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Retail data are one of the most requested commodities by commercial companies. Unfortunately, from this data it is possible to retrieve highly sensitive information about individuals. Thus, there exists the need for accurate individual privacy risk evaluation. In this paper, we propose a methodology for assessing privacy risk in retail data. We define the data formats for representing retail data, the privacy framework for calculating privacy risk and some possible privacy attacks for this kind of data. We perform experiments in a real-world retail dataset, and show the distribution of privacy risk for the various attacks.
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Assessing Privacy Risk in Retail Data
Roberto Pellungrini1, Francesca Pratesi1,2, and Luca Pappalardo1,2
1Department of Computer Science, University of Pisa, Italy
2ISTI-CNR, Pisa, Italy
Abstract. Retail data are one of the most requested commodities by
commercial companies. Unfortunately, from this data it is possible to
retrieve highly sensitive information about individuals. Thus, there exists
the need for accurate individual privacy risk evaluation. In this paper, we
propose a methodology for assessing privacy risk in retail data. We define
the data formats for representing retail data, the privacy framework for
calculating privacy risk and some possible privacy attacks for this kind
of data. We perform experiments in a real-world retail dataset, and show
the distribution of privacy risk for the various attacks.
1 Introduction
Retail data are a fundamental tool for commercial companies, as they can rely
on data analysis to maximize their profit [7] and take care of their customers by
designing proper recommendation systems [11]. Unfortunately, retail data are
also very sensitive since a malicious third party might use them to violate an
individual’s privacy and infer personal information. An adversary can re-identify
an individual from a portion of data and discover her complete purchase history,
potentially revealing sensitive information about the subject. For example, if an
individual buys only fat meat and precooked meal, an adversary may infer a
risk to suffer from cardiovascular disease [4]. In order to prevent these issues,
researchers have developed privacy preserving methodologies, in particular to
extract association rules from retail data [3,10,5]. At the same time, frameworks
for the management and the evaluation of privacy risk have been developed for
various types of data [1,13,2,9,8].
We propose privacy risk assessment framework for retail data which is based
on our previous work on human mobility data [9]. We first introduce a set of data
structures to represent retail data and then present two re-identification attacks
based on these data structures. Finally, we simulate these attacks on a real-world
retail dataset. The simulation of re-identification attacks allows the data owner
to identify individuals with the highest privacy risk and select suitable privacy
preserving technique to mitigate the risk, such as k-anonymity [12].
The rest of the paper is organized as follows. In Section 2, we present the data
structures which describe retail data. In Section 3, we define the privacy risk and
the re-identification attacks. Section 4, shows the results of our experiments and,
finally, Section 5 concludes the paper proposing some possible future works.
2 Data Definitions
Retail data are generally collected by retail companies in an automatic way:
customers enlist in membership programs and, by means of a loyalty card, share
informations about their purchases while at the same time receiving special offers
and bonus gifts. Products purchased by customers are grouped into baskets. A
basket contains all the goods purchased by a customer in a single shopping
session.
Definition 1 (Shopping Basket). A shopping basket Su
jof an individual u
is a list of products Su
j={i1, i2, . . . , in}, where ih(h= 1, . . . , n) is an item
purchased by uduring her j-th purchase.
The sequence of an individual’s baskets forms her shopping history related
to a certain period of observation:
Definition 2 (History of Shopping Baskets). The history of shopping bas-
kets HSuof an individual uis a time-ordered sequence of shopping baskets
HSu={Su
1, . . . , Su
m}.
3 Privacy Risk Assessment Model
In this paper we start from the framework proposed in [9] and extended in [8],
which allows for the assessment of the privacy risk in human mobility data.
The framework requires the identification of the minimum data structure, the
definition of a set of possible attacks that a malicious adversary might conduct
on an individual, and the simulation of these attacks. An individual’s privacy
risk is related to her probability of re-identification in a dataset w.r.t. a set of
re-identification attacks. The attacks assume that an adversary gets access to a
retail dataset, then, using some previously obtained background knowledge, i.e.,
the knowledge of a portion of an individual’s retail data, the adversary tries to
re-identify all the records in the dataset regarding that individual. We use the
definition of privacy risk (or re-identification risk) introduced in [12].
The background knowledge represents how the adversary tries to re-identify
the individual in the dataset. It can be expressed as a hierarchy of categories,
configurations and instances: there can be many background knowledge cate-
gories, each category may have several background knowledge configurations,
each configuration may have many instances. A background knowledge category
is an information known by the adversary about a specific set of dimensions
of an individual’s retail data. Typical dimensions in retail data are the items,
their frequency of purchase, the time of purchase, etc. Examples of background
knowledge categories are a subset of the items purchased by an individual, or
a subset of items purchased with additional spatio-temporal information about
the shopping session. The number kof the elements of a category known by the
adversary gives the background knowledge configuration. This represents the
fact that the quantity of information that an adversary has may vary in size. An
example is the knowledge of k= 3 items purchased by an individual. Finally,
an instance of background knowledge is the specific information known, e.g., for
k= 3 an instance could be eggs, milk and flour bought together. We formalize
these concepts as follows.
Definition 3 (Background knowledge configuration). Given a background
knowledge category B, we denote by Bk∈ B ={B1, B2, . . . , Bn}a specific back-
ground knowledge configuration, where krepresents the number of elements in
Bknown by the adversary. We define an element bBkas an instance of
background knowledge configuration.
Let Dbe a database, Da retail dataset extracted from D(e.g., a data struc-
ture as defined in Section 2), and Duthe set of records representing individual
uin D, we define the probability of re-identification as follows:
Definition 4 (Probability of re-identification). The probability of re-identi-
fication P RD(d=u|b)of an individual uin a retail dataset Dis the probability
to associate a record d∈ D with an individual u, given an instance of background
knowledge configuration bBk.
If we denote by M(D, b) the records in the dataset Dcompatible with the
instance b, then since each individual is represented by a single History of Shop-
ping Baskets, we can write the probability of re-identification of uin Das
P RD(d=u|b) = 1
|M(D,b)|. Each attack has a matching function that indicates
whether or not a record is compatible with a specific instance of background
knowledge.
Note that P RD(d=u|b) = 0 if the individual uis not represented in D.
Since each instance bBkhas its own probability of re-identification, we define
the risk of re-identification of an individual as the maximum probability of re-
identification over the set of instances of a background knowledge configuration:
Definition 5 (Risk of re-identification or Privacy risk). The risk of re-
identification (or privacy risk) of an individual ugiven a background knowledge
configuration Bkis her maximum probability of re-identification Risk(u, D) =
max P RD(d=u|b)for bBk. The risk of re-identification has the lower bound
|Du|
|D|(a random choice in D), and Risk(u, D)=0 if u /D.
3.1 Privacy attacks on retail data
The attacks we consider in this paper consist of accessing the released data in the
format of Definition (2) and identifying all users compatible with the background
knowledge of the adversary.
Intra-Basket Background Knowledge. We assume that the adversary has as back-
ground knowledge a subset of products bought by her target in a certain shopping
session. For example, the adversary once saw the subject at the workplace with
some highly perishable food, that are likely bought together.
Definition 6 (Intra-Basket Attack). Let kbe the number of products of an
individual wknown by the adversary. An Intra-Basket background knowledge
instance is b=S0
iBkand it is composed by a subset of purchase S0
iSw
j
of length k. The Intra-Basket background knowledge configuration based on k
products is defined as Bk=Sw[k]. Here Sw[k]denotes the set of all the possible
k-combinations of the products in each shopping basket of the history.
Since each instance b=S0
iBkis composed of a subset of purchase S0
iSw
jof
length k, given a record d=HSuDand the corresponding individual u, we
define the matching function as:
matching(d, b) = (true Sd
j|S0
iSd
j
false otherwise (1)
Full Basket Background Knowledge. We suppose that the adversary knows the
contents of a shopping basket of her target. For example, the adversary once
gained access to a shopping receipt of her target. Note that in this case it is
not necessary to establish k, i.e., the background knowledge configuration has a
fixed length, given by the number of items of a specific shopping basket.
Definition 7 (Full Basket Attack). A Full Basket background knowledge in-
stance is b=Sw
jBand it is composed of a shopping basket of the target win
all her history. The Full Basket background knowledge configuration is defined
as B=Sw
iHSw.
Since each instance b=Sw
iBis composed of a shopping basket Sw
i, given a
record d=HSuDand the corresponding individual u, we define the matching
function as:
matching(d, b) = (true Sd
j|Sw
i=Sd
j
false otherwise (2)
4 Experiments
For the Intra-basket attack we consider two sets of background knowledge con-
figuration Bkwith k= 2,3, while for the Full Basket attack we have just one
possible background knowledge configuration, where the adversary knows an
entire basket of an individual. We use a retail dataset provided by Unicoop3
storing the purchases of 1000 individuals in the city of Leghorn during 2013,
corresponding to 659,761 items and 61,325 baskets. We consider each item at
the category level, representing a more general description of a specific item,
e.g., “Coop-brand Vanilla Yogurt” belongs to category “Yogurt”.
We performed a simulation of the attacks for all Bk. We show in Fig. 1
the cumulative distributions of privacy risks. For the Intra-basket attack, with
k= 2 we have almost 75% of customers for which privacy risk is to equal 1.
3https://www.unicooptirreno.it/
Fig. 1. Cumulative distributions for privacy attacks.
Switching to k= 3 causes a sharp increase in the overall risk: more than 98% of
individuals have maximum privacy risk (e.g., 1). The difference between the two
configurations is remarkable, showing how effective an attack could be with just
3 items. Since most of customers are already re-identified, further increasing the
quantity of knowledge (e.g., exploiting higher kor the Full Basket attack) does
not offer additional gain. Similar results were obtained for movie rating dataset
in [6] and mobility data in [9], suggesting the existence of a possible general
pattern in the behavior of privacy risk.
5 Conclusion
In this paper we proposed a framework to assess privacy risk in retail data.
We explored a set of re-identification attacks conducted on retail data struc-
tures, analyzing empirical privacy risk of a real-world dataset. We found, on
average, a high privacy risk across the considered attacks. Our approach can be
extended in several directions. First, we can expand the repertoire of attacks
by extending the data structures, i.e., distinguishing among shopping sessions
and obtaining a proper transaction dataset, or considering different dimensions
for retail data, e.g., taking into account spatio-temporal information. Second, it
would be interesting to compare the distributions of privacy risk of different at-
tacks through some similarity measures, such as the Kolmogorov-Smirnov test.
Another possible development is to compute a set of measures commonly used
in retail data analysis and investigate how they relate to privacy risk. Finally,
it would be interesting to generalize the privacy risk computation framework to
data of different kinds, from retail to mobility and social media data, studying
sparse relation spaces across different domains.
Acknowledgment
Funded by the European project SoBigData (Grant Agreement 654024).
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