Detecting Permanent and Intermittent Purchase Hotspots via
Computational Stigmergy
Antonio L. Alfeo
1
, Mario G. C. A. Cimino
1
, Bruno Lepri
2
,
Alex “Sandy” Pentland
3
and Gigliola Vaglini
1
1
Department of Information Engineering, University of Pisa, Largo Lazzarino 1, Pisa, Italy
2
Bruno Kessler Foundation, via S. Croce, 77, Trento, Italy
3
M.I.T. Media Laboratory, 75 Amherst Street, Cambridge 02142, U.S.A.
Keywords: Computational Stigmergy, Stigmergy, Spatio-temporal Patterns, Hotspot, Purchase Behavior.
Abstract: The analysis of credit card transactions allows gaining new insights into the spending occurrences and
mobility behavior of large numbers of individuals at an unprecedented scale. However, unfolding such
spatiotemporal patterns at a community level implies a non-trivial system modeling and parametrization, as
well as, a proper representation of the temporal dynamic. In this work we address both those issues by means
of a novel computational technique, i.e. computational stigmergy. By using computational stigmergy each
sample position is associated with a digital pheromone deposit, which aggregates with other deposits
according to their spatiotemporal proximity. By processing transactions data with computational stigmergy,
it is possible to identify high-density areas (hotspots) occurring in different time and days, as well as, analyze
their consistency over time. Indeed, a hotspot can be permanent, i.e. present throughout the period of
observation, or intermittent, i.e. present only in certain time and days due to community level occurrences
(e.g. nightlife). Such difference is not only spatial (where the hotspot occurs) and temporal (when the hotspot
occurs) but affects also which people visit the hotspot. The proposed approach is tested on a real-world dataset
containing the credit card transaction of 60k users between 2014 and 2015.
1 INTRODUCTION
The extensive usage of nowadays pervasive
technologies generates a large number of digital
traces associated with each human activity. Few well-
known examples are social media posts (Cimino et
al., 2018), vehicle GPS traces (Alfeo et al., 2018),
mobile phone records (Louail et al., 2014), smart
cards usage (Zhong et al., 2015), and credit card
transactions (Dong et al., 2018). Among the many
possible sources, transactions datasets can provide
insights about the daily activities of large numbers of
individuals, allowing the analysis of both their
spending occurrence and mobility behavior at
unprecedented scale (Dong X. et al., 2018). Indeed,
individuals’ purchases result from the combination of
their needs, habits, well-being and where they can go
shopping. Moreover, each shopping choice drives
individuals’ movement (Krumme et al., 2013). By
analyzing both the spending occurrences and the
mobility patterns of the consumers it is possible to
gain new insights about individuals’ behavior (Singh
et al., 2015), as well as understanding the structure
and usage of a given urban area (Long & Liu, 2016).
One method for such urban areas characterization
employs the detection of purchase hotspots, i.e.
locations with a significant occurrence of purchase
events (Sobolevsky et al., 2015). By means of a
hotspots analysis, many works in the field address the
managing of different urban operational problem
(Sobolevsky et al., 2014), such as transportation
services demand (Fuchs et al., 2015) (Oh et al.,
2004). However, the results provided by the hotspots’
detection should also take into account the hotspot
dynamics, i.e. their changing over space and time
(Brimicombe, 2005). Indeed, hotspots’ occurrence
may be due to large time-scales (e.g. seasonal,
weekly) regularities, or according to real world events
such as holidays and sales (Uncles et al., 1995). In
this context, there has not been sufficient research on
characterizing hotspots from a dynamic perspective
(Khan et al., 2017). To address this problem, we
propose an approach aimed at unfolding purchase
hotspots and characterize their spatial and temporal
822
Alfeo, A., Cimino, M., Lepri, B., Pentland, A. and Vaglini, G.
Detecting Permanent and Intermittent Purchase Hotspots via Computational Stigmergy.
DOI: 10.5220/0007581308220829
In Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2019), pages 822-829
ISBN: 978-989-758-351-3
Copyright
c
2019 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
dynamics. Our approach employs a novel
computational technique based on the principle of
Stigmergy, a self-organization mechanism used by
social insect colonies and based on the deposit of
pheromone marks. Since pheromones are volatile, a
pheromone trail (i.e. the marks aggregation) appears
only in areas characterized by a consistent deposit
activity. By applying this pheromone-like
aggregation to purchase event occurrences, the
resulting trail is able to summarize their
spatiotemporal density, enabling the detection of
hotspots. Such approach is known as Computational
Stigmergy, and can be used to detect the hotspots
(Alfeo et al., 2018) and characterize their occurrence
over time according to their similarity in different
time instants. An interesting property is that this
similarity between hotspots can be extracted from
data, and then used to carry out a clustering process
on the corresponding relational space (Cimino et al.,
2006). In this paper, the Computational Stigmergy is
used with a real world dataset provided by a large
Turkish financial institution’s, consisting of all credit
card transactions made in 12 months between 2014
and 2015 from more than 60k customers. In the
following sections we present our approach and the
results obtained by analyzing those data. In Section 2
we briefly present a literature review about the
approaches based on hotspot analysis. In Section 3 we
detail the proposed approach, whereas in Section 4
the experimental setup and the obtained results are
discussed. Finally, we draw the conclusions of this
study in Section 5.
2 RELATED WORKS
The notion of hotspots, i.e. a location with relatively
high levels of activity, was firstly used in order to
understand the occurrence of criminal activities
(Sherman et al., 1989) (Chainey et al., 2008).
Nowadays, the usage of the concept of hotspot has
been extended to a number of different context such
as epidemiology (Martinez-Urtaza et al., 2018),
transportation (Alfeo A.L. et al., 2017), and social
science (Zhu & Newsam, 2016).
Indeed, the hotspot detection and analysis is more
and more exploited by researchers, thanks to its
ability of summarize and gain insights into complex
phenomena, resulting in applications ranging from
urban planning (Liu et al., 2012) to behavioral
analysis and activities forecasting (Dong et al., 2018)
(Scholz & Lu, 2014). In this context, two main
approaches are used to detect the hotspots: those are
respectively based on a statistical and density-based
characterization the occurrences (e.g. smart card
usage, trips) under investigation.
As an example, an approach of the first group
aims at detecting hotspots by employing spatial
autocorrelation indicators (Yang et al., 2016). In (Yu
& He, 2017) authors exploit a heat map to study the
discrete distribution of travel demand at the bus stops
in order to unfold trip hotspots. However, one of the
main difficulties with these approaches remains the
inclusion of the time domain in the analysis (Klemm,
et al., 2016).
The second group of approaches aimed at
detecting hotspot employs the concept of spatial and
temporal density. As an example, in (Hu et al.,
2014) authors exploit a kernel density approach to
represent multiple mobile objects as a density surface
and extract its geometric features to analyze the
hotspot distribution. Again, in (Senaratne et al., 2014)
authors utilizes a kernel density estimation to detect
hotspot clusters of social network activities and
analyze their trajectory over time, allowing the
detection of urban events (e.g. concerts). However,
two shortcomings characterize most of these
approaches: (i) the temporal component is neglected
or represented by just adding a further dimension to
the problem, thus a proper representation and analysis
of the temporal dynamics is missing (Yuan et al.,
2017); (ii) the hard-to-manage exploration of
different analysis parametrization, which is a
fundamental feature since each phenomenon is
visible at a specific scale and resolution (Atluri et al.,
2018)(Yuan & Raubal, 2012). In this work, we
address both those issues by using Computational
Stigmergy. Indeed, Computational Stigmergy
intrinsically embodies the time domain (Barsocchi et
al., 2015) and allows adapting the analysis by tuning
its structural parameters. Specifically, in (Alfeo et al.,
2018) the design of a stigmergic similarity with
parametric adaptation is driven by evolutionary
computation, and based on spatio-temporal context
history. This approach represents a valid alternative
to spatio-temporal similarities based on semantic
rules (Ciaramella et al., 2010), which are
characterized by domain-dependence and limited
adaptability, even when applying evolutionary
parametric adaptation.
3 FUNCTIONAL DESIGN
The proposed approach is based on the principle of
stigmergy, a self-organization mechanism used in
ants’ colonies (Marsh & Onof, 2008). With
stigmergy, the occurrence of a specific condition (e.g.
Detecting Permanent and Intermittent Purchase Hotspots via Computational Stigmergy
823
Figure 1: Architectural modules of the mechanism aimed at detecting hotspots via Computational Stigmergy.
Figure 2: Samples processing phases. Each sample in a given time instant (a) is transformed into a mark (b); each mark
aggregates with the marks released in previous time instants and properly “evaporated” (c-d); a threshold is used to identify
the areas corresponding to the significant part of the trail (e-f); those areas are compared to measure their similarity (g).
an individual discovering food) corresponds to the
release of a pheromone mark in a shared environment.
Due to the volatility of the pheromones, isolated
marks evaporate and eventually disappear, whereas
marks subsequently deposited in proximity to each
other aggregate, resulting in a long-lasting and stable
pheromone trail. By following the pheromone trail,
the colony is steered toward the region in which the
condition above (e.g. the discovery of food) occurs
consistently, since only such consistency generates
the density of marks needed to generate a stable trail.
To the end of unfolding spatiotemporal density in
the data, we process them by employing such
mechanism.
The overall processing schema is known as
Computational Stigmergy (Alfeo A.L. et al., 2017).
Specifically, with Computational Stigmergy, a virtual
pheromone deposit (i.e. a mark) is released in a virtual
environment (Fig. 1b) in correspondence to the
location and time of appearance of each data sample
(Fig. 1a) , i.e. a credit card transaction. The marks are
represented by a truncated cone with a given width Ԑ
and intensity (height). Moreover, marks are subject to
an evaporation process, i.e. a temporal decay with rate
δ (Fig. 1c). Thanks to the evaporation, isolated mark
progressively disappears, whereas marks that are
frequently released in proximity to each other
aggregate forming the trail. In a nutshell, the trail
appears and stays only in correspondence of
consistent marks depositing activity, thus can be
considered as a summarization of spatiotemporal
density in the data (Alfeo A.L. et al., 2017). Eq. 1
describes the trail T
i
at time instant i, resulting by the
evaporation of the trail T
i-1
and the aggregation of the
set of Marks
i
at the time instant i.

   
(1)
As shown in Fig. 1d, in order to detect the significant
part of the trail (i.e. corresponding to a potential
hotspot H
i
at time i), it is necessary to set a threshold
, i.e. a given percentage of the maximum intensity of
the trail ( Eq. 2).
 (2)
Different hotspots can be compared by means of the
Jaccard similarity (Niwattanakul et al., 2013). Such
measure of similarity is computed as the ratio
ICPRAM 2019 - 8th International Conference on Pattern Recognition Applications and Methods
824
between the intersection () and the union () of the
areas underlying the hotspots (e.g. H
A
and H
B
in Fig.
1e and Eq. 3), and it is defined between 0 (completely
different hotspots) and 1 (identical hotspots).





(3)
Thanks to this similarity measure it is possible to
identify hotspots on the basis of their temporal
consistency, i.e. their similarity in different time
instants. For the sake of clarity, we depict the phases
of the hotspot detection and analysis with a set of
samples belonging to 3 consecutive time slots in Fig.
2. Each of the presented processing steps is
parameterized, and each parameter represents a
feature of the potential hotspot. Specifically, the
marks width Ԑ and the evaporation δ results in the
spatial and temporal proximity allowing marks to
aggregate and form the trail; by tuning such
parameters we define the spatio-temporal density of a
potential hotspot. On the other hand, the threshold
defines the significant amount of spatiotemporal
density corresponding to a hotspot. By employing a
heuristic or a measure of the quality of the hotspots
detection process, it is possible to tune those
parameters with the aim at specializing the detection
of the hotspots to the peculiarities of the scenario
under analysis, as specified in Section 4.
4 EXPERIMENTAL RESULTS
The approach presented in Section 3 has been
developed in Matlab, a well-known versatile high-
performance environment equipped with functions
and syntax to work with big data. We experiment our
approach on a credit card transactions dataset
provided by a major financial institution in Turkey.
Such dataset consists of more than 10 million
transactions instances made by more than 64k
individuals during a period of twelve months. Each
instance is composed by the following attributes:
customer id, timestamp, amount, shop id, online,
expense type, currency, latitude coordinates, and
longitude coordinates. Moreover, we work with an
additional dataset containing a number of
demographic information about each individual, such
as age, gender, education level, income, home, and
work location. The customer-level data are
anonymized by representing each customer with a
pseudo-unique number. By exploring the spatial
distribution of the transactions in the dataset it is
evident that most of them occur in Istanbul
metropolitan area, thus we decide to focus the
analysis on such area. The data undergo a pre-
processing phase consisting of the spatial and
temporal discretization. Each bin corresponds to a
square area of 100 meters side and a time interval of
20 minutes. As mentioned in Section 2, the
occurrence of hotspots alone provides an incomplete
overview of the purchase phenomenon (Uncles et al.,
1995). What is really interesting is the consistency of
the hotspots’ over time. Indeed, a hotspot can be
permanent, i.e. present throughout the period of
observation, or intermittent, i.e. present only in
certain times and days of the week (Louail et al.,
2014). Most of the works in the field detect a weekly
hotspot routine (Alfeo A.L. et al., 2018). Thus, we
define two types of days (weekends and weekdays)
and we split each day into 12 time slots, 2 hours each.
In contrast to permanent hotspots, the intermittent
hotspots are peculiar for each tuple [day type; time
slot] within the same month.
Figure 3: Transactions’ location (GPS) spatial distribution.
To detect both intermittent and permanent hotspots, a
number of parameters have to be properly set. The
evaporation must guarantee the preservation of (even
a part of) the information (i.e. the mark) for the whole
time of the analysis. If looking for permanent
hotspots, this time corresponds to a whole day, while
with intermittent hotspots, it corresponds to 2 hours
(a time slot). Thus, in the first case, the evaporation
δ
P
is set to 0.01 whereas in the former one δ
I
is set to
0.15. The mark intensity is set to 1, whereas its width
Ԑ is set to 10, enabling the aggregation of marks
which distance is up to 1 km. The most sensitive
parameters of the analysis are the thresholds for
permanent τ
P
and intermittent τ
I
hotspots. For this
reason, they are set through an iterative exploratory
analysis aimed at maximizing only the similarity
between intermittent hotspots of similar temporal
tuples. As an example, in Fig. 4 we show a similarity
matrix obtained from the comparison of the
intermittent hotspots for each time slot of each day of
September 2014. To a lighter color corresponds a
greater similarity (1 on the diagonal). Clearly, there is
a consistency of the hotspots (a greater similarity) in
Detecting Permanent and Intermittent Purchase Hotspots via Computational Stigmergy
825
correspondence of time windows corresponding to
similar occurrences. For example, it is possible to
identify a strong similarity between weekend
daytimes hours, the evening and night hours between
Saturday and Sunday and the daytime hours of the
working days. The clearer the distinction between
these groups of days, the better the parameterization
of the analysis.
By definition, intermittent hotspots of a given
tuple are supposed to be similar to each other within
the same month. On the other hand, the permanent
hotspots occur on average all days and time slots, thus
their presence may interfere with the similarity
computation between hotspots obtained with
different tuples. For this reason, we (i) firstly, identify
permanent hotspots as the intersection of the areas
underlying the significant part of the trails in all days,
then (ii) we remove the transactions occurring in
those areas, and finally (iii) intermittent hotspots are
targeted in order to maximize the similarity between
hotspots of the same tuples or temporally close tuples.
Fig. 5 shows the procedure described above
together with the 10 permanent (in red) and the 9
intermittent (in cyan) hotspots discovered.
Figure 4: Similarity matrix obtained by matching the
Intermittent hotspots during September 2014.
In the absence of a ground truth on the distribution
and nature of the hotspots, we discuss the obtained
results according to the features of the people
spending in the hotspots. Specifically, it is possible to
evaluate the characteristics of the users using the
permanent or intermittent hotspots from the
demographic data associated with the transactions
dataset.
For each customer it is known his/her income,
age, and level of education, i.e. unknown (reported as
0), non-educated (as 1), elementary school (as 2),
middle school (as 3), high school diploma (as 4),
college (as 5), university degree (as 6), master degree
(as 7), and Ph.D. (as 8). Moreover, it is known the
location of customers' home (home
u
), workplace
(work
u
), and transactions (shop
ui
). Using such
information it is possible to calculate the bin-wise
distance of each purchase event (Eq. 4) as the
minimum distance d(home
u
shop
ui
) between the shop
and the workplace, and the distance d(work
u
, shop
ui
)
between the shop and the home (Singh, Bozkaya, &
Pentland, 2015).
Dist
ui
= min( d(home
u
, shop
ui
), d(work
u
, shop
ui
) ) (4)
Figure 5: Discovery process and resulting intermittent
(cyan) and permanent (red) purchase hotspots in Istanbul.
By using the purchase distance, it is possible to
evaluate few behavioral traits of the customers: (i)
how exploratory each customer is when looking for
places to shop, measured as the average purchase
distance (avgDist in Fig. 6); and (ii) how erratic each
customer is when looking for places to shop,
measured as the standard deviation of the purchase
distance (stdDist in Fig. 6).
Fig. 6 shows the results obtained from this
analysis by means of violin plots. The violin plots
represent the distribution of the demographic features
for the population purchasing in each type of hotspot.
As demographic features, we show individuals’
education level (edu in Fig. 6), income, age, and the
metrics for exploratory and erratic behavior. Overall
their distribution is not significantly different,
exception made for their average income, which is
greater in the case of intermittent hotspots.
The different average incomes among the people
using the intermittent and permanent hotspots can be
explained by considering the number of credit card
transactions per customer, which is relatively low, i.e.
ICPRAM 2019 - 8th International Conference on Pattern Recognition Applications and Methods
826
on average 68 transactions per user throughout the
year of observation. Therefore, for a hotspot to be
“permanent” it must be able to attract as many people
as possible, and this results in an average income
closer to the one of the whole dataset, i.e. 2979
Turkish liras. On the other hand, intermittent hotspots
are associated to occasional activities such as those
related to nightlife, and these activities are more
likely to be performed by people with higher incomes.
Figure 6: Demographic features of the population
purchasing in the hotspots. Log scale. The average income
of the population purchasing in each type of hotspot is
reported in squares.
5 CONCLUSIONS
In this work, we have proposed an approach based on
Computational Stigmergy to detect and analyze
purchase hotspots according to their spatial
distribution and temporal occurrence. The presented
approach overcomes the limitations of many
approaches in the literature that is the poor
representation of the temporal dynamic and the
inadequate exploration of the solutions space. By
using our approach, we analyze the occurrence of the
transactions of 60k Istanbul residents between 2014
and 2015. The results of such analysis confirm the
validity of our approach to identify permanent and
intermittent hotspots. Moreover, the analysis of the
users spending in each type of hotspot is provided. As
future works we aim at (i) studying the attractiveness
of the areas identified as hotspots using a gravity
model, and (ii) carrying out an analysis of the
anomalies in the purchase activity, such as the one
detectable by observing Fig. 4, in the group time slots
immediately ahead of the 200th; apparently those are
characterized by intermittent hotspots very similar to
each other but completely different from all the others
in any time slot, therefore a potential anomaly in the
purchase activity.
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