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2008), the authors proposed an algorithm that con-
verts a purchase to an implicit rating by considering
the launch-time of the item and the time of the pur-
chase. This implicit rating is then used in collabora-
tive filtering framework for recommendation. A rec-
ommender system based on tag and time information
for social tagging systems is presented in (Zheng and
Li, 2011). It uses a combination of a tag-weight ma-
trix and a time-weight matrix for this purpose. For
each user-tag pair, the tag-weight matrix stores the
fraction of times the user has used the tag. The time-
weight matrix, for a user-tag pair, stores a value that is
dependent on the time when the user entered the tag.
Temporal algorithms have also been used for solv-
ing various other types of recommendation problems.
In (Parameswaran et al., 2010), the authors propose a
precedence mining model that estimates the probabil-
ity of future consumption based on temporal patterns.
The algorithm is used for a course recommendation
application where depending on the past courses that
a student has taken new courses are suggested to the
student. There are algorithms that study temporal-
ity where there is a strict order or path followed by
the user, and the goal is to predict the next step in
that sequence. A typical example of such a task is
the next-page prediction problem in which the system
tries to predict the next web page a user will access
given a sequence of pages visited up to now ((Desh-
pande and Karypis, 2004)). In (Shani et al., 2005),
purchase sequences are viewed as states of a dynamic
system. If one sequence leads to another sequence,
then the system is considered to have made a transi-
tion to the new state. This state transition model is
described as a Markov Decision Process and is used
to generate recommendations. Algorithms based on
precedence mining may not be appropriate for solving
the recommendation problem in a more general case
where such precedence information are not much use-
ful. Two users who purchase the same set of products,
but in different order, may have similar tastes of the
items. One of these users can be used for generating
recommendations for the other. (Rendle et al., 2010)
uses a matrix factorization technique over personal-
ized Markov chains representing sequential purchase
patterns of users. This method called FPMC (Fac-
torizing Personalized Markov Chains) is used for the
next basket recommendation problem. The method
assumes that a user may purchase the same item mul-
tiple times.
A related problem where time aware algorithms
have also been used is the rating prediction problem.
Rating prediction problem is used in systems where
users give ratings to different items. In (Ding and
Li, 2005; Ding et al., 2006), the authors assign time
weights for items so that the recently rated items are
able to contribute more to the prediction. (Campos
et al., 2010) calculates the most similar users with all
the available information from the dataset. After that,
only the most recent ratings of the neighbors are used
to find the predicted rating. (Koren, 2008) merges the
factor and neighborhood models for collaborative fil-
tering to solve the task of rating prediction. A factor
model that looks at several temporal aspects from rat-
ing data is discussed in (Koren, 2009).
A combination of bias model and time weighted
similarity model is presented in (Rongfei et al., 2010).
3 PRELIMINARIES AND
PROBLEM DEFINITION
Let U and I be the set of users and items respectively.
Let D be a collection of past purchase records. Each
record in D is called a purchase or a transaction, and
is of the form (u,i,t
ui
) which represents the fact that
user u has purchased item i at time t
ui
.
Given a target user u ∈ U and past purchase data
D, the goal of a recommender system is to find a set
R
u
⊆ I of items that the target user may want to pur-
chase in future.
4 OUR ALGORITHMS
For the systems where the same users generally do
not purchase the same items multiple times, the user
based collaborativefiltering frameworkis widely used
for generating the recommendations. Algorithms us-
ing this framework work in two phases: expert selec-
tion and recommendation generation. As discussed in
Section 1, giving importance to the recent purchases
of the user in the expert selection phase may address
the issues related to the users’ interest shift. Giving
more importance to the recent purchases of the ex-
perts may capture the item dynamics. For both the
target user and the experts, the system can look at
their purchase histories in three different ways: (a)
treat all items as equal, (b) consider items purchased
in a small time window, or (c) look at the entire his-
tory but with discounted importance assigned to the
items purchased long back. We explore four out of
these nine different combinations and present those
algorithms in this section.
4.1 Algorithm 1: Count (CNT)
The first among these four algorithms does not look
at time information. We call this algorithm as Count,
UserbasedCollaborativeFilteringwithTemporalInformationforPurchaseData
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