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Citation: Pereira, F.M.; Sofia, R.C. An
Analysis of ML-Based Outlier
Detection from Mobile Phone
Trajectories. Future Internet 2023,15, 4.
https://doi.org/10.3390/fi15010004
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Mustafa Atay, Ajita Rattani and
Claude Chaudet
Received: 12 August 2022
Revised: 7 November 2022
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Published: 23 December 2022
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future internet
Article
An Analysis of ML-Based Outlier Detection from Mobile
Phone Trajectories
Francisco Melo Pereira 1,*,† and Rute C. Sofia 2,†
1COPELABS, University Lusofona, 1749-024 Lisbon, Portugal
2Fortiss GmbH—Research Institute of the Free State of Bavaria for Software Intensive Systems and Services,
80805 Munich, Germany
*Correspondence: p2809@ismat.pt
† These authors contributed equally to this work.
Abstract:
This paper provides an analysis of two machine learning algorithms, density-based spatial
clustering of applications with noise (DBSCAN) and the local outlier factor (LOF), applied in the
detection of outliers in the context of a continuous framework for the detection of points of interest (PoI).
This framework has as input mobile trajectories of users that are continuously fed to the framework
in close to real time. Such frameworks are today still in their infancy and highly required in large-
scale sensing deployments, e.g., Smart City planning deployments, where individual anonymous
trajectories of mobile users can be useful to better develop urban planning. The paper ’s contributions
are twofold. Firstly, the paper provides the functional design for the overall PoI detection framework.
Secondly, the paper analyses the performance of DBSCAN and LOF for outlier detection considering
two different datasets, a dense and large dataset with over 170 mobile phone-based trajectories and a
smaller and sparser dataset, involving 3 users and 36 trajectories. Results achieved show that LOF
exhibits the best performance across the different datasets, thus showing better suitability for outlier
detection in the context of frameworks that perform PoI detection in close to real time.
Keywords: outliers; DBSCAN; LOF; GPS trajectories; machine learning
1. Introduction
In the continuous pursuit of Smart City planning and development, municipalities
try to find areas of interest for both residents and visitors, in order to better plan available
services. Accordingly, it is necessary to find new points of interest (PoIs) that truly meet
the cultural or even leisure and entertainment needs of the population. In this context,
pervasive computing and pervasive technology play a key role, as pervasive technology
can support tracking and learning of PoIs in a continuous way, without impact on personal
data privacy, and based on the citizen’s preferences.
Over the last decade, pervasive technology has been emerging with people-centric
hardware and systems and has become more efficient and sustainable. Personal mobile IoT
devices [
1
] such as smartphones are carried around by citizens and can assist in inferring
trajectories in an anonymous way, without an impact on privacy. Continuously collected
anonymous trajectories represent a set of waypoints. Individual trajectories can then
be combined and analysed via different machine learning (ML) approaches to provide an
estimation of PoIs that relate to the social habits of a population. Related work has been
addressing the feasibility and accuracy of relying on pervasive technology as a basis for
developing large-scale sensing frameworks that can assist Smart City planning [2,3].
Such frameworks often address planned PoIs by relying on offline data analysis, but
not a continuous detection of PoIs over time, e.g., related to seasonal events, or with
collective interest, which may change with time. There are, therefore, PoIs that are not
implicitly considered so in Smart Cities, and those are usually the ones that are harder to
Future Internet 2023,15, 4. https://doi.org/10.3390/fi15010004 https://www.mdpi.com/journal/futureinternet
Future Internet 2023,15, 4 2 of 19
detect. However, they are highly relevant to achieve efficient city planning, as they are
derived from citizens’ social behaviour and mobility preferences.
In the traditional definition, a PoI is a point of interest (a location) that may be of
interest to someone. Our definition of PoI attempts to capture such locations, currently
unknown to a municipality or to a community, and that is revealed to us by the social
trajectories of a large number of people, which cross a specific location. The aim of our
work is to consider non-intrusive technology to detect such PoIs. To discover them, we use
cell phone traces data that reflect the trajectories followed by people in their daily lives.
These trajectories reveal their individual stopping points (stop points). A cluster in time and
in space of stop points can turn out to be a PoI for the local community or for an individual
visitor. While trajectories collected from smartphones assist in detecting PoIs, they also
include outliers. By definition, an outlier is a representation of a point that is beyond the
limits of a well-defined population [
4
]. The traces of stored cell phones, which represent the
trajectories followed by users, experience several problems, from communication failures
to problems with data recording on the cloud. Hence, an outlier is a cluster of points that
derive from an error, and not from stop points. It is this discovery of outliers, in the pursuit
of data cleansing, that is reflected in our current work.
In this context, this work proposes a design for a novel non-intrusive framework for
inference of PoIs based on mobility trajectories derived from anonymised smartphone data,
and performs a performance analysis of DBSCAN and LOF for outlier detection, in the
context of a first functional block of such framework, related to outlier detection.
We consider that a relevant framework in this context would be a framework that
could assist in inferring similarity in individual (and collective) mobility patterns. Data
would be obtained via external devices (e.g., smartphones and other embedded devices
carried by citizens), and the inference could be done (a) in real time or (b) close to real time.
The initial framework described in this paper considers that trajectory data can be obtained
from the city Internet of Things (IoT) infrastructure and also from citizens’ personal devices,
such as smartphones, upon consent.
Such a framework would, therefore, infer some form of human behaviour and map
such behaviour in time and space to potential PoIs which can then be deployed on a Smart
City dashboard, or on Smart City user applications. To reach such a level of inference, it is
necessary to design a framework that can assist a continuous PoI detection, by comparing
different ML approaches, and this aspect is currently a major gap in the literature. This
work contributes to overcoming such a gap by providing the following contributions:
1.
Provides the initial functional design of a novel framework for continuous detection of
PoIs based on smart and anonymised trajectory data collected from personal devices
and IoT Smart City infrastructure.
2.
Addresses the issue of outlier detection and provides a validation of outlier detection
based on two ML algorithms, density-based spatial clustering of applications with noise
(DBSCAN) and local outlier factor (LOF).
The first reason for selecting these two specific algorithms, DBSCAN and LOF, lies
in the fact that related literature states that these two algorithms are within the ones most
relevant in the identification of outliers as shall be debated in Section 2. Some authors, such
as Osmar et al., prefer LOF [
5
]. Other authors, such as Allhussein et al., prefer DBSCAN to
analyse outliers [
6
]. While both algorithms exhibit interesting properties, there is no study
comparing both of them in terms of capability to support outlier detection, assuming a
framework that relies on trajectory data captured by IoT and personal devices.
A second reason for considering these two specific algorithms lies in the simplicity of
both algorithms, a key aspect to consider in a continuous PoI detection framework, which
is further addressed in Section 3.
The remainder of this paper is organised as follows. Section 2provides a description
of related literature and of our contributions in comparison to prior work. Section 3defines
our proposal for continuous PoI detection, and its functional blocks, debating PoI detection
and inference aspects and introducing also challenges with outlier detection. Section 4
Future Internet 2023,15, 4 3 of 19
is dedicated to an explanation of which ML algorithms are used to detect outliers giving
preference to the most reputable ones and explaining in detail DBSCAN and LOF. Section 5
provides a performance evaluation of the two algorithms based on datasets with distinct
features. The paper is summarised in Section 6, where the next steps are also debated.
2. Related Work
The use of mobile crowd sensing (MCS) [
7
] applications for urban planning within the
context of Smart Cities has been increasing over the last decade. For instance, Yang et al.
analyse mobile phone traces to detect specific PoIs such as home and work [
2
]. The authors
show that mobile trajectories can be used to infer specific areas of interest of the user with a
fine-grained detail level. However, the detection of outliers is not a core topic in this work.
Butron-Revilla et al. address the detection of mobility patterns (and PoIs) based on mobile
phone data [
8
]. Viswanathan et al. focus on situational awareness to define the nature of
PoIs (stopovers, specific interest in an area, or occasional stop) [
9
]. The focus of the authors
is on situational awareness and not on semi-automated outlier detection.
Another category of work in regard to PoI detection specifically focuses on outlier
detection aspects. The way of approaching the problem of outliers varies from author to
author, not only due to different applied methodologies but also due to the different use
cases where outlier detection is required.
In this context, Ma et al. rely on the use of LOF for outlier detection in a traffic
study [
10
], primarily using principal component analysis (PCA) as an orthogonal linear
transformation that transforms the data to a new coordinate system, so that the largest
variance by any projection of the data lies along the first coordinate (the so-called first
component), the second largest variance lies along the second coordinate, and so on. What
the authors aim at is to analyse LOF as an effective and efficient method for outlier detection
on data using PCA. Their study is relevant as they analyse the efficacy of LOF based on the
variance of coordinates considering different dimensions. However, the efficacy in terms of
different datasets and comparison with DBSCAN or any other algorithm is not addressed
by the authors.
Alghushairy et al. focus on the difference between global and local outlier detectors
giving primacy to LOF [
5
]. Their study refers to data streams used in big data, analysing
both parametric and non-parametric methods, and indicating a new methodology for
the use of LOF in data streams. This work corroborates the applicability of LOF to data
streams and provides a sound methodology for the use of LOF. However, the work does
not compare LOF to other algorithms, such as DBSCAN.
Several authors, such as Markou and Singh [
11
], Goldstein et al. [
12
], Patcha et al. [
13
],
and Alimohammadi et al. [
14
], have published surveys and reviews about outlier detection
methods, some of which provide an analytical comparison of the features of existing
outlier detection methods. In this context, LOF and DBSCAN are among the most popular
solutions for outlier detection.
Sabarish et al. propose trajectory outlier detection algorithms using boundary (TODB) [
15
]
and as they state “The main contribution in this paper is outlier trajectories are identified using
boundary method and their classification is done based on the constructed boundary.” The authors
rely on a convex hull algorithm for all trajectories, classifying them as being outlier trajecto-
ries or not. So, they have to use a boundary, in which the trajectories are inserted. For a
continuous assessment, this is not feasible.
In the path of finding outlying sub-trajectories [
16
], Zhipeng and Dechang propose
the density-based trajectory outlier detection (DBTOD), using Hausdorff distance computed
in metric spaces, becoming a highly complex method with numerous steps. In our case,
we are not interested in eliminating sub-trajectories, but points in sub-trajectories that
are outliers.
Similarly, in the case of Youcef and Djenouri, the goal of applying the group trajectory
outlier detection (GTOD) and the closed DBSCAN k-nearest (CDkNN-GTOD) [
17
] algorithms
Future Internet 2023,15, 4 4 of 19
is to detect groups of trajectories that can be considered as outliers in reference to most
trajectories in a dataset.
Recently, Goodge et al. have proposed a graph neural network method, Lunar, to
provide learning within the context of outlier detection, citing LOF and DBSCAN as two
key approaches in this context due to their simplicity and proved efficacy [
18
]. This is an
interesting approach, which we expect to analyse in a later phase of the development of
this work.
3. Framework for Continuous PoI Detection in Smart Cities
3.1. Smart Cities and Urban Sensing Background
A key aspect in the development of Smart Cities or Smart Communities relates to the
use of data collected via cyber–physical systems (CPS) installed in specific IoT infrastructures
across the city, or data collected from mobile personal devices, such as smartphones. MCS
applications, therefore, rely on available IoT infrastructures and on personal CPS to improve
people-centric services provided by Smart Cities. MCS is today applied to a wide range of
services that enrich the notion of a Smart City, for instance, monitoring of infrastructures
(e.g., energy consumption); increased awareness on social behaviour [
19
,
20
]; improvement
of traffic patterns [
21
]; detection of PoIs based on user behaviour and user preferences [
22
].
The use of MCS based on pervasive, opportunistic sensing [
20
] needs to be seen as a
key component of Smart Cities, where collected data can be used to better plan the city,
by incorporating personal preferences of users to planned PoIs. In the related literature,
most work focuses on recommendations for PoIs, where PoIs are defined in a static way
by municipalities, and PoI detection is considered in recommendation engines, e.g., to
provide recommendations about potential itineraries around a city [
23
]. However, MCS
brings in the possibility to detect PoIs in a passive way, derived from data collected from
city infrastructures and users’ personal devices. Here, the key aspect is not to provide
recommendations based on pre-established points; instead, it is to derive PoIs based on the
mobility behaviour of users in a city. For this purpose, the next sections start by explaining
the proposed architecture and then explain the concept of PoI in the context of our work.
Then, debate on how the detection of PoIs and outlier detection can be carried out.
3.2. Proposed Framework Functional Blocks
Figure 1provides a functional illustration for the proposed continuous PoI detec-
tion framework.
The presented order of steps is not arbitrary, but some functional blocks may also
be placed in a different order. For instance, outliers can be computed before or after the
detection of stop points (SPs), i.e., possible PoIs in a trajectory. We chose to perform a prior
detection of SPs based on visit time (time a user stays stationary in a location), distance
travelled, and speed between SPs.
Once trajectory data is received by the framework, such data is analysed to extract
parameters that may assist in a fine-grained detection of PoIs, e.g., speed, distance traversed
between two readings, and visit time. Additional information may be inferred, e.g., the
type of transportation considered by the user may be relevant also to detect similarity in
different trajectories and thus assist in the detection of PoIs. The next functional block
handles the detection of outliers (B), and afterwards, the data without outliers are used
to estimate SPs. While outlier detection may also be handled after estimating SPs, in our
opinion, outlier detection is the first step to handle. Before the SP inference, the undesirable
values (outliers) must be removed so that no erroneous conclusions can be drawn.
Both the outlier detection and the SP inference require ML application. Therefore,
in the context of this paper, we focus on the next sections on the application of ML for
outlier detection.
Still, in the context of SP inference, there is the need to validate next the obtained SPs,
by removing SPs that may occur sporadically, for instance.
Future Internet 2023,15, 4 5 of 19
For instance, it is feasible to consider the number of times that the detected SPs are
visited, and then cross-reference each SP across different individual trajectories. PoIs can
then be obtained after validating the number of different trajectories sharing a common SP,
and comparing the average visit time against individual visit times of that SP. Then, a final
list of PoIs will be created.
However, this process is continuous, and when repeated for new data sources and
respective trajectories, the PoIs already found are automatically removed during the SP
detection in order to discover new PoIs.
The next section provides further detail concerning PoI detection, and Section 3.4
provides more detail concerning outlier detection.
Figure 1.
Functional blocks of a framework for continuous detection of PoIs in a Smart City, assuming
data obtained in close to real time from MCS applications.
3.3. Interdisciplinary PoI Definition and Detection Aspects
The definition of PoI [
4
] in the context of our work relates to MCS and integrates user
social behaviour.
Our PoI concept goes beyond the usual spatial data (e.g., GPS coordinates), and
follows the line of work that considers PoIs to be a product of space, time, and some
measure of influence/attraction [
24
]. For instance, Chan et al. defined a framework for
personalised tour recommendations based on user interests and network visit duration [
25
].
Their work assumes that there are already pre-established PoIs (municipality data), and
the recommendation engine provides a recommendation based on such a PoI set only.
However, the overlapping of different individual trajectories can also assist in detecting
PoIs which are based on user preferences.
From an individual (one user perspective) a PoI is related to the social attractiveness of
a user to a specific event or activity, which is defined by different attributes, geo-location
being one such attribute. The social attractiveness level varies with time and space and
increases with a larger visit to a specific location.
For instance, a person can, in his/her daily routine, stop at a specific location due to
having met an acquaintance, or even for curiosity and not necessarily due to an activity or
event. This would be a transient SP and should not result in a PoI.
From an aggregated perspective, a PoI can be detected by analysing the similarity of dif-
ferent trajectories in terms of social interaction and similarity patterns in
social interaction.
While PoI detection is a well-addressed issue in the context of geo-location systems
where large and dense datasets are usually applied, we want to be able to detect PoIs
Future Internet 2023,15, 4 6 of 19
seamlessly, based on MCS and on individual anonymous trajectories collected by Smart
City infrastructures and personal devices. Related literature concerning geo-location
and localisation aspects describe several techniques for this purpose, e.g., collecting only
geographic data users’ paths for specific time windows (location), and collecting data from
a triangulation of cellular transmitters (location).
In the context of our work, it is relevant to consider seamless ways to correlate the
trajectory data collected in close-to-real-time from different users. Such data may be then
correlated with existing PoIs (geo-location) as well.
The detection of new PoIs is, therefore, derived from cluster similarity obtained when
considering multiple individual trajectories. For this purpose, our work currently considers
two different definitions to detect PoIs.
Definition 1.
A PoI is defined by its edge betweenness, i.e., it is defined based on the number of
individual trajectories crossing a specific point or within a specific radius. A PoI in this context can
be detected via similarity analysis within a specific time and space range.
Definition 2.
A PoI is defined by the clustering derived from the spatial overlap of individual
trajectories. A PoI in this context is detected when there are clusters that have high density.
Both definitions are impacted by other parameters, for instance, speed, visit time, and
time granularity.
Speed (v), defined in Equation (1), concerns the average speed that an individual user
experiences during his/her periodic routine. In Equation (1), ecorresponds to the distance
travelled (in meters) and tcorresponds to the time of travel.
δv=δe
δt(1)
Another possibility to define speed is to consider speed as a result of the displacement
between points in a trajectory, as provided in Equation (2).
v=e2−e1
δt(2)
Across multiple individual trajectories, a similarity analysis not just derived from
Definitions 1 and 2, but also incorporating speed on segments of multiple trajectories, can
assist in reaching a finer-grained detection of PoIs. For instance, let us assume that a specific
point is detected by juxtaposing different individual trajectories at an instant in time t. By
considering in addition the speed of different users, it may be feasible to detect whether
this is really a PoI.
Visit time (VT)
corresponds to the time interval in seconds that each user spends on
a potential PoI. VT is relevant to define the relevancy of such PoI for a cluster of users. Let
us consider a potential PoI detected due to a large number of overlapping trajectories (high
edge betweenness). Let us assume that 80% of such trajectories exhibit a low VT (seconds).
Then, such a PoI should be disregarded.
Time granularity
is related to the time scale applied in individual trajectories. Differ-
ent time granularities associated with different trajectories will also impact the detected
PoIs as defined in Definitions 1 and 2.
3.4. Outlier Detection Aspects
An outlier is, as explained in Section 1, a representation of a point that is beyond
the limits of a well-defined population. The detection of outliers is a first step to be
worked upon in our proposed framework, as outliers can lead, in data aggregation, to
inaccurate values.
Outliers may occur due to pervasive sensing errors, e.g., some malfunctioning of the
equipment or software, or even due to migration of data from user devices to the edge
Future Internet 2023,15, 4 7 of 19
or cloud. However, they may also occur due to some individual change in the citizens’
mobility behaviour.
Outliers require detection and correction through ML algorithms. Outlier detection is
the focus of this work and is, therefore, addressed in detail in Section 4.
3.5. Privacy Preservation and Security Considerations
MCS requires first of all consent by the user. Then, MCS relies on collected data (e.g.,
visits to wireless networks) that may be piggybacked and thus impact privacy.
It is understood that sometimes, in order to obtain results about citizens’ behaviour,
the personal data of the user or the smartphone are identified, which can lead to a privacy
breach. While MCS do not necessarily collect personal data, according to the General Data
Protection Regulation (GDPR) adopted in the European Union, any use of MCS applications
needs to be consented to by the users.
A continuous PoI detection framework does not, however, require any personal data.
In fact, trajectories sensed by a Smart City IoT infrastructure, or by personal phones are
usually anonymous and attributes such as the identifier of the user device (e.g., MAC
address) are usually obfuscated.
While the handling of these aspects is carried out on user equipment (data source), a
PoI framework detection can also be devised in a privacy-preserving manner, where all
datasets are equally treated, so that potentially sensitive data is obfuscated, for instance.
Privacy-preserving mechanisms have been addressed over the last decade, for instance,
Liu et al. presented several location privacy models and techniques to perform location data
protection and anonymisation [
26
]. Ali et al. drew attention to privacy issues derived from
data aggregation based on data from multiple independent sources. Most protocols and
algorithms do not integrate security by design, thus requiring a security adjustment [27].
Kifer et al. propose the “no-free-lunch” theorem, which defines non-privacy as a game,
to argue that it is not possible to provide privacy and utility without making assumptions
about how the data are generated [
28
]. Recently, Li et al. have proposed the k-anonymity-
based privacy protection for trajectory data [29].
Moreover, several entities provide open data so that researchers can benefit from
data that has to be cleaned, because without such a procedure data inevitably brings in
significant challenges for the protection of data privacy.
4. ML for Outlier Detection
Outlier detection in the context of the framework explained in Section 3.2 is the first
functional block to realise the overall framework. If outliers are not removed, then the
resulting PoIs will be inconsistent. Such inconsistency may relate to poor data collection,
for instance.
Another use of outlier detection is to discover abnormal patterns. We intend to exclude
all points and/or trajectory segments that impair trajectory detection.
ML is, therefore, relevant to be considered in this context. The choice of specific ML
algorithms requires an approach that best serves the requirements of the specific solution.
ML algorithms relevant to outlier detection can be categorised as follows [30]:
1. Nearest neighbour-based
. Based on the comparison of the distances between various
points and their nearest neighbours [31].
2. Density-based
[
32
]. Based on the measurement of the higher or lower density of
points in a given region, which has resulted in a new definition of local outliers,
with the same principle. Here we consider both LOF and DBSCAN as representative
algorithms of this category.
3. Distance-based
[
33
]. Defined by measuring the distances from a given point O
to other points, resulting in points in its neighbourhood and outliers. Examples
are k-nearest neighbours (kNN), k-means (k-MEANS) clustering, and learning vector
quantisation (LVQ).
Future Internet 2023,15, 4 8 of 19
Out of the mentioned approaches, this work considers DBSCAN and LOF as the basis
for outlier detection in the proposed framework. DBSCAN and LOF are anomaly detection
algorithms that use distance to track down the nearest neighbour clusters, based on the
k-NN algorithm.
The next subsections explain the two algorithms.
4.1. DBSCAN
DBSCAN [
34
] follows a data clustering approach. Given a set of points in some
space, it groups together points that are closely packed together (points with many nearby
neighbours), marking as outliers points that are further away in low-density regions (whose
nearest neighbours are too far away). Key strengths of DBSCAN, relevant to our work are:
(i) it does not require setting up a specific number of clusters to detect; (ii) it can handle
clusters of different shapes, sizes, and densities; (iii) it can identify global outliers; (iv) it
does not need to have previous knowledge about the number of clusters to form, not even
the format of its clusters.
In terms of weaknesses, DBSCAN often misses the detection of varying density clusters
and is known to not work well with high dimensional data. For the specific case of outlier
detection, none of these disadvantages apply.
DBSCAN requires two parameters as a base for its calculation. Firstly, it requires the
size and boundary of its neighbourhood given by eps
(e)
. Two points are considered to
be neighbours if the distance between them is less than or equal to eps
(e)
. Secondly, it
requires the minimum number of points that the cluster can contain, given as MinPts and
described in Equation (3):
Ve(x) = y|δ(x,y)≤e(3)
where
Ve(x)
corresponds to the epsilon neighbourhood of a point x
∈
R given
δ(x,y)
which
corresponds to the Euclidean distance between two points x and y. Therefore, Equation (3)
means mathematically that the neighbourhood of x with an
e
radius is formed by all the
points y, given that the distance between these two points is less than e.
In Equation (4), the epsilon neighbourhood of point x must contain at least MinPts
number of points.
Ve(x)≥MinPts (4)
With eps and MinPts, DBSCAN classifies points according to their position in the
vicinity of a point [34].
DBSCAN categorises points as follows:
•Core point
. The point has at least A point is a core point if there are at least MinPts
number of points (including the point itself) in its surrounding area with radius eps.
•Border point
. The point is reachable from a core point and there are less than MinPts
number of points (including the point itself) in its surrounding area with radius eps.
•Outlier point. The point is not reachable from any core point (and not a core point).
The following concepts are the basis of the DBSCAN algorithm:
•Direct density reachable:
A point “A” is directly density reachable from another
point “B” if:
1. “A” is in the eps-neighbourhood of "B" and,
2. “B” is a core point.
•Density reachable:
A point “A” is density reachable from “B” if there are a set of
core points leading from “B” to “A.
•Density connected:
Two points “A” and “B” are density connected if there is a core
point “C”, such that both “A” and “B” are density reachable from “C”.
Future Internet 2023,15, 4 9 of 19
4.2. LOF
LOF [
35
] is an algorithm capable of detecting outliers based on the local deviation of a
given point in regard to its positioning to its neighbours.
It is, therefore, also a density-based algorithm that shares with DBSCAN the concepts
of core distance and reachability distance. LOF can consider nearby local neighbourhoods
and not the global distribution of the data. Outliers are detected as points that have a low
density in comparison to the rest of the neighbourhood.
LOF is known to perform better when datasets have a variable density (clusters of
variable density). LOF depends on how isolated a point is from its neighbours.
LOF is based on the principles, illustrated in Figure 2, namely, the k-distance of
an object p from a point o and the k-distance neighbourhood of p,
Nk
, as provided in
Equation (5).
Figure 2.
LOF principles: k-distance of an object p from a point 0 and k-distance neighbourhood of p,
Nk, and range distance (rdist) (p).
Nk−distance(p)(p) = {q∈D\ {p}|d(p,q)≤k−distance(p)(5)
Nk−distance(p)
can be greater than k since several objects can have an identical distance
to o. The range distance rdist(p)of p with respect to a point o is provided in Equation (6):
rdist(o,p) = maxdist(o,p),kdist(p)(6)
Then, the local range density of p is provided in Equation (7):
lrd(o) = |R(o)|/(∑
p∈R(o)
rdist(o,p)) (7)
where:
R(o) = {p|dist(o,p)<kdist(o)(8)
The local outlier factor for o is computed via Equation (9):
lo f (o) = ∑p∈R(o)lrd(p)
|R(o)|/lrd(o)(9)
or better applied to our case:
LOFMinPts(p) =
∑n∈NMinPt s(p)LrdMinPts (o)
LrdM inPts (p)
|NMinPts(p)|(10)
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The lower the local reachability density of o and the higher the local reachability
density of o’s k-NN, the higher the value of LOF. Given a set of points, LOF computes the
potential of each point being an outlier.
LOF is, therefore, capable of capturing local outliers whose local density is relatively
low compared to the local densities of its k neighbours.
4.3. Additional Algorithm Variants
There are several variants of DBSCAN, such as VDBSCAN, FDBSCAN, DD_DBSCAN,
IDBSCAN, OPTCIS, and CRARANS [
36
], and variants of LOF algorithm, namely, CLOF,
LDOF, and NDOT, which serve specific applications dictated by the nature of the project or
research in which they are employed [37].
However, in this document, we focus on the real values of DBSCAN and LOF, trying
to understand what improvements we can make by varying their parameterisation as well
as infer their advantages and disadvantages in finding outliers in trajectories.
5. Performance Analysis and Evaluation
This section describes the performance evaluation developed to detect outliers. We
have carried out experiments with DBSCAN and LOF for the same datasets.
5.1. Methodology
With regard to the methodology used, it can be described as follows:
1. Selection and analysis of different datasets
. Specific PoI databases are still sparse,
in particular considering the parameters proposed for the PoI definition, e.g., speed,
visit time, time granularity and geo-location. The dataset selection and cleanup are
presented in Section 5.2
2. Dataset cleanup and validation
. Selected datasets have been transformed into new
datasets also integrating time travelled across sequential waypoints of a trajectory;
distance travelled; speed; day of the week; user id (obfuscated); means of transport.
3. Selection of ML algorithms
. The algorithms proposed in this work, DBSCAN and
LOF, were applied to detect outliers with the help of Python programming language,
proceeding where necessary to any adjustments of parameters or possible tuning of
the algorithms.
4. Performance evaluation
. The accuracy of the algorithms used was measured, verify-
ing their validity and applicability throughout the study, and verifying which factors
were preponderant for the analysis.
5.2. Datasets
The analysis has been done based on two types of datasets. The first is Geolife (GEO)
(https://www.microsoft.com/en-us/download/details.aspx?id=52367, accessed on 12
August 2022 ), provided by Microsoft Research Asia and comprising trajectories involving
178 users from April 2007 to October 2011 across China. Each trajectory is based on a set
of GPS-based points ordered in time, comprising longitude, latitude, and altitude. In our
study, after an analysis of the different data of GEO, we have randomly selected a total
of 380 trajectories from three different users, some of them rejected by the algorithms for
having less than twenty points, which is not enough to analyse stop points, and others for
not having (according to both algorithms) any outliers.
A second dataset (PTM) has been considered as an example of a smaller, sparser
dataset, collected by our team via smartphones with the tool Persense (https://m.apkpure.
com/persense-mobile-light/com.senception.persenselight, accessed on 12 August 2022)
based on the trajectories of three users in the municipality of Portimão, Algarve, Portugal,
over 2 months in 2017, in a total of 36 trajectories. Each trajectory provides latitude,
longitude, and speed v.
For the analysis, we have used the sci-kitlearn (https://scikit-learn.org/stable/, ac-
cessed on 12 August 2022) Python implementation of DBSCAN and LOF.
Future Internet 2023,15, 4 11 of 19
5.3. Performance Evaluation Parameters
We have evaluated the capability of DBSCAN and LOF in detecting outliers based on
the classification parameters precision and recall. We have also analysed the overall model
accuracy.
Accuracy
provides a measure of the overall performance of the algorithm. It corre-
sponds to all true classifications (true positives, true negatives) over all classified values
(positive and negative).
By definition,
precision
corresponds to the number of items correctly labelled as true
positives, divided by the total number of elements belonging to the positive class. Precision,
defined in Equation (11), provides a measure of how well an algorithm can detect only
outliers. Precision is provided as a percentage of the number of outliers in the dataset. The
precision is as close to one as the false positives are close to zero.
Recall
, defined in Equation (12), provides a measure of how well all outliers are
identified. The recall is defined as the number of true positives divided by the total number
of elements that actually belong to the positive class (i.e., the sum of true positives and false
negatives, which are items which were not labelled as belonging to the positive class but
should have been). A model that produces no false negatives has a recall of 1.
Precision =T P
TP +FP (11)
Recall =TP
TP +F N (12)
where TP—true positives; FP—false positives; TN—true negatives; FN—false negatives.
5.4. Outlier Detection with DBSCAN
In the context of this work, DBSCAN is applied to different individual trajectories.
This is not a trivial task, as the two parameters eps and MinPts require calibration for
each individual trajectory. On our proposed framework for continuous detection of PoIs,
this implies that the inference engine will have to use a large range of MinPts and eps,
as exemplified in Table 1, that is, with the DBSCAN algorithm, a range of eps parameter
values has been tested, and for each, a range of MinPts values has also been tested. For
instance, assuming an EPS of 7, then a MinPts value of 2 or of 3 has the same result, it
assists in detecting 35 outliers.
An eps of 8 and a MinPts of 6 or 7 results in 39 outliers detected. Varying the MinPts
from 8 to 9, while keeping eps at 8, provides changes in the detected outliers. From this
simple exercise, the aim is to highlight that there is not a clear selection of the eps and
MinPts that results in a better selection of outliers. The values presented in Table 1represent
only a manual selection of the wide range of values tested.
To find a way to circumvent this issue, the first approach considered was to use a
wide range of values for the radius of the neighbourhood and the number of points to be
checked around the core of a cluster. This idea seemed to overcome the problem of having
to select different parameters for each trajectory. However, as explained in the previous
paragraph, this approach became difficult due to the variability of the results in relation
to the parameters used. Due to these results, we abandoned the previous method and
redirected our approach to the methodology proposed by Ester et al. [
38
] and revisited by
Starczewski et al. [39]. For each trajectory the following parameters have been selected:
•
MinPts = 2
∗
DIM, where DIM corresponds to the dataset dimension, i.e., the number
of features provided in the dataset. If the dimension is high (more than 5 or 6 features),
then MinPts = DIM + 1.
•
Using nearest neighbours, the average Euclidean distance between points is calculated.
•
After sorting these points, the obtained curve is the basis to fix the eps within the value
of the inflection of the curve (knee), which normally occurs above the 95th percentile.
Future Internet 2023,15, 4 12 of 19
Table 1. DBSCAN parameters variation and outlier detection impact.
Values EPS Min Samples Outliers Detected
7 2 35
7 3 35
7 4 42
7 5 42
7 6 44
7 7 44
7 8 47
7 9 60
8 2 31
8 3 33
8 4 35
8 5 38
8 6 39
8 7 39
8 8 40
8 9 42
The result of applying this methodology is illustrated in Figure 3.
Figure 3. DBSCAN knee visualisation example.
This methodology requires human support in the sense that the adaptation requires
an analysis of the visual result. This implies an excessive amount of work to be done on
each trajectory, an aspect which is not compatible with a continuous detection engine.
Our approach relies on the detection of the knee point, where this point is loosely
defined as the point of maximum curvature in a system but also the optimal value in
regards to an eps value. This approach is followed, e.g., in Kaggle https://www.kaggle.
com/kevinarvai/knee-elbow-point-detection, accessed on 12 August 2022) and better
suited for a continuous engine that has to handle multiple trajectories (multiple dataflows).
With the eps value optimised for a chosen MinPts, we provide the calculation with
DBSCAN which led us to detect the outliers for each trajectory. A visual representation of
Future Internet 2023,15, 4 13 of 19
the detected outliers is illustrated in Figure 4for the two datasets GEO (Geolife) and PTM
(Portimão).
Figure 4.
Illustration of detected outliers in the GEO and PTM datasets with DBSCAN. Outliers are
highlighted in red.
5.5. Outlier Detection with LOF
Table 2illustrates a subset of the computed precision and recall values for some
trajectories with LOF. The first column of Table 2provides the trajectory identifier (named
“File Name” in GEO); columns 2 and 3 provide the precision and recall values that have
been computed for each trajectory. The number of detected outliers is provided in column 7,
while column 8 holds the number of neighbours. For this sample, it can be seen that the
values reached for both precisions are usually high (99% or even 100%). Moreover, 0 values
mean that the precision or recall could not be computed by LOF.
Table 2. Precision and Recall values for LOF.
Precision Recall Accuracy F-Score N Reg Outliers Neighb
0.996 0.822 0.820 0.901 907 6 4
0.000 0.000 0.000 0.000 243 7 1
1.000 0.769 0.800 0.870 49 5 3
0.976 0.820 0.815 0.891 181 13 4
0.000 0.000 0.000 0.000 1476 67 1
1.000 0.876 0.877 0.934 680 8 11
1.000 0.747 0.750 0.855 493 5 11
0.000 0.000 0.000 0.000 336 23 2
0.985 0.817 0.824 0.893 304 31 3
0.913 0.955 0.875 0.933 80 8 19
0.933 1.000 0.936 0.966 313 32 18
1.000 0.250 0.333 0.400 31 3 3
1.000 0.909 0.917 0.952 80 8 3
0.000 0.000 0.000 0.000 54 6 2
LOF depends on an adequate calibration of MinPts in order not to have a significant
impact on outlier detection.
Future Internet 2023,15, 4 14 of 19
LOF intrinsically depends on K to determine the scale of local neighbourhoods; how-
ever, LOF does not differentiate outliers, and unlike DBSCAN is influenced by the size of the
dataset, as can be seen in the correlation provided in Figure 5, which shows a comparison
of the dependency of both algorithms on the respective parameters.
Figure 5. Correlation of DBSCAN and LOF to parameters.
Figure 5shows how the statistical measures (mean, median, quartiles, interquartile
distance, and the number of points of each trajectory) are correlated with each other and
the clusters obtained through DBSCAN and LOF.
The illustration of the detected outliers with LOF is illustrated in Figure 6.
Figure 6. Detection of outliers with LOF in the GEO and PTM datasets.
For each point, LOF decides whether it is an outlier or not by checking whether the
LOF is close to the value 1. If this value is much higher than 1, it is considered an outlier
factor, while if it is close to 1, it is a normal point.
5.6. LOF and DBSCAN Comparison
5.6.1. GEO Dataset Results
A global perspective on the performance (precision, recall, accuracy) of LOF, when
applied to the GEO dataset, is provided in Figure 7, while the same performance perspective
for DBSCAN is provided in Figure 8. For each chart, the X-axis represents the number of
individual trajectories available. LOF (refer to Figure 7) reaches a stable precision across all
trajectories, while the accuracy varies still within a good level. The recall (how well outliers
are detected) results show, however, that LOF exhibits some difficulty in detecting outliers.
Future Internet 2023,15, 4 15 of 19
Figure 7. LOF performance for the GEO dataset: precision, recall, and accuracy.
Figure 8. DBSCAN performance for the GEO dataset: precision, recall, and accuracy.
DBSCAN (refer to Figure 8) results in more variability in terms of the three evaluation
dimensions (precision, accuracy, and recall). Therefore, LOF is the algorithm that performs
best in terms of outlier detection for the GEO dataset.
5.6.2. PTM Dataset Results
For the smaller dataset, PTM, LOF results are shown in Figure 9and DBSCAN results
are provided in Figure 10. LOF exhibits a good level of accuracy again, but precision and
recall are lower.
DBSCAN (refer to Figure 10) has a significantly lower precision, recall, and accuracy.
Future Internet 2023,15, 4 16 of 19
Figure 9. LOF performance for the PTM dataset: precision, recall, and accuracy.
Figure 10. DBSCAN performance for the PTM dataset: precision, recall, and accuracy.
5.7. Discussion of Results
Table 3provides the achieved accuracy for LOF and GEO. Overall, LOF provided the
best results in terms of outlier detection. The reason for this is related to the fact that LOF
gives more importance to local outlier detection than other methods such as DBSCAN.
Table 3. Average accuracy of DBSCAN and LOF for the datasets GEO and PTM.
ML Approach GEO PTM
DBSCAN 0.76 0.19
PTM 0.86 0.80
Moreover, LOF is easier to parameterise because it varies by only one parameter
(MinPts) and the variability of this factor can be tested more easily. LOF also shows better
accuracy on dense datasets (GEO).
DBSCAN is more difficult to parameterise due to the fact that one has to articulate
two parameters, eps and MinPts, even if a refinement approach, such as kNN (as we have
considered) is applied. DBSCAN exhibited better performance on the sparser dataset
(PTM), but overall, lower performance in terms of outlier detection. In the same way, we
can compare the performance of DBSCAN in the different datasets, highlighting the fact
Future Internet 2023,15, 4 17 of 19
that the PTM dataset is very small and, in addition, each trajectory is much smaller and
covers a much smaller distance than that revealed by the GEO Dataset.
However, as mentioned, LOF behaves very well in both datasets, showing an accuracy
above 80%. While DBSCAN exhibits a more variable behaviour, as accuracy significantly
lowers when DBSCAN is applied to a sparse dataset such as PTM.
6. Summary and Next Steps
This paper presents an innovative framework for the continuous detection of PoIs
based on mobile phone trajectories, and analyses ML-based algorithms, specifically, DB-
SCAN and LOF, to be applied for the continuous detection of outliers. The detection of
outliers corresponds to one of the relevant functional blocks in the proposed PoI detection
framework. To the best of our knowledge and as corroborated in Section 2, where we
have analysed related work, the framework for continuous detection of PoIs is novel and
presents the basis for a much-desired aspect in urban planning in Smart Cities. This is
the possibility to improve services via existing data, via a consented, non-intrusive, and
pervasive data-collecting approach. In addition to the architectural design of such a frame-
work, the paper focuses on the detection of outliers. After checking different algorithms as
explained in Section 4, DBSCAN and LOF have been selected as they are representative
algorithms for both density-based outlier detection and distance-based outlier detection.
The aim was to understand which algorithm could best suit a continuous PoI detection
framework in the context of outlier detection (one of the proposed blocks).
DBSCAN and LOF have been applied to two datasets with very different characteristics
in terms of universe, size, and location features. The paper explains how to best set
DBSCAN and LOF, and performs an analysis for accuracy, precision, and recall. Overall,
LOF is the algorithm that seems to be better suited to be used as the basis for the continuous
detection of outliers.
As the next steps, we will continue with the development of the proposed framework.
Once outliers are removed (by applying LOF), we shall work on the detection of PoIs by
integrating learning and correction approaches.
Author Contributions:
Conceptualization, F.M.P. and R.C.S.; methodology, F.M.P.; software, F.M.P.;
validation, F.M.P. and R.C.S.; formal analysis, F.M.P. and R.C.S.; investigation, F.M.P.; resources,
F.M.P.; data curation, F.M.P.; writing—original draft preparation, F.M.P.; writing—review and editing,
F.M.P. and R.C.S.; visualization, F.M.P.; supervision, R.C.S. All authors have read and agreed to the
published version of the manuscript.
Funding:
This work has been partially funded by the research unit COPELABS, University Lusofona,
Lisbon, FCT strategic project COPELABS UID/MULTI/04111/2019.
Data Availability Statement:
The datasets used in this work can be found here: https://github.com/
fjmper/PHD-Outliers, accessed on 12 August 2022.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
MDPI Multidisciplinary Digital Publishing Institute
DOAJ Directory of Open Access Journals
ML Machine Learning
MCS Mobile Crowd Sensing
LOF Local Outlier Factor
DBSCAN Density-Based Spatial Clustering of Applications with Noise
Future Internet 2023,15, 4 18 of 19
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