Detecting Permanent and Intermittent Purchase Hotspots via

Computational Stigmergy

Antonio L. Alfeo

, Mario G. C. A. Cimino

, Bruno Lepri

Alex “Sandy” Pentland

and Gigliola Vaglini

Department of Information Engineering, University of Pisa, Largo Lazzarino 1, Pisa, Italy

Bruno Kessler Foundation, via S. Croce, 77, Trento, Italy

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

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

at time instant i, resulting by the

evaporation of the trail T

i-1

and the aggregation of the

set of Marks

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

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

and H

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

is set to 0.01 whereas in the former one δ

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

and intermittent τ

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

), workplace

(work

), and transactions (shop

). Using such

information it is possible to calculate the bin-wise

distance of each purchase event (Eq. 4) as the

minimum distance d(home

shop

) between the shop

and the workplace, and the distance d(work

, shop

)

between the shop and the home (Singh, Bozkaya, &

Pentland, 2015).

Dist

= min( d(home

, shop

), d(work

, shop

) ) (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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