Clustering Big Urban Dataset

Abstract

Cities are producing and collecting massive amount of data from various sources such as transportation network, energy sector, smart homes, tax records, surveys, LIDAR data, mobile phones sensors etc. All of the aforementioned data, when connected via the Internet, fall under the Internet of Things (IoT) category. To use such a large volume of data for potential scientific computing benefits, it is important to store and analyze such amount of urban data using efficient computing resources and algorithms. However, this can be problematic due to many challenges. This article explores some of these challenges and test the performance of two partitional algorithms for clustering Big Urban Datasets, namely: the K-Means vs. the Fuzzy c-Mean (FCM). Clustering Big Urban Data in compact format represents the information of the whole data and this can benefit researchers to deal with this reorganized data much efficiently. Our experiments conclude that FCM outperformed the K-Means when presented with such type of dataset, however the later is lighter on the hardware utilisations.

Full text

Clustering Big Urban Dataset
Ahmad Al Shami, Weisi Guo, Ganna Pogrebna
Warwick Institute for the Science of Cities, School of Engineering, The University of Warwick
Coventry, CV4 7AL, United Kingdom
Email: a.al-shami@warwick.ac.uk, weisi.guo@warwick.ac.uk
Abstract—Cities are producing and collecting massive amount
of data from various sources such as transportation network,
energy sector, smart homes, tax records, surveys, LIDAR data,
mobile phones sensors etc. All of the aforementioned data, when
connected via the Internet, fall under the Internet of Things
(IoT) category. To use such a large volume of data for potential
scientific computing benefits, it is important to store and analyze
such amount of urban data using efficient computing resources
and algorithms. However, this can be problematic due to many
challenges. This article explores some of these challenges and
test the performance of two partitional algorithms for clustering
Big Urban Datasets, namely: the K-Means vs. the Fuzzy c-
Mean (FCM). Clustering Big Urban Data in compact format
represents the information of the whole data and this can benefit
researchers to deal with this reorganized data much efficiently.
Our experiments conclude that FCM outperformed the K-Means
when presented with such type of dataset, however the later is
lighter on the hardware utilisations.
Index terms— Big Data; LIDAR, Fuzzy c-Mean; K-Means,
Hardware Utilisation, Smart City
I. INTRODUCTION
The challenges of Big Data are due to the 5Vs which are:
Volume, Velocity, Variety, Veracity and Value to be gained
from the analysis of Big Data [1]. Many researchers are
dealing with different types of data sets, the concern here is
to wither to introduce a new algorithm or to use the existing
ones to suit large datasets. Currently, two approaches are
predominant: First, is known as Scaling-Up which focuses
the efforts on the enhancement of the available algorithms.
This approach risks them becoming useless for tomorrow, as
the data continues to grow. Hence, to deal with continuously
growing in size datasets, it will be necessary to frequently scale
up algorithms as the time moves on. The second approach is
to Scale-Down or to reduce the data itself, and to use existing
algorithms on the skimmed version of the data after reducing
its size. The scaling down of data may also risk the loss of
valuable information due the summarising and size reductions
techniques. But, still it is argued that using the scaling down
technique may only risk the information that is comparatively
unimportant or redundant. Since there is still a great scope
for the research in both areas, this article focuses on the
scale-down of data sets by comparing clustering techniques.
Clustering is defined as the process of grouping a set of items
or objects which have same attributes or characteristics.
II. K-MEA NS V S. FUZ ZY C -MEA NS
To highlight the advantages to scientific computing for Big
Data and to avoid the above mentioned disadvantages for the
hierarchical clustering techniques, this article is focusing on
comparing two trendy and computationally attractive parti-
tional techniques which are:
1) K-Means: This is a widely used clustering algorithm
as it partition a data set into K clusters (C1;C2; :::
;CK), represented by their arithmetic means called the
centroid, which is calculated as the average of all data
points (records) belonging to certain cluster.
2) Fuzzy c-Means (FCM) was introduced by [16] and it is
derived from the K-means concept for the purpose of
clustering datasets, but it differs in that the object may
belong to more than one cluster at the same time with
a certain degree of belonging to each cluster.
The FCM clustering is obtained by minimizing the
objective function at each iteration, an objective function
is minimized to find the best location for the clusters
and its values are returned in objective function. Fuzzy
clusters can be characterised by class membership func-
tion matrix, and cluster centres are determined first at
the learning stage, and then the classification is made
by the comparison of Euclidean distance between the
incoming features and each cluster centre [17]. For a
data set represented as X={x1,x2,...,xj. . . , xn} ⊂ Rs
into cclusters, where 1 <c<n; the fuzzy clusters can
be characterized by a c×nmembership function matrix
U, whose entries satisfy the following conditions:
c
∑
i=1
ui,j=1,j=1,2,...,n(1)
0<
n
∑
j=1
ui,j<n,i=1,2,...,c(2)
where ui,jis the grade of membership for xjdata
entry in the ith cluster. Cluster centres are determined
initially at the learning stage. Then, the classification
is made by comparison of distance between the data
points and cluster centres. Clusters are obtained by
the minimisation of the following cost function via an
iterative scheme.
J(U,V) =
n
∑
j=1
c
∑
i=1
(ui,j)2
xj−vi
(3)
where V={v1,v2,...,vi, . . . vc}are cvectors of cluster
centres with virepresenting the centre for ith cluster.

To calculate the centre of each cluster, the following
iterative algorithm is used.
a) Estimate the class membership U.
b) Calculate vectors of cluster centres
V={v1,v2,...,vi, . . . vc}using the following ex-
pression:
vi=∑n
j=1(ui,j)2xj
∑n
j=1(ui,j)2i=1,2,...,c(4)
c) Update the class membership matrix Uwith:
ui,j=1
∑c
r=1kxj−vik
kxj−vrk2i=1,...,c;j=1,...,n
(5)
d) If control error defined as the difference between
two consecutive iterations of the membership ma-
trix Uis less than a pre-specific value, then the
process can stop. Otherwise process will repeat
again from step 2.
After a number of iterations, cluster centres will satisfy
the minimisation of the cost function Jto a local
minimum [17].
III. EXP ER IM EN TS SE TU P
Lidar dataset were used for this experiment as it is gaining
importance for urban planning such as floodplain mapping,
hydrology, geomorphology, landscape ecology, coastal en-
gineering, survey assessments, and volumetric calculations.
The experiments carried to compare how the candidate K-
Means and FCM clustering techniques cope with clustering
big urban dataset using mid-range level computer hardware.
The experiment were performed using an AMD 8320, 4.1
GHz, 8 core processor with 8 GB of RAM and running a
64-bit Windows 8.1 operating system. The algorithms were
implemented against a a LIDAR data points [3], taken for our
campus location at Latitude: 52.23◦- 52.22◦and Longitude:
1.335◦- 1.324◦. This location represents the University of
Warwick main campus with an initialization of 1000000 x
1000 digital surface data points.
IV. COMPARATIVE ANA LYSI S
1) K-Means Clustering: This clustering technique is applied
to the specified dataset starting with a small cluster
number K = 5 and gradually increased to K = 25 clusters.
Fig. 1 shows how on average the used hardware fared
to obtain the desired number of Kclusters and Table
I lists a summary of the statistics of elapsed time and
resources used for K-Means algorithm to converge.
2) FCM Clustering: This clustering technique was also
applied to the same generated dataset with cluster num-
ber starting with 5 and gradually increased to reach
25 clusters. Fig. 2-a and Fig. 2-b show the CPU and
RAM usage while executing the large dataset with FCM
clustering function and Table II lists summary of the
(a) CPU-K-Means
(b) RAM-K-Means
Fig. 1: Average CPU and Memory usage during K-Means
execution.(a) CPU, (b) RAM.
TABLE I: Time elapsed and resources used for K-Means
clustering.
Clusters counts Time/Seconds CPU used RAM used
5161.178 21% of 4.0 GHz 36% of 8.0 GB
10 244.642 27% of 4.0 GHz 42% of 8.0 GB
15 338.345 36% of 4.0 GHz 47% of 8.0 GB
20 409.618 48% of 4.0 GHz 53% of 8.0 GB
25 484.013 55% of 4.0 GHz 58% of 8.0 GB
Average 327.558 37.4% 47.2%
main time and resources it took the FCM algorithm to
converge for the different number of assigned clusters.
TABLE II: Time elapsed and resources used for FCM cluster-
ing.
Clusters counts Time/Seconds CPU used RAM used
542.190 56% of 4.0 GHz 65% of 8.0 GB
10 83.577 59% of 4.0 GHz 67% of 8.0 GB
15 127.848 65% of 4.0 GHz 75% of 8.0 GB
20 168.994 67% of 4.0 GHz 87% of 8.0 GB
25 214.995 69% of 4.0 GHz 91% of 8.0 GB
Average 127.520 63.2% 77.0%
By comparing the results in Table I and Table II, it is clear
that the lowest average time measured for FCM to regroup the
data was 127.520 seconds, while it took K-Means an average
of 327.558 seconds to form the same number of clusters. On

(a) CPU-FCM
(b) RAM-FCM
Fig. 2: Average CPU and Memory usage during FCM execu-
tion.(a) CPU, (b) RAM.
average FCM used up between 5-7 out of the eight available
cores, with 63.2 percent of the CPU processing power and 77
percent of the RAM memory. The K-Means on the other hand
utilised between 4-6 cores with the rest remain as idle cores
with an average of 37.4 percent of the CPU processing power
and 47.2 percent of the RAM memory.
On average FCM used up between 5 −7 out of the eight
available cores, with 63.2 percent of the CPU processing
power and 77 percent of the RAM memory. The K-Means
on the other hand utilised between 4 −6 with the rest remain
as idle cores with an average of 37.4 percent of the CPU
processing power and 47.2 percent of the RAM memory.
Overall, both algorithms are scalable to deal with Big Data,
but, FCM is fast and would make an excellent clustering algo-
rithm for everyday computing. In addition, it would offer some
extra added advantages such as its ability to handle different
data types [18]. Also, this fuzzy partitioning technique and
due to its fuzzy capability, FCM could produce a better quality
of the clustering output [19] which could benefit many data
analysts.
V. CONCLUSIONS AND FUTURE WORK
A comparative case study for clustering Big Urban Data set
using handy and simple techniques is proposed. The K-Means
and FCM were tested to cluster a Big Data set hosted on a
PC for everyday computing. The presented techniques can be
instantly mobilised as a robust methods to handle partitional
clustering for a large dataset with ease. However, FCM would
be a better choice if speed and quality are priority. In the
near future we plan to focus our attention on the quality of
the clusters produced here and to compare more clustering
techniques against another types of big datasets.
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