u
1
u
2
u
a
u
m
.
.
.
.
i
1
i
2
i
j
i
n
. .
. .
Input (ratings table)
Active user
Item for which prediction
is sought
Prediction
Recommendation
CF-Algorithm
P
a,j
(prediction on
item j for the active
user)
{T
i1
, T
i2
, ..., T
iN
} Top-N
list of items for the
active user
Output interface
Figure 1: The Collab orative Filtering Pro cess.
a typical CF scenario, there is a list of
m
users
U
=
f
u
1
; u
2
; : : : ; u
m
g
and a list of
n
items
I
=
f
i
1
; i
2
; : : : ; i
n
g
.
Each user
u
i
has a list of items
I
u
i
, which the user has expressed his/her opinions about. Opinions can be
explicitly given by the user as a
rating score
, generally within a certain numerical scale, or can be implicitly
derived from purchase records, by analyzing timing logs, by mining web hyperlinks and so on [28, 16]. Note
that
I
u
i
I
and it is possible for
I
u
i
to b e a
nul l-set
. There exists a distinguished user
u
a
2 U
called the
active user
for whom the task of a collab orative ltering algorithm is to nd an item likeliness that can b e
of two forms.
Prediction
is a numerical value,
P
a;j
, expressing the predicted likeliness of item
i
j
62
I
u
a
for the active
user
u
a
. This predicted value is within the same scale (e.g., from 1 to 5) as the opinion values provided
by
u
a
.
Recommendation
is a list of
N
items,
I
r
I
, that the active user will like the most. Note that the
recommended list must b e on items not already purchased by the active user, i.e.,
I
r
\
I
u
a
= . This
interface of CF algorithms is also known as
Top-N recommendation
.
Figure 1 shows the schematic diagram of the collaborative ltering pro cess. CF algorithms represent the
entire
m
n
user-item data as a ratings matrix,
A
. Each entry
a
i;j
in
A
represent the preference score
(ratings) of the
i
th user on the
j
th item. Each individual ratings is within a numerical scale and it can
as well b e 0 indicating that the user has not yet rated that item. Researchers have devised a numb er of
collaborative ltering algorithms that can b e divided into two main categories{
Memory-based (user-based)
and
Model-based (item-based)
algorithms [6]. In this section we provide a detailed analysis of CF-based
recommender system algorithms.
Memory-based Collab orative Filtering Algorithms.
Memory-based algorithms utilize the entire
user-item database to generate a prediction. These systems employ statistical techniques to nd a set
of users, known as
neighbors
, that have a history of agreeing with the target user (i.e., they either rate
dierent items similarly or they tend to buy similar set of items). Once a neighb orhoo d of users is formed,
these systems use dierent algorithms to combine the preferences of neighbors to pro duce a prediction or
top-
N
recommendation for the active user. The techniques, also known as
nearest-neighbor
or user-based
collaborative ltering are more p opular and widely used in practice.
Mo del-based Collab orative Filtering Algorithms.
Model-based collab orative ltering algorithms pro-
vide item recommendation by rst developing a model of user ratings. Algorithms in this category take a
probabilistic approach and envision the collab orative ltering pro cess as computing the exp ected value of a
user prediction, given his/her ratings on other items. The mo del building pro cess is p erformed by dierent
machine learning
algorithms such as
Bayesian network, clustering,
and
rule-based
approaches. The
Bayesian network mo del [6] formulates a probabilistic mo del for collab orative ltering problem. Clustering
4
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