of features  where i and , in this

case, with  representing the sketch map and  the metric map to align.

The main tasks of this module are to return values for:

• Similarity: the similarity between the two pairs,  and  is recovered

from the similarity matrix . Moreover, it is evaluated as:

3.27

  

  

• Type Compatibility: the type compatibility for a pair is evaluated

from the QCM feature type attributes QM as:



   

• Candidate-Solution Compatibility: given a current solution , for a

candidate pair  the compatibility with  is:

  

   

The definition of these values helps to filter the search space during the

selection of candidate pairs for a current solution to the ones who add value

to the final solution.

3.5 SCORE SYSTEM

The evaluation of a pair is a critical process in the alignment problem

as the decision of the next most fitting step must contemplate the impact of the

extension of every QCN, each relation set, and additional considerations

(Chipofya, 2013). In this thesis, the additional considerations are based on the

graph matching solutions for discrete problems in a closed graph, which state

the influence of the vicinity configuration (R. Battiti & Protasi, 2001). From the

Similarity Matrix, a Link Analysis is used to extract the ranking scores of each

node in terms of their connectivity, taking these results to extract an initial

solution with the Spectral Solution Technique studying, in this case, the

clustering behavior of the nodes. Finally, from the neighborhood properties of

the LCM, two heuristic scores are calculated.

3.5.1 Page Rank

PageRank is an algorithm developed to ranking a node according to the

number of links in a web graph, by assigning a score between 0 and 1; during

the graph exploration, some nodes are more visited than others, creating a

network in which profoundly explored nodes share a high number of

connections in between. (Ceri et al., 2013; Page, Brin, Motwani, & Winograd,

3.28

1998a). The result is a distribution probability vector or also called the left-

eigenvector, representing the ranking score for the candidate pairs in the

Similarity Matrix A.

Consider a web graph G in which pages are represented by nodes .

Let  be a web page (node) pointing to a set of pages (nodes)  and in the

same way  the set of nodes pointing to . Let  be the number of

links (edges) from  and  to be a normalization factor. The equation gives the

simplified version of PageRank ranking value R:

  



 

In order to calculate the corresponding PageRank score, the following

variables and procedures are addressed:

• Teleport operation: if  is the total number of nodes in the web graph ,

the operation to move from one to another happens with a probability

of 

 A teleport rate with probability  is defined to avoid

looping in nodes with low compatibility and encourage exploration.

• Initial probability distribution vector: base vector for the distribution

probability vector as it represents each node value procured by dividing

the sum of the number of nodes connected to it by the total number of

features connected. In the case of the sketch to map alignment, the

number of nodes connected is the ones with value 1 in the Similarity

Matrix, as it represents the compatibility of each one of the features in

the search space.

• Transition Probability Matrix P: Consider a graph G with a set of nodes

N= {A, B, C}. The matrix P represents the distributed probability of

moving from one node to another, as seen in Figure 15:

Figure 15 Transition probabilities for a graph G (Ceri et al., 2013)

3.29

A row represents a candidate pair in the Similarity Matrix, and

it is divided by the number of compatible features in that row. For the

resulting base matrix P, a Teleport Distribution ( ) and Teleport

Variation ) is applied.

• Power iteration: the method implemented to calculate the left-

eigenvector and the corresponding largest eigenvalue of a matrix,

named the Distribution Probability Vector, the ranking score. Some of

the advantages of this method include that it does not affect the

transition probability matrix P, can handle large sizes of data, and it

returns the values of interest in less computational and complexity

expenses.

The Link Analysis (PageRank) score computation in DPSM is executed

with the Similarity Matrix, calculated from the input sketch and metric maps,

as an argument, and the system retrieves the ranking scores for all candidate

pairs. The link analysis results are used in the Spectral Score Technique (SST)

as an argument to calculate an initial solution and, in the Tabu Search, to make

a move in the selection process. In Figure 16, the PageRank implementation

for the sketch to map aligning problem is detailed.

Figure 16 Link Analysis evaluation diagram

3.30

3.5.2 Spectral Solution Technique

The Spectral Solution Technique is an algorithm from Leordeanu and

Hebert's research, able to find secure correspondences between a pair set of

features as nodes in the graph matching problem, by calculating the

eigenvector of a graph matrix M and processing these scores to get a collection

of highly linked assignments. In this algorithm, selected features are highly

related and expose high links scores showing a clustered behavior among

them. On the other hand, low related features do not show any links rates, or

if they appear, they show a considerable distance concerning the central

cluster (Leordeanu & Hebert, 2005).

Consider a graph G with a set of nodes N represented by the matrix A.

Initially the similarity matrix is constructed, followed by the definition of

environment variables: L as the number of nodes, x as the elements of the row

in the iteration, and x* the maximum eigenvalue or affinity scores for the

Similarity Matrix M. As the SST addresses the use of maximum eigenvalue, it

makes use of an algorithm that pursues the identification of links between

large amounts of objects connected. One approach is Google’s algorithm,

PageRank, which calculates a feature relevance inside a network according to

the number of links shared with other features (Page, Brin, Motwani, &

Winograd, 1998b). The algorithm will reject all the objects in the iteration with

a lower value and a corresponding label in conflict with x* and collect the high

scored and compatibles ones as long there are features left to analyze in L.

Finally, x will contain the pairs candidates with the highest confidence of being

correct assignment. The algorithm executes the steps described in Figure 17.

In general, in the graph matching problem, the SST candidate pairs serve as a

start point for the exploration in the search space. For the sketch to map

alignment, these selected features represent the pairs candidates with the most

number connections or relation labels inside the sketch-metric map graphs

being good candidates for initializing the search. Moreover, according to the

Link Analysis theory and Leordeanu findings, from the analysis of the

candidate pair’s vicinity and identifying the existence of robust correlated

features, the definition of the first steps during the search task make the results

more profitable than resume from a point with no information available (R.

Battiti & Protasi, 2001).

3.31

Figure 17 Diagram for the Spectral Solution Technique algorithm

3.5.3 Heuristic scores from LCM

The third score component is based on the properties of the Local

Compatibility Matrices described in section 2.3.3, especially the non-

overlapping labels property in which matrix cell with the same label generate a

non-overlapping square submatrix inside the LCM from which two heuristic

scores are derived (Malumbo Chipofya et al., 2013):

Consider a candidate pair  with LCM and its corresponding

submatrices denoted by  with rows  and columns

, where R is a label . The first observation of this configuration

is the possibility of identifying a set of submatrices inside furthermore

considering the square submatrix property, get the minimum submatrix

3.32

dimension which indicates the highest contribution of each  into the

extension of the current candidate pairs match  in the future: the highest the

total sum of the min dimension of the submatrices in the LCM, higher the

chances to find in the future more compatible candidates in the solution as

indicated in the equation:

 

 

The result is a greedy selection of candidate pairs, as the selection

follows the paths labeled as useful in the first consideration. The second

heuristic H2 complements the first heuristic H1 by providing a peak in the

estimation of a good pair in the solution evaluating the impact of the current

pair  into future solutions by ordering the candidate pairs in ascending

order of H1 and considering the most significant feature,  as the possible

solution that contains the node  (M. C. Chipofya et al., 2016) as described

in the equation:

  

In the DPSM implementation, the first heuristic is calculated by

recovering the LCM from the Qualitative Constraint Map (QCM) for a set of

candidate pairs. The result is a batch of scores indicating the value of H1 per

each relation set identified from the QCM and finally summarizing them to

get a global score. Secondly, the heuristic H2 is updated for the input map

(sketch map) and extended by the SmartSkeMa framework, merging the

implementation of the first heuristic. The procedure happens as the candidate

pairs are evaluated during the calculus of H1, maintaining an updated score

structure as the search is executed, adding new features into the solution.

Figure 18 describes the implementation for generating the LCM and

calculating the H1 and H2 scores:

3.33

Figure 18 Heuristic scores calculation workflow

3.6 SEARCHING ALGORITHMS

The aligning of a sketch map feature to a feature in a metric map is the

examination of a large set of options that comply with specific characteristics

to be a good match. We explore all the options on the metric map to find which

one is the most like to match a specific feature in the sketch map. Diverse

techniques from non-learning and learning algorithms have arisen from

research. In this thesis, we implement two different search algorithms, with

different approaches, advantages, and configurations: a Tabu Search and a

SARSA, an incremental dynamic programming algorithm to solve

reinforcement learning problems (Saad, 2011).

3.6.1 Tabu Search

Tabu search approach is to solve combinatorial optimization problems

like the ones in graph theory by using a list of banned or taboo moves obtained

from a number of iterations in a local search to construct a final solution

(Roberto Battiti & Tecchiolli, 1994; Glover, 1989a).

3.34

For the configuration of the Tabu algorithm, the main arguments are

the search space, the local search space or neighborhood, the list of banned

moves, and the criteria to establish whether they belong to the current solution

or need to be penalized at each iteration. An overview of the general workflow

is shown in Figure 19:

Figure 19 Tabu Search workflow diagram

In the context of the sketch to metric map alignment, the overview for

each of these aspects and their processing is as follows:

• Search Space: the space of every possible item that can be contemplated

as part of the final solution during the search (Gendreau & Potvin, 2005).

For the interest of this study, the search space is all possible

combinations  composed only by compatible candidate pairs  

 where  and  represent a feature from the sketch and metric map.

3.35

• Current solution: denoted by . The solution used as the initial one is the

output from the Spectral Solution Technique.

• Neighborhood: the set of available pairs to add to the current solution.

For each iteration, a modification or move is applied to the solution  to

add or remove a pair. The result is a collection of available compatible

pairs called neighboring solutions, a subset of the search space. The

evaluation of items belonging to the neighboring solutions is done

using the functions created in the Qualitative Analysis module. Each new

pair added to the current solution  during the Tabu Search is

compared to every item in the search space  to check their

compatibility. If old items are not compatible with the most recently

added one, they are removed. In the same way, if items from the search

space are compatible with the recently added one and with the

remaining items, the neighborhood is updated with new available

moves.

• Move: for each iteration, the algorithm performs a modification to the

currently available solution considering all potential actions. For the

current implementation, two actions are possible: ADD or REMOVE.

The criteria for choosing one or another depends on the evaluation of

the neighborhood explained in the following points. The dynamics of a

move during the search are displayed in Algorithm 1.

Algorithm 1. Tabu Search

input: , number iterations iter, LA, QSM, QMM, metric_size

output: 

// initialize

1 Set S=initial solution ;

2 Set tabu_in list;

3 Set tabu_out list;

4 while iterations

5 Update available moves

6 Select best non-tabu available move

7 if move is ADD

8 Insert move into S

9 Insert move into tabu_out

10 else move is REMOVE

11 Remove move from S

12 Insert move into tabu_in

13 return best matching result S

3.36

• Best non-tabu available move (best_move): for each iteration, the item with

the highest LA score in the neighborhood is selected as the best

candidate to be considered in the current solution .

• ADD pair: the search next action is said to be ADD if the best_move does

not exist in the current solution. The new pair is evaluated using the

Qualitative Analysis module. For each item in the neighborhood, it

assesses the Candidate-Solution and Types Compatibility values. If both

values are positive, the pair is added and labeled as best_add.

• REMOVE pair: the search next action is said to be REMOVE if best_move

already exists in  or there are not useful items to be added in the

current solution , with not useful meaning a candidate pair that is

incompatible with one or more features in . The procedure is to

discard the item with the lowest LA score in , named best_remove.

After executing an ADD or REMOVE move, in both cases, the

output element, best_add or best_remove, is appended to a tabu list. In this

implementation, two lists are created: tabu_in and tabu_out.

• Tabu lists update: These are managed by a FIFO (First-In, First-Out)

method; each time a new element is added to the bottom of the list, the

first added element on the list is removed (Glover, 1986). The tabu_in

list manages the items that we discarded from  and tabu_out list the

ones we join to the solution. At the beginning of each iteration, the

available moves are updated additionally by removing the items in the

tabu lists. Instead of using a unique list, we implemented two list, this

with the objective of encouraging exploration but on the other hand to

not over consider useful elements into the solution, this approach seems

to have an advantage in terms of the activity of each list in the algorithm

assuring no duplicated solutions while considering candidates inside

the solution  (Glover, 1986, 1989b). The size of the tabu lists is fixed to

25% of the size of the current solution.

The algorithm search is executed, and for a given number of iterations,

it explores a set of solutions, adjusts the initial solution  by adding or

removing pairs from a neighborhood  of , appearing according to the

compatibility to a new solution . (Glover, Taillard, & Taillard, 1993). Finally,

3.37

the best solution is returned with a set of compatible pairs with a size at least

equal or more significant than the initial solution.

3.6.2 SARSA

SARSA learns an optimal action-value function  from experience

gained by an agent while interacting with an environment in an iterative

manner in a set of episodes by regularly calculating the value of each state-

action  (Saad, 2011; Sutton & Barto, 1999). In Figure 20, the dynamics of

the SARSA algorithm are described:

Figure 20 SARSA dynamic

On every step into the environment, the value of the state-action pair

 in a step , is updated according to the received reward at step and

the following selected state-action pair  with a probability  alternately

to selecting it at random (Sutton & Barto, 1999), using a discounted rate

(Ratitch & Precup, 2015) to encourage the exploration and avoid cycling

behaviors during the search in contrast with the tabu scheme based on a fixed

list size, that is not strict and, therefore, the possibility of cycles remains

(Roberto Battiti & Tecchiolli, 1994). The updating of the action-value function

is given by:

  

The equation leads to the progression of to  by using the

values  in a sequence of State, Action, Reward, State,

Action. The algorithm learns during the episode that some policies are weak

and switch to another one. For the specific case of the sketch to metric map

alignment, we define the following attributes for the algorithm set up:

3.38

• Step: a step is an iteration in which the agent will take action for the

current state

• Action: an action in the graph matching problem is each one of the

candidates' pairs the search space as they are the options available to

move into the environment. Each action returns a reward if they are

added to the current state or solution. An action is said to be the next

action when a new candidate pair is selected among the available pairs

from the calculus of the action probabilities. The action probabilities are

returned by the policy and represent the probability for each action to

be chosen in the next step. The values are calculated based on the LCM

scores modified by .

• State: a state in the graph matching problem is every set of compatible

candidate pairs. Every state is different, has a different accumulated

reward at a step , and represents a possible solution for the search. At

every step into the environment, a new action is executed (this means a

pair is added to the solution) and creates a new state (a new solution is

generated from the previous solution plus the new pair). In the SARSA

algorithm implementation, the initial state is selected randomly from

the action space or candidate pairs returned by SST. The final state is

found when there are no more items compatible with the current

solutions, this means, a peak has been found and the algorithm “walked”

into a dead end while connecting the candidate pairs.

• Reward: is a numerical value that the algorithm maximizes in the search.

At each step, a reward is calculated based on the effects of future action

on the current state. For the sketch to map alignment, the reward is

based on the score of the candidate pair from the LCM calculus.

• Discount rate : determinates the current value of the next rewards by

considering a reward earned in the forthcoming  time steps with .

The discount rate   is a constant, the closest to 0 it will maximize

the most recent rewards; the closest to 1 the later rewards will have

more weight. From empirical results, a discounted rate   is used

in most of the cases to avoid getting into a greedy algorithm, that is,

maximizing only immediate rewards (Sutton & Barto, 1999, p. 55)

3.39

• Step-size : fixes the updating pace for the values. The step-size

parameter  is a constant, as the reward probabilities do not

change over time (Sutton & Barto, 2018, p. 32)

• Probability : to avoid selecting the best option while evaluating the

available actions that is a greedy action, they are affected by a

probability  , resulting in a random selection. For all the actions

, the low scored actions are given a probability of selection equal

to 

 and for the high scored actions, in the case of this

implementation only to the best possible action from the LCM scores,

the probability  

 is given.

For the current implementation, the workload is divided into two

modules: the SARSA Main, which controls the action-value function updates,

and the SARSA Environment, which contains the logic behind the policy

evaluation.

• Episode: An episode consists of an alternating sequence of states and

state-action pairs (Sutton & Barto, 1999). The number of episodes is a

set parameter. The larger the number of episodes, the longer the

exploration into the environment.

• Environment: contains the set of functionalities behind every step the

agent takes. The general template is based on OpenAI Gym for reset,

step, and policy. Other functionalities are included to support the

policy in assessing the actions. In reset, the environment restarts the

search and set the initial action and initial state by selecting a candidate

pair randomly from a portion size of the SST solution, to avoid

frequently selecting the same high scored item. For step, the

environment updates the current state with the provided action.

• Policy: returns the actions to be considered for the next step and the

probability of each one, affected by . The set of actions returned are the

ones compatible with the current state. Each action represents a

candidate pair compatible with the current solution represented by a

state. In order to measure the compatibility, the LCM scores are

calculated for the available features and per relation set. The global

score is returned per candidate pair, and the policy selects as the best

3.40

action the one with the maximum LCM score. Additionally, it selects the

best action according to the current state from  if the state has been

experienced, or it will create a new entry.

Algorithm 2 SARSA Main

input: env, number episodes episode,

output: 

// initialize

1 Set Q(s,a)= initial value-function

2 Set 

3 Set 

4

5 for each episode

6 reset environment

7 get action a using policy

8 do

9 Take step, set s’,r, terminal state

10 Get a’ from s’ using policy

11 Set  

12 Set   

13 Update   

14 Update a=a’

15 Update s=s’

16 while terminal state is False

17 return Q

Algorithm 3 SARSA Environment: Policy

input: observation, QSM, QMM, metric_size, similarity, compatible_pairs

output: LCM scores, terminal state

// initialize

1 Set LCM=0

2 Set 

3 Set terminal state = False

4 Get available pairs

5 if available pairs length is 0

6 Set terminal state = True

7 else

8 Get LCM scores

9 Set nA=number of LCM values

10 Set action probabilities LCM_p =LCM*

11 Set best_a=max(LCM_p)

12 Update LCM_p[best_a]=LCM_p[best_a]+(1-)

13 return LCM, terminal state

3.41

SARSA searches for solutions for a set of episodes, for which it will run

several iterations until the final state is reached. In the main algorithm, new

actions and states are found on every step into the environment, and the

action-value function  is updated, to be used in the policy evaluation. The

first action is selected randomly from the SST scores to take the agent one step

inside the environment. In the environment, with the provided action and

state at step , the policy will calculate the next action probabilities with the

LCM scores. As the search continues, and the following episodes are

completed, the agent learns which combinations of action-states are the best

ones according to the rewards received and applied this knowledge to make a

better decision in the remaining episodes.

Finally, the algorithm returns the action-value function , with the

assortment of all states (solutions), actions (candidate pair), and rewards (total

score) that modified that solution. The last added solution is the result of an

on-policy approach, whereas the complete set of solutions represents an off-

policy procedure.

3.7 EVALUATION

Once the algorithm design is stable, the performance analysis includes

a review of the matched features. Consider a decision process to evaluate

correctly aligned sketch to metric features labeling a correct or incorrect

assignment. There are four possible combinations (categories) organized in a

Confusion Matrix, as in Table 6, containing the labels True Positive, False

Positive, False Negative, and True Negative.

True Condition

Predicted

Condition

Condition Positive

Condition Negative

Predicted Positive

True Positive

False Positive

Predicted Negative

False Negative

True Negative

Table 6 Confusion Matrix

A True statement refers to a correctly classified feature (positive or

negative), and the False statement refers to an incorrect classified feature

3.42

(positive or negative), then a True Negative label out an alignment correctly

rejected (Davis & Goadrich, 2006). Based on the Confusion Matrix

configuration, four metrics can be derived:

 



 

 



 

Then, it is possible to define the concepts of Precision and Recall as:

• Precision: the portion of positive features correctly aligned by the

algorithm implementation (True Positives)

• Recall: the portion of positive features correctly labeled by the algorithm

implementation

For the environment performance measure and analysis, as the

algorithm implementation is in Python, each algorithm is executed for several

steps to stress the environment. The results are stored in a data frame to be

exported with the following values: iteration number, execution time in

seconds, true positives features, true negatives, false positives, false negatives,

and final iteration solution.

4.43

CHAPTER 4 RESULTS AND DISCUSSION

The implementation results for the Tabu and SARSA algorithms, as

well as their backup functionalities from the Qualitative Analysis and the

Score System, are presented in this chapter. Initially, we describe the overall

results from the processing and scoring modules. The first subsection (4.1)

describes the performance rates in terms of the execution time during the

alignment process for each one of the datasets. Secondly, the alignment results

are displayed, followed by their discussion. Finally, we highlight some of the

limitations encountered.

For Input Processing, the sketch maps are processed in the SmartSkeMa

framework creating the vectorized features per dataset. The three datasets'

attributes are then edited on the Inkscape software. In order to illustrate these

steps in Figure 21, the Mailua Ranch processed features are recovered from the

SmartSkeMa vectorization to remove the small features later not associated

with the smart schema data type.

Figure 21 Mailua Ranch vectorized sketch map

For all sketch and metric maps datasets, the SmartSkeMa’s id and name

attributes are revised in the XML feature editor to aid the match identification.

In Table 7 for the Marsh feature in the Mailua ranch dataset, the attribute and

values for the sketch and metric map are described:

4.44

Table 7 Mailua Ranch Marsh feature attributes

Feature

Attribute

Value

Sketch map

id

sm_marsh1

name

sm_marsh1

smart_skema_type

marsh

Metric map

id

mm_marsh1

name

mm_marsh1

smart_skema_type

marsh

In Qualitative Analysis, the vectorized sketch maps are handled to

calculate the QCN matrix in the SmartSkeMa framework. The qualitative

representation process is carried per feature in both maps constructing the

relations network and assigning a label from each relation set considered. In

Figure 22, the arrangement for some features from the Mailua sketch and

metric map data set are displayed:

Figure 22 Qualitative representation input maps







  

































4.45

Each object is represented by a node with labels describing the spatial

relationship between each other according to the spatial calculi detailed in

2.3.1. The purple line connecting the sketch and metric map label, highlights

the relation identified for the sketch and metric map in

  as this type of similarities give

insights about their characteristics in the search space for the matching process.

The same mechanism is applied to every feature in the three data sets resulting

in three different QCN matrices used by the Scored System and the Qualify

Analysis modules to asses and measure the compatibility between candidate

pairs. Some calculi return an N/A value as the geometry type arguments to

calculate the relation are not met. One of the considered calculi, starVars, is

removed due to incompatibilities with the current inputs during the

qualification.

As for the Scoring System, the Link Analysis process is executed with

the QCN matrices, delivering the score ranking to the SST evaluation function

from which we retrieved a subset of candidate pairs highly connected with

other features in the search space. In some cases, the output included correctly

aligned features; one example is shown in Table 8:

Table 8 Link Analysis sample results

Dataset

Link Analysis Sample

Artificial SVG

'sm815': 'rect815', 'sm817': 'rect817', '

El Remanso

'sm_lake': 'mm_lake', 'sm_marsh1': 'mm_marsh1'

Mailua

'sm_river': 'mm_river', 'sm_road': 'mm_road'

For the LCM scores, we derived two different approaches to evaluate

future-promissory candidate pairs to add in the solution: the first heuristic H1

evaluates each pair candidate local compatibility before adding during the

iteration process returning the scores per each one of the considered relation

sets as shown in Table 9. Next, the second heuristic H2 is calculated after adding

based on the pairs in the current solution, providing a set compatible pairs

additionally from the qualitative representation. These differentiations had an

essential repercussion in the learning algorithm reviewed in the discussion

section.

4.46

Table 9 LCM(H1) score sample

Calculi

H1 Score

RCC8

29

RCC11

29

REL_DIST

27

LEFT_RIGHT

21

ADJACENCY

20

Finally, the Searching algorithms module is executed. The Tabu Search

algorithm implements a scoring system based on LA and the SST. SARSA

employs two different configurations: the first one is solely based on the H1

heuristic and SST, the second one analyzes the H2 heuristic and SST. This

distinction arises from two separate results returned during the

implementation. In the following subsections, the algorithm's results are

illustrated in more detail.

4.1 PERFORMANCE

4.1.1 Execution time

Both algorithms execute their tasks for a maximum of 1000 iterations,

and a built-in function in Python measures the timing. In general, for a small

number of iterations, Tabu is faster, but as the number increases, SARSA

shows a recovery using less time despite the number of tasks needed to

compute a sub solution.

In the smallest dataset, Artificial SVG, with six features in the sketch

map for aligning to 7 features in the metric map, in Figure 23, Tabu takes more

time after 350 iterations approximately. SARSA consumes more time in the

beginning, but as the search continues, it spends less time computing the

results. Due to the backup nature of SARSA, in a lower number of iterations

employs more time assessing all the subset solutions (states) to recover the

values later when they are recalled.

4.47

Figure 23 Artificial SVG execution time

For a larger dataset, El Remanso, with 13 features in the sketch map for

aligning to 15, in Figure 24, the Tabu algorithm execution time increases with

some peaks: as the number of iterations increases, the population of the

neighborhood consumes more time as the tabu lists banned the access to

compatible candidate pairs. The peaks in SARSA, are related to states in which

new items are being explored and added to the solution.

Figure 24 El Remanso execution time

0

0.1

0.2

0.3

0.4

0 100 200 300 400 500 600 700 800 900

time in seconds

Number of iterations

Artificial SVG: Tabu versus Sarsa (execution time)

TABU SARSA

0

0.5

1

1.5

2

1 101 201 301 401 501 601 701 801 901

time in seconds

Number of iterations

El Remanso: Tabu versus Sarsa (execution time)

TABU SARSA

4.48

Finally, for the most extensive dataset Mailua Ranch, with 17 features

in the sketch map and 106 in the metric map, in Figure 25, the behavior of both

algorithms is more visible. In the beginning, SARSA consumes the most

considerable amount of time, but it decreases over time. Tabu displays peak

points over time due to the available neighborhood update once the tabu lists

are full, limiting the access to compatible pairs and encouraging exploration.

Figure 25 Mailua ranch execution time

4.1.2 Precision and Recall

By using the formulas described in section 3.7, and the results obtained

from the algorithms’ execution, the precision and recall metrics are calculated.

For each one of the datasets, a maximum of 1000 rounds of alignment are

executed per algorithm, and the identification of correct alignment is made by

code evaluating the number of True Positives, True Negatives, False Positives, and

False Negatives from the output results. In the case of the sketch to metric map

alignment, a True Positive is every feature correctly aligned with the expected

feature from sketch to the metric map, a False Positive is every feature wrongly

aligned with another feature than the expected one, and a False Negative is

every feature that should have been aligned, but it is not present in the solution.

In the final solution, there are no True Negatives to consider, as every feature

in the sketch map dataset is obligated to be aligned to at least one feature in

the metric dataset.

0

5

10

15

20

25

30

35

1 101 201 301 401 501 601 701 801 901

time in seconds

Number of iterations

Mailua Ranch: Tabu versus Sarsa (execution time)

TABU SARSA

4.49

For the Artificial SVG dataset, the average precision and recall statistics

in Table 10 for Tabu are higher for 11.62% and 4.84%. In the alignment results

review, the SARSA algorithm varies the precision every number of iterations

in between 40% and 100% with a maximum recall of 83%, whereas Tabu from

54% reaches 80% of precision with a maximum recall of 80%, and it does not

improve in future iterations once the solution is stable.

Table 10 Artificial SVG: Precision and Recall Results

Algorithm

Tabu

SARSA

AVG. Precision

80%

68%

AVG. Recall

80%

75%

Min. Precision

60% (0%)*

40%

Max. Precision

80%

100%

Min. Recall

75% (0%)*

67%

Max. Recall

80%

83%

* For the first iteration, the algorithm did not find a solution and returned an empty list

The precision and recall statistics for El Remanso dataset are displayed

in two different tables to illustrate the difference between the implementation

of SARSA(H1) and SARSA(H2). In Table 11, the average precision in Tabu is

7% higher than SARSA(H2), with average recall differing for 15%, with 99%.

In terms of minimum and maximum precision, SARSA(H2) has higher results,

returning on every iteration a solution, whereas, for the recall, Tabu aligns

100% of the relevant items selected in contrast to SARSA(H2), with 89%.

Table 11 El Remanso: Precision and Recall Results (H2)

Algorithm

Tabu

SARSA (H2)

AVG. Precision

58%

51%

AVG. Recall

99%

84%

Min. Precision

55% (0%)*

27%

Max. Precision

58%

73%

Min. Recall

86% (0%)*

75%

Max. Recall

100%

89%

* For the first iteration, the algorithm did not find a solution and returned an empty list

4.50

In the course of the approach implementation, we run several times the

SARSA algorithm with only the first heuristic scores. The results differ from

SARSA(H2) in terms of precision, recall, performance, and spatial

configuration. For the SARSA(H1), the average precision displayed in Table

12 is higher than Tabu and SARSA(H2) algorithms with an 84% average recall.

With just the first score of the LCMs, we surpassed the 70% window. On the

other hand, SARSA(H1) takes more time computing the final solution: for a

range of 400 iterations, it takes 35 seconds.

Table 12 El Remanso: Precision and Recall Results (H1)

Algorithm

Tabu

SARSA (H1)

AVG. Precision

58%

73%

AVG. Recall

99%

84%

The Mailua Ranch data set presents the lowest statistics for both

algorithms, as shown in Table 13. For the average precision and recall, the

Tabu search is 20% higher, with maximum values reached without variation

in future iterations. SARSA(H2) keeps a variation during the search as it

explores newer candidate pairs returning in some cases a final solution with

False Negative results, indicating a requirement for a more substantial number

of iterations to explore all candidates' information and return a solution for the

non-considered features during the matching process.

Table 13 Mailua Ranch: Precision and recall results

Algorithm

Tabu

SARSA (H2)

AVG. Precision

31%

11%

AVG. Recall

46%

21%

Min. Precision

0%

Max. Precision

56%

53%

Min. Recall

0%

Max. Recall

100%

89%

4.51

4.2 ALIGNMENT RESULTS

The algorithms are executed for a maximum of 1000 iterations, and the

output result contains the sketch map feature and an assigned metric map

feature. We present three samples from the alignment results for each

algorithm, per dataset in which we compare both approaches, followed by the

discussion in the next subsection.

For the smallest dataset displayed in Table 14, SARSA aligned more

items in less time for the same number of iterations. Most of the results from

Tabu are concentrated in one area with one False Positive item returned. The

SARSA alignment is more dispersed in the search space aligning 5 of 6 features

correctly with one False Negative.

Table 14 Artificial SVG: Alignment result sample

Tabu Results

SARSA Results

Execution time

0.068991 s

Execution time

0.0203 s

Number Iterations

996

Number Iterations

996

Number of features aligned

5/6

Number of features aligned

5/6

True Positives

4

True Positives

5

False Positives

1

False Positives

0

El Remanso dataset doubles the features from the simple sketch map.

In this scenario, Tabu is faster and returned one additional False Positive

aligned feature in half of the time. In the case of SARSA, the additional feature

not displayed is a False Negative. Both algorithms return a similar solution.

















4.52

Table 15 El Remanso: alignment result sample

Tabu Results

SARSA Results

Execution time

0.25819 s

Execution time

0.56543 s

Number Iterations

986

Number Iterations

986

Number of features aligned

12/13

Number of features aligned

12/13

True Positives

7

True Positives

7

False Positives

5

False Positives

4

The Mailua Ranch dataset is the largest one with both algorithms

returning similar matches for which the differences are noticeable in the not

correctly aligned features. Tabu returns an additional True Positive feature and

SARSA one False Negative. The alignment stats are illustrated in Table 16:

Table 16 Mailua Ranch: alignment result sample

Tabu Results

SARSA Results

Execution time

3.9044 s

Execution time

4.5988 s

Number Iterations

901

Number Iterations

901

Number of features aligned

16/16

Number of features aligned

15/16

True Positives

9

True Positives

8

False Positives

7

False Positives

7

























4.53

4.3 DISCUSSION

The Score System module results can be sensitive to the quality of the

input sketch map. With the wrong feature type, the LA and SST scores can be

corrupted by giving more scores to meaningless objects such as triangles

derived from the vectorization process in the SmartSkeMa. We recommend

reviewing the quality of the vectorized sketch map and clean the features with

a non-compatible object type. Additionally, it is necessary to examine further

the dangling factor and the number of iterations for the LA scores, considering

factors such as the size of the graph and the geometries type as they influence

the size of the initial solution in SST. For the LCM scoring, the outcome for the

LCM(H1) provide to the learning algorithm a free exploration inside the

environment space as it evaluates the score per pair.

On the other hand, LCM(H2) heuristic is restricted to future promissory

pairs in the current solution. The immediate effects of this finding are visible

from the alignment results, as the first heuristic recall is higher than the second

heuristic. Due to the time constraint, experimenting with the single use of H2

instead of the SST solution for the SARSA algorithm and the corresponding

environment configuration update is open for future work.

For the Tabu and SARSA algorithms, the execution time, the number of

correct matches, spatial configuration, and complexity are the main aspects

evaluated. Tabu works faster with a small number of iterations due to the less

elaborated processes required for searching, and with a higher number of

iterations, the contribution to the solution decreases to a point in which the

output solution is stable, and no significant changes occur. As the number of

features to align increases, the longer time will take to arrive at this

convergence point. By using two tabu lists instead of one, the exploration was

encouraged to add non-high-scored features in the solution, but as the process

continues with the same configuration in the search space, nevertheless it is

possible to keep receiving the same candidate pairs subset and get into cycling

solutions. On the other hand, changing the size of the tabu list can cause the

solution to break as the search space is constrained to the number of available

features; thus, the minimum size should be related to the length of the initial

solution, in our case the SST.

4.54

Concerning the alignment results, features aligned by Tabu are

attached to a clustering behavior: as displayed in Figure 26, for the Mailua

Ranch sketch map, features A, B, C and R share their immediate space, but

they are not located correctly in the metric map solution (left side).

Furthermore, the distribution does not consider the orientation between them:

feature R is in front of the A-B-C neighborhood, and in the output solution, it

is in between and far from the feature M.

Figure 26 Tabu clustering alignment

Despite SARSA taking a longer time to complete a high volume of tasks

initially, the precision of the solution varies over time, coming to values higher

than 80% for small to medium-sized datasets for both SARSA(H1) and

SARSA(H2). By comparing the results from SARSA(H2) for the same cluster

discussed in Tabu for Figure 26, the solution is distributed, not only

considering how close the objects are but also is visible the relationships with

vicinity features, as illustrated in Figure 27. The A-B-C features are distributed

closer to the feature M as well as R. Moreover, feature A should be the one very

far from M in the original arrangement in the Mailua Ranch dataset, with

SARSA(H2) returning the displayed spatial configuration correctly.









 







4.55

Figure 27 SARSA(H2) clustering alignment

The improvement in H1 from the observation present in H2 has its roots

in the state-value function in SARSA, the sub-solution-score backup. As

SARSA(H1) explores more the environment, better-rewarded solutions for the

same configuration are calculated, and eventually, it selects the best one,

contrary to SARSA(H2), that is constrained to a subset of future solutions and

may not find an appropriate match in the environment on time. In the results

for both configurations in Figure 28, SARSA(H2) ignores aspects of the spatial

configuration for feature C as it needs to be the closest to features B and A,

regardless of the objects in between as SARSA(H1) solution returned.

Figure 28 SARSA(H2) compared to SARSA(H1) alignment

















































4.56

For the second heuristic, the spatial configuration is preserved, but the

search space is limited to the compatible pairs derived from the similarity

matrices evaluation. The algorithm is considering highly connected features

as the initial solution, and not all of them exist as promissory candidates

according to the H2 criteria. Until both conditions are meet, the algorithm

keeps exploring the environment, and thus, the solutions are linked to this

restriction. One approach to encourage the search from the second heuristic is

to implement the identified subset as an initial solution, instead of looking for

highly connected features in SST. Another procedure includes the

modification of the Link Analysis process and combining the H2 subset for a

hybrid approach.

Correctly aligning features between sketch and the metric maps are

linked to the spatial configuration complexity and the number of features in

the sketch and the metric map. Both algorithms increased the precision once

the vectorized sketch map was cleaned from small polygons as the matching

process consists of an exhaustive evaluation of candidate pairs. In order to

boost the alignment process, it is crucial to filter the data included in the

Qualitative Representation to avoid using resources on meaningless relations.

4.4 LIMITATIONS

One of the limitations encountered for the alignment process is the

definition of the number of iterations needed for each algorithm to reach their

potential. It is necessary to analyze the conditions to calculate an equivalent

ratio for the running times as it can be derived from the performance results in

El Remanso dataset in which the inflection point for SARSA to overcome the

Tabu results is not reached.

Another limitation encountered for the alignment process in the

SmartSkeMa framework is the noise caused by vectorized features such small

triangles or the split of sketch map features into smaller pieces that are included

or excluded in the qualitative segmentation. To overcome this challenge, the use

of the module Geometry Editor at the beginning offered a didactic way to

digitalize features, but it needed to run a first version of the Vectorize module

from which small, not useful features were created. The final procedure was to

manually add the objects to artificial vectorized sketch and metric maps by using

4.57

the Inkscape software and exporting them to SVG, providing the corresponding

geoJSON file for the metric map. Additionally, we encountered conflicts in the

use of the relation set starVars as it faced long execution times and raising

errors during the qualitative representation. The temporary solution was to

remove starVars from the functionality’s arguments until a more in-depth

analysis is done for understanding the implementation of this calculi during

the qualitative analysis. Lastly, because the Sketch to Metric alignment

problem is very particular to our interest, the current configurations defined

in OpenAI Gym to run learning algorithms had limited use, leading to the

implementation of a new setting based on the predefined templates.

5.58

CHAPTER 5 CONCLUSIONS

For the Sketch to Map alignment problem, we proposed the use of two

different algorithms and a scoring system to evaluate each possible candidate

match. The workflow combines five main modules: input processing,

qualitative analysis, score system, search algorithms, and evaluation. In the

input processing module, we provided the SmartSkeMa framework with the

sketch and metric maps to be processed and vectorized, for which we

manually edit the SmartSkeMa attributes, providing three input maps with

different levels of complexity in terms of the number of features and spatial

configurations. In the qualitative analysis component, we outline the process

for evaluating compatibility between each candidate pair in terms of

consistency of the constrained network and feature type with the retrieved

QCN using these functionalities during the scoring process. The Score System

offers the possibility to calculate four scores that can be used combined or

some separately: the Link Analysis (LA) score provided information about the

level of connectivity of each feature in our search space, Spectral Solution

Technique (SST) processes the LA ranking to return a set of highly compatible

features giving us an initial solution, and finally, the two Heuristics Scores

based on the Local Compatibility Matrices deliver a measure for forthcoming

solutions derived from each candidate pair. Then, the different scores are used

in the Searching Algorithms module which consists of two implementations:

a new Tabu Search incorporating LA and SST scores, returning a set of features

from the sketch and metric maps from iteratively evaluating the compatibility

of each pair candidate and banning time to time the ones considered to be out

of the solution or recently added; on the other hand, the SARSA algorithm by

using SST and LCM scores experiences several sub solutions with different

sizes, and selects over time the ones with the highest scores to construct a final

solution based on the best possible combination of subset matching solutions.

At the end of this thesis, we analyzed the results of the workflow and

mentioned the limitations encountered. The Qualitative Analysis module

helped to accurately identify the compatibility between features, visible in the

results as the output solutions are coherent regarding the type and the shared

constraints. Secondly, the Score System delivered on each call the evaluation

5.59

measurements making use of the SST initial solution showing the influence of

highly connected pairs in the search space, as well as the calculus of Local

Compatibility Matrices with the evaluation of the corresponding heuristics per

candidate set. The new Tabu algorithm surpasses the statistics of average

precision for the SARSA algorithm with LCM(H2) (80% vs. 68% smallest

dataset), increasing the gap as the number of features increases (31% vs. 11%

largest dataset). Nevertheless, analyzing the solutions derived from both

algorithms, it is vital to notice that the False Positives features for SARSA are

closer to the original spatial configuration in the sketch map, especially for the

implementation with only LCM(H1), and the maximum precision of the

algorithm varies as the number of iterations changes, reaching 100% in specific

cases indicating a relevant percentage of True Positives matches compared to

Tabu.

The Tabu solution is faster in a shorter number of iterations, more

straightforward and offers higher results in terms of precision, but on the other

hand, the SARSA performance improves over time with consistent spatial

distribution compared to Tabu. As the number of iterations goes on, the

dynamic programming algorithm can offer a range of matches, giving

highlights about how the search is being approached thanks to the backup of

the subset solutions and their scores, whereas for Tabu once the solution is

stable, it will be returned repeatedly over the time without further exploration

of the search space or improvement. Two main configurations for the policy

calculus in the learning algorithm were implemented: solely the first heuristic

and with both LCM(H1) and LCM(H2) heuristics, returning higher or lower

precision and recall statistics than Tabu, which leaves the door open to

implement different LCM scores configurations in the same environment.

In conclusion, the main contributions of this master thesis are the

performance improvement for QCNs in large scale datasets, and the support

during the matching process with a global overview of the spatial

configuration described on them by including the implementation of four

different scores: link analysis, spectral solution, and two heuristics from the

Local Compatibility Matrix. In SARSA, the Q values summarize the

information about the SST and LCM scores allowing the search to invest the

time saved, exploring more the search space updating information about the

5.60

candidate pairs and sub solutions, whereas Tabu only uses information from

the immediate neighborhood. Next, we implemented the module for the

construction of the LCM scoring: the search results retrieved from the

implementation of both heuristic scores returns consistent information about

the local spatial configuration for the pairs belonging to the subset solution in

the SARSA algorithm avoiding wrong alignments with a less complete

solution compared to Tabu, which returns a more complete set of matched

features by allowing mistakes.

Finally, we implemented two different searching algorithms with

distinct advantages: Tabu is more straightforward and works in this case for

immediate analysis of alignment results. For long-term, more spatially

structured matches, SARSA by taking advantage of the backup of subset

solutions and learning from the exploration process in the search space,

presents a selection of pairs with coherent arrangements with reference to

other features.

5.1 FUTURE WORK

During the workflow implementation, different ideas to improve the

current solution arose from the use of the score modules to the learning

algorithms. One approach is to analyze the features clusters retrieved from the

Spectral Solution Technique and review how the different clusters can be

labeled to work as subset solutions to limit the search space and apply the

Local Compatibility Matrices score to answer the question: Does clustering

identification or limiting the search to identified clusters improve the alignment

solution?

Secondly, the inclusion of the qualitative calculus starVars into the

algorithm should be reviewed as orientation type relationships can add value

to the matching score during the search, enlarging the subset of compatible

pairs to keep improving the spatial configuration. Lastly, new dynamic

programming algorithm implementations compatible with the characteristics

of the QCN should be considered given the potential found in reinforcement

learning algorithms in the graph matching problem.

6.61

CHAPTER 6 REFERENCES

Anaconda. (2020). Anaconda Distribution. Retrieved January 2, 2020, from

Anaconda Documentation website: https://docs.anaconda.com/

Battiti, R., & Protasi, M. (2001). Reactive local search for the maximum clique

problem. Algorithmica (New York).

https://doi.org/10.1007/s004530010074

Battiti, Roberto, & Tecchiolli, G. (1994). The Reactive Tabu Search. ORSA

Journal on Computing, 6(2), 126–140. https://doi.org/10.1287/ijoc.6.2.126

Brockman, G., Cheung, V., Pettersson, L., Schneider, J., Schulman, J., Tang, J.,

& Zaremba, W. (2016). OpenAI Gym. Retrieved from

https://arxiv.org/pdf/1606.01540.pdf

Broelemann, K. (2011). A System for Automatic Localization and Recognition

of Sketch Map Objects. In: Wang, J., Broelemann, K., Chipofya, M.,

Schwering, A., and Wallgrün, J.-O. (eds.). COSIT 2011 Workshop on

Understanding and Processing Sketch Maps, 11–20. Belfast, Maine.

Heidelberg, AKA GmbH.

Broelemann, Klaus, & Jiang, X. (2013). A region-based method for sketch map

segmentation. Lecture Notes in Computer Science (Including Subseries Lecture

Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7423 LNCS,

1–14. https://doi.org/10.1007/978-3-642-36824-0_1

Broelemann, Klaus, Jiang, X., & Schwering, A. (2016). Automatic

understanding of sketch maps using context-aware classification. Expert

Systems with Applications. https://doi.org/10.1016/j.eswa.2015.09.037

Bunke, H. (2000). Recent developments in graph matching. Proceedings -

International Conference on Pattern Recognition.

https://doi.org/10.1109/ICPR.2000.906030

Bunke, H., & Jiang, X. (2000). Graph Matching and Similarity.

https://doi.org/10.1007/978-1-4615-4401-2_10

Ceri, S., Bozzon, A., Brambilla, M., Della Valle, E., Fraternali, P., Quarteroni,

S., … Quarteroni, S. (2013). An Introduction to Information Retrieval. In

Web Information Retrieval. https://doi.org/10.1007/978-3-642-39314-3_1

Chipofya, M. C., Schultz, C., & Schwering, A. (2016). A metaheuristic approach

for efficient and effective sketch-to-metric map alignment. International

Journal of Geographical Information Science.

https://doi.org/10.1080/13658816.2015.1090000

6.62

Chipofya, M, Jan, S., Schultz, C., & Schwering, A. (2017). Towards Smart

Sketch Maps for Community-driven Land Tenure Recording Activities.

Agile. Retrieved from https://agile-

online.org/conference_paper/cds/agile_2017/shortpapers/155_ShortPa

per_in_PDF.pdf

Chipofya, Malumbo. (2018). Matching Qualitative Constraint Networks with

Online Reinforcement Learning. https://doi.org/10.29007/1g5q

Chipofya, Malumbo, Schwering, A., & Binor, T. (2013). Matching qualitative

spatial scene descriptions á la Tabu. Lecture Notes in Computer Science

(Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes

in Bioinformatics). https://doi.org/10.1007/978-3-642-45111-9_34

Chipofya, Malumbo, Wang, J., & Schwering, A. (2011). Towards cognitively

plausible spatial representations for sketch map alignment. Lecture Notes

in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence

and Lecture Notes in Bioinformatics). https://doi.org/10.1007/978-3-642-

23196-4_2

Cho, M., Lee, J., & Lee, K. M. (2010). Reweighted random walks for graph

matching. Lecture Notes in Computer Science (Including Subseries Lecture

Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).

https://doi.org/10.1007/978-3-642-15555-0_36

Conte, D., Foggia, P., Sansone, C., & Vento, M. (2004). Thirty years of graph

matching in pattern recognition. International Journal of Pattern Recognition

and Artificial Intelligence. https://doi.org/10.1142/S0218001404003228

Cook, D. J., & Holder, L. B. (2006). Mining Graph Data. In Mining Graph Data.

https://doi.org/10.1002/9780470073049

Cour, T., Srinivasan, P., & Shi, J. (2007). Balanced graph matching. Advances in

Neural Information Processing Systems.

https://doi.org/10.7551/mitpress/7503.003.0044

Davis, J., & Goadrich, M. (2006). The relationship between precision-recall and

ROC curves. ACM International Conference Proceeding Series.

https://doi.org/10.1145/1143844.1143874

Dehmer, M. (2008). Information processing in complex networks: Graph

entropy and information functionals. Applied Mathematics and Computation.

https://doi.org/10.1016/j.amc.2007.12.010

Dehmer, M., Emmert-Streib, F., & Kilian, J. (2006). A similarity measure for

graphs with low computational complexity. Applied Mathematics and

Computation. https://doi.org/10.1016/j.amc.2006.04.006

6.63

Emmert-Streib, F., Dehmer, M., & Shi, Y. (2016). Fifty years of graph matching,

network alignment and network comparison. Information Sciences.

https://doi.org/10.1016/j.ins.2016.01.074

Foggia, P., Percannella, G., & Vento, M. (2014). Graph matching and learning

in pattern recognition in the last 10 years. International Journal of Pattern

Recognition and Artificial Intelligence.

https://doi.org/10.1142/S0218001414500013

Freska, C. (1991). Qualitative Spatial Reasoning. Cognitive and Linguistic

Aspects of Geographic Space, 361–372.

Gendreau, M., & Potvin, J.-Y. (2005). Tabu Search. In Search Methodologies:

Introductory Tutorials in Optimization and Decision Support Techniques (pp.

165–186). Montreal: Springer.

Glover, F. (1986). Future paths for Integer Programming. Computers and

Operations Research, 13(5), 533–549.

https://doi.org/http://dx.doi.org/10.1016/0305-0548(86)90048-1

Glover, F. (1989a). Tabu Search - Part I. Orsa Journal on Computing, 1(3), 190–

206.

Glover, F. (1989b). Tabu Search - Part II. Journal on Computing, 1 and

2(December 2018), 190–206, 4-32,. https://doi.org/10.1287/ijoc.2.1.4

Glover, F., Taillard, E., & Taillard, E. (1993). A user’s guide to tabu search.

Annals of Operations Research, 41(1), 1–28.

https://doi.org/10.1007/BF02078647

Jan, S., Chipofya, M., Murcia, C., Schwering, A., Schultz, C., Karamesouti, M.,

… Wayumba, R. (2018). its4land Derivable 3.3: technical report. Retrieved

from https://its4land.com/wp-

content/uploads/2018/08/its4land_deliverable_D3.3.pdf

Jan, S., Schwering, A., Schultz, C., & Chipofya, M. (2015). RCC11: A Finer

Topological Representation for the Alignment of Regions in Sketch Maps.

28th International Workshop on Qualitative Reasoning (QR-2015).

Karamesouti, M., Schultz, C., Chipofya, M., Jan, S., Murcia Galeano, C. E.,

Schwering, A., & Timm, C. (2018). The Maasai of Southern Kenya domain

model of land use. ISPRS Annals of the Photogrammetry, Remote Sensing and

Spatial Information Sciences. https://doi.org/10.5194/isprs-annals-IV-4-

105-2018

Lee, J. H., Renz, J., & Wolter, D. (2013). StarVars-effective reasoning about

relative directions. IJCAI International Joint Conference on Artificial

Intelligence.

6.64

Leordeanu, M., & Hebert, M. (2005). A spectral technique for correspondence

problems using pairwise constraints. Proceedings of the IEEE International

Conference on Computer Vision. https://doi.org/10.1109/ICCV.2005.20

Ligozat, G. (2005). Categorical methods in qualitative reasoning: The case for

weak representations. Lecture Notes in Computer Science (Including

Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in

Bioinformatics). https://doi.org/10.1007/11556114_17

Ligozat, G. (2013). Qualitative Spatial and Temporal Reasoning. In Qualitative

Spatial and Temporal Reasoning. https://doi.org/10.1002/9781118601457

Murcia, C. (2018). Automatic understanding of sketch maps using deep learning and

computer vision. University of Muenster.

Ng, R. T., & Han, J. (2002). CLARANS: A method for clustering objects for

spatial data mining. IEEE Transactions on Knowledge and Data Engineering.

https://doi.org/10.1109/TKDE.2002.1033770

NumPyCommunity. (2020). NumPy. Retrieved January 3, 2020, from

https://numpy.org/

Page, L., Brin, S., Motwani, R., & Winograd, T. (1998a). The PageRank Citation

Ranking: Bringing Order to the Web. MIT Press.

https://doi.org/10.1109/IISWC.2012.6402911

Page, L., Brin, S., Motwani, R., & Winograd, T. (1998b). The PageRank Citation

Ranking: Bringing Order to the Web. World Wide Web Internet And Web

Information Systems. https://doi.org/10.1.1.31.1768

Pavony, G. R. M. (2000). Los años del cambio: historia urbana de Bogotá, 1820-1910.

Bogotá, Colombia: Pontificia Universidad Javeriana.

QGISORG. (2002). QGIS - The Leading Open Source Desktop GIS. Retrieved

January 3, 2020, from https://www.qgis.org/es/site/about/index.html

Randell, D. A., Cui, Z., & Cohn, A. G. (1992). A Spatial Logic based on Regions

and Connection. 3rd International Conference On Knowledge Representation

And Reasoning. https://doi.org/10.1.1.35.7809

Ratitch, B., & Precup, D. (2015). Sparse Distributed Memories for On-Line

Value-Based Reinforcement Learning Bohdana. Lecture Notes in Computer

Science, (July). https://doi.org/10.1007/978-3-540-30115-8

Robson, E., van Kerkhoff, L., & Cork, S. (2019). Understanding citizen

perceptions of the Eastern Hills of Bogota: a participatory place-based

ecosystem service assessment. Urban Ecosystems.

https://doi.org/10.1007/s11252-018-0739-9

6.65

Saad, E. (2011). Bridging the gap between reinforcement learning and

knowledge representation: A logical off- and on-policy framework.

Lecture Notes in Computer Science (Including Subseries Lecture Notes in

Artificial Intelligence and Lecture Notes in Bioinformatics), 6717 LNAI, 472–

484. https://doi.org/10.1007/978-3-642-22152-1_40

Schwering, A., & Wang, J. (2010). SketchMapia–A framework for qualitative

mapping of sketch maps and metric maps. Las Navas 20th Anniversary

Meeting on Cognitive and Linguistic Aspects of Geographic Spaces.

Schwering, A., Wang, J., Chipofya, M., Jan, S., Li, R., & Broelemann, K. (2014).

SketchMapia: Qualitative Representations for the Alignment of Sketch

and Metric Maps. Spatial Cognition and Computation.

https://doi.org/10.1080/13875868.2014.917378

Scivos, A., & Nebel, B. (2005). The finest of its class: The natural point-based

ternary calculus ℒℜ, for qualitative spatial reasoning. Lecture Notes in

Artificial Intelligence (Subseries of Lecture Notes in Computer Science).

https://doi.org/10.1007/978-3-540-32255-9_17

Štěpánková, O. (1992). An introduction to qualitative reasoning.

https://doi.org/10.1007/3-540-55681-8_47

Sutton, R., & Barto, A. (1999). Reinforcement Learning: An Introduction.

Trends in Cognitive Sciences. https://doi.org/10.1016/s1364-

6613(99)01331-5

Sutton, R., & Barto, A. (2018). Reinforcement Learning— An Introduction. In

Proceedings of the Annual Conference of the Western College Reading

Association (Second). https://doi.org/10.1080/24699365.1977.11669658

The Python Software Foundation. (2003a). 8.3. collections — High-

performance container datatypes. Retrieved January 3, 2020, from

https://docs.python.org/2/library/collections.html

The Python Software Foundation. (2003b). 9.7. itertools — Functions creating

iterators for efficient looping. Retrieved January 3, 2020, from

https://docs.python.org/2/library/itertools.html

The Python Software Foundation. (2009). What is Python? Retrieved January

3, 2020, from Python.org website:

https://docs.python.org/3/faq/general.html#what-is-python

Wallgrün, J. O., Wolter, D., & Richter, K. F. (2010). Qualitative matching of

spatial information. GIS: Proceedings of the ACM International Symposium

on Advances in Geographic Information Systems.

https://doi.org/10.1145/1869790.1869833

6.66