A new collaborative filtering approach utilizing item’s popularity

Abstract

Collaborative filtering (CF) is one of the most successful technologies in recommender systems, and widely used in many personalized recommender areas, such as e-commerce, digital library and so on. However, most collaborative filtering algorithms suffer from data sparsity which leads to inaccuracy of recommendation. In this paper, we focus on nearest-neighbor CF algorithms and propose a new collaborative filtering approach. First, we suggest a new missing data making up strategy before user's similarity computation, which smoothes the sparsity problem. Meanwhile, the notion of item's popularity weight is defined and introduced into the computation. After then, when facing with new users, we also find a kind way to alleviate the difficulty in recommendation. The experimental results show our proposed approach outperforms the other existing collaborative filtering algorithms. It can efficiently smooth the inaccuracy caused by ratings sparsity, and can work well in generating recommendation for new users.

Full text

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Abstract - Collaborative filtering (CF) is one of the most
successful technologies in recommender systems, and widely
used in many personalized recommender areas, such as e-
commerce, digital library and so on. However, most
collaborative filtering algorithms suffer from data sparsity
which leads to inaccuracy of recommendation. In this paper,
we focus on nearest-neighbor CF algorithms and propose a
new collaborative filtering approach. First, we suggest a new
missing data making up strategy before user’s similarity
computation, which smoothes the sparsity problem.
Meanwhile, the notion of item’s popularity weight is defined
and introduced into the computation. After then, when
facing with new users, we also find a kind way to alleviate
the difficulty in recommendation. The experimental results
show our proposed approach outperforms the other existing
collaborative filtering algorithms. It can efficiently smooth
the inaccuracy caused by ratings sparsity, and can work well
in generating recommendation for new users.

Keywords – Collaborative Filtering, Recommender
System, Item’s Popularity Weight, Sparsity Problem


I. INTRODUCTION

Since the beginning of the 1990s, with the widespread
Internet, Web has become an important way to access
information. But on the other side, with the increasing
web information, we have to spend much time on finding
the interesting content we just need. Personalized
recommendation has emerged in response to the
information overload problem. It can understand customer
tastes by analyzing user activities on the platform, then
recommend content tailored to user preferences. At
present, personalized recommendation technology is
popular in many fields, such as e-commerce, digital
library, news sites, entertainment sites and IPTV.
Collaborative filtering is one of the most successful
technologies in recommender systems [1,2]. There are
many famous sites using CF to develop their personalized
recommendation, such as WebWatcher [3], GroupLens
[4], Firefly [5], SELECT [6], and SiteSeer [7]. CF is
based on the truth of friends’ recommendation or “word
of mouth”. The main idea is that the target user is likely to
enjoy the items which other users with common interests.
This methodology can recommend information for users
only according to user-item ratings data, without taking
content’s detail into account. Especially, it has proved to
be very successful in multi-value rating data domain [8].



unsettled, such as sparsity problem and new user problem,
which result in the inaccurate recommendation. In
addition, because finding user’s neighbors is key step of
CF, it’s important to accurately measure user’s similarity.
But we also find that the existing methods seldom think
about the items with different popularity may reflect
different importance in computation. For example, a
popular film “Gone with the wind” and an unpopular film
“Autumn Spring” indicate different weight in evaluating
user’s similarity. So in computing user’s similarity
process in CF, it’s necessary to take the factor of item’s
popularity into account.
In this paper, we focus on nearest-neighbor CF
algorithms. First, we propose a new missing data making
up strategy before computing user’s similarity. This
method can smooth the sparsity problem to a certain
extent. Second, we define item’s popularity weight and
introduce it into the computation of similarity. The result
will be accurate to generate user’s true neighbors. Finally,
in the prediction and recommendation step, we try a new
method for new users by defining item’s composite
recommendation value (ComRV), by which whether an
item is recommended or not is decided. All of these
contribute to more accurate recommendation. We have
carried out experimental evaluation, which takes into
account the above new aspects. The result demonstrates
the superiority of our method, which achieves about 20%
improvements of precision over existing CF algorithms.
The rest of this paper is arranged as follows: In the
following section, collaborative filtering and its related
research are introduced. In section 3, we present our
proposed approach in detail. Section 4 presents the
experimental evaluation. Finally, in section 5 we
summarize our discussion and provide directions for
future research.


II. BACKGROUND

In this section, we review traditional collaborative
filtering algorithms and several major improvements in
collaborative filtering. We also analyze the problem in
traditional work and clarify our contributions in CF
process on the existing problems.

A. Collaborative Filtering

But there are several weaknesses in CF process still
This study was fully supported by the grants of “Shanghai Key
Technology R&D Project” (06DZ15008) and “Shanghai Science and
Technology Professional Project” (07QB14036).
A New Collaborative Filtering Approach Utilizing Item’s Popularity


Weiwei Xia, Liang He, Lei Ren, Meihua Chen, Junzhong Gu
Department of Computer Science and Technology, East China Normal University, Shanghai, China

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opinions to predict the interests of others. It has three
basic steps as follows:
•
Obtain User-Item Ratings Data
System collects the explicit or implicit interests
information of users. After preprocess and normalize the
original information, we can form a rating matrix, in
which user’s personalized preferences is implied.
•
Compute Similarity and KNN Selection
Based on the former matrix, we should find the most
similar users or items of the target user or target item.
They are respectively called user-based and item-based
CF. Computing similarity is the key step in CF. Weather
the neighbors are selected rightly based on the results will
directly affect the quality of recommendation.
Two commonly used algorithms are the Pearson
Correlation Coefficient (PCC) algorithm [10] and the
Vector Space Similarity (VSS) algorithm [11]. These two
approaches differ in the computation of similarity. As
described in [11], the PCC algorithm generally achieves
higher performance than VSS method.
•
Predict Missing Data and Generate Recommendation
Finally, we can use the neighbors’ preferences to do a
prediction for the target user on the non-rated items, and
select the items with high scores as recommendations.
And here CF comes to an end.

B. Other Related Work

To alleviate the data sparsity problem, [12] proposed
to reduce the dimensionality of recommender system
database using the method called Singular Value
Decomposition (SVD) and then users have ratings on
every item on reduced dimension. But [13] indicated that
this method may lead to loss of information and its effects
are very data dependent. In high dimension domain,
dimensionality reduction can’t achieve good performance.
Reference [14] proposed a generative probabilistic
framework to exploit more of the data available in the
user-item matrix by fusing all ratings with a predictive
value for a recommendation to be made. However,
methods mentioned above can’t get high-quality
recommendation.
After Herlocker [10,15] proposed to add a correlation
significance weight in computing similarity to balance the
affects of rating’s sparsity. Reference [16] used the
enhanced Pearson Correlation Coefficient algorithm by
adding one parameter which overcomes the potential
decrease of accuracy when computing the similarity of
users or items. This parameter did a little change on
Herlocker’s significance weight to bounds the similarity
to the interval [0,1]. Reference [17] provided a thorough
analysis of factors involved in CF and then proposed
several extensions and new approaches, which greatly
improved the entire CF approaches.
To improve the accuracy, another way is to set a
threshold in the selection of nearest neighbors, rather than
to select based on a certain number of nearest neighbors.
Reference [16] also introduced a user threshold and an
Collaborative filtering [9] is a technique of using peer
item threshold to overcome the flaws of Top-N neighbors’
selection. It achieved more accurate predictions for the
active user, and then made more precise recommendations
for him.

C. Existing Problems and Our Contributions

•
Sparsity problem – employing a new making up
strategy
Almost all CF Algorithms are confronted with
sparsity problem. Because the ratings data are not
sufficient, the similarity computation isn’t so accurate and
leads to a serious degradation of recommendation quality.
We proposed a novel ratings data making up strategy
better utilizing the item’s category information. After the
making up, according to the modified ratings data, the
following calculation will be well-founded and the result
will be more accurate. It also solves new item problem to
a certain extent.
•
Neglect items’ difference – utilizing item’s popularity
weight in similarity computation
The existing CF algorithms didn’t think of the
different significance weights of items with different
popularity in correlation computation. So based on this
truth, we define a notion of item’s popularity, and
introduce it as an importance weight in the successive
computation, which leads to more accurate predictions
and recommendations.
•
New user problem – alleviating with ComRV
When a new user comes, there are no ratings data or
small number ratings about him, so it’s hard to form his
neighbors and recommend the proper items for him. In the
recommendation step, when facing with new users, we
give a composite recommendation value which combines
the popularity and mean rating value of item. The items
with the Top-N highest ComRV will be recommended to
new users and satisfy them.


III. PROPOSED METHODOLOGY
WITH SMOOTHING

In the sequel, we describe our proposed approach in
detail. First, we define the notations that are used
throughout this paper. Let
U
{
12
, ,,n
Tt tt
=
…
be a set of items in database;
( , )A m n is the rating matrix, and
R by the user i (here1
{}
12
,,,
m
u uu
=
?
be a set of
users,
}
, i j
R indicates that item j
≤ ≤
，1
is rated as
, i j
im
jn
≤≤
);
au is an active user—the user for whom we need to
provide recommendations of the items that he hasn’t seen
before; ( )
U t denotes the users set in which every user has
rated the item t; ( )
T u denotes the items set in which
every item has been rated by user u;
average rating; The rating scale goes from 1 to
r
;
denotes the item’s popularity significance weight of item t.
u R denotes user u’s
maxtP denotes the popularity value of item t; and
tw

Page 3

A. Item’s Popularity Computation

As we know, how many times the item has been rated
can reflect weather it is popular or not. The rated number
is larger, it is more popular. So it’s simple to get every
item’s popularity value just via scanning every column
of ( , )
A m n . It represents like this:
( )
tP U t
=
.

B. User’s Similarity Computation and KNN Selection

a) Ratings data making up
Because of the extreme sparsity of ratings data, the
traditional similarity computing methods can’t rightly
select the nearest neighbors of the active user, and it’s
hard to generate the high-quality recommendation for him.
This paper gives a new strategy to make up the sparse
ratings, which makes the common rated items more
between every two users. Steps are as follows:
Step 1: Calculate the union set ( , )
voted by usera or useru , that is ( , )
Step 2: For user a , find the item set he hasn’t rated
in ( , )
T a u , we denote it as
N a ,
then make up the missing data on every item j in
The strategy is like this: First, get the category
information of item j. Then calculate a ’s mean rating
value on the items he has rated in this category. Here we
should note that if he has never rated any item in this
category, we use the mean rating value on all items he has
rated instead. Finally, use the result as the making up data.
Likewise, for user u, we make up the missing data on
every item in ( )
N u . After this done, the number of
common rated items bya and u becomes more.
b) Similarity computation utilizing item’s popularity
In the existing similarity measures, neither PCC nor
VSS thinks of the pop items and the unpopular items
reflect different weight in similarity computation. All
items make no difference in these measures. But the truth
is that the universally rated items are not as useful in
capturing similarity as less common items. So after the
former step A, we define the popularity significance
weight of item t as follows:
(
log
t
w m P
=
Here, m is the total number of users in the database.
Via the above definition, this weight accords with the fact
that more popular items reflect lower significance and less
popular items contrarily reflect higher significance.
After then, we introduce this weight in PCC measure.
The similarity calculation is modified as follows:
w
sim a u
wR
∈
c) K-nearest neighbors’ selection
After computing all similarity values between the
active user a and every other user in the database, we
sort the results in descending order, and form a neighbor
T a u of the items
( )
T a uT a
=
( )
T u
∪
.
( )( ) ( , )
T a u
( )
( )
N a .
N a T a
=−
,
)
t
(1)
()
()()
2
,,
,
2
222
,,
,,
( )()
( , )
()()
t a ta u tu
t T a u
∈
t a tat u tu
t T a ut T a u
∈
RRRR
RwRR
−−
=
−−
∑
∑∑
(2)
set
( ) {
,
}
1
sim a knn
2
,
,,,
k
?
KNN a knn knn
)
≥
knn
)
2
=
?
, here
≥
( )
aKNN a
)
k
∉
,
and

C. Prediction and Recommendation for Active Users

The predictions on the non-rated items for the active
user are computed by the neighbors’ ratings data on those
items.
sim a u
P a iR
=+
(((
1
,
sim a knnsim a knn
≥
.
,
( )
( )
( , ) ()
( , )
( , )
u iu
u KNN a
∈
a
u KNN a
∈
RR
sim a u
⋅−
∑
∑
(3)
Then generate the recommendation items list for user
a based on the Top-N highest prediction value.
In this step, we find that if there is a new user first
using the system, it’s hard to recommend the proper items
for him, because of no rating data from him. How to deal
with this situation? So we try a novel way. We make
statistics to get Top-N most popular items and which are
also rated well. We define a composite recommendation
value for every item t denoted as
calculated by the equation as follows：
( )ComRV t
( )ComRV t . It is
tt
P R
⋅=
(4)

value of item t. Then select the items with the Top-N
highest ComRV as the positive items for the new user and
recommend them. The goal of this way is to improve the
quality of recommendation for new users, trying best to
recommend the items he possibly likes.


IV. EXPERIMENTAL ANALYSIS

We conduct following experiments to examine the
effectiveness of our new approach for collaborative
filtering with other methods, and address the following
issues: (1) How does the neighbor size affect the accuracy
of recommendation? (2) How does our method compare
with traditional user-based CF, item-based CF and other
existing approaches? (3) How do the recommendations
produced by our proposed ComRV satisfy new users? In
section A and B, we introduce the dataset and metrics for
the experiment, then we present the experimental results
and give an analysis in section C.

A. Dataset

One movie rating datasets called MovieLens
(http://www.cs.umn.edu/Research/Grouplens/) are applied
in our experiments. It provides two datasets. The first one
contains 100,000 ratings (1-5 scales) rated by the 943
users on 1682 movies, and each use at least rated 20
movies. The other contains 1,000,000 ratings (1-5 scales)
rated by 6040 users on 3900 movies. We use the first one
in our experiments and extract 31468 rating records by
300 users on 1533 movies, sparsity is given as:
1 31468/(300 1533)93.16%
−×=
Here,
tP is the popularity, and
tR is the mean rating
.

Page 4

We also get the movie-category matrix from attribute
description file of 1682 movies. They array as follows:
Unknown, Action, Adventure, Animation, Children’s,
Comedy, Crime, Documentary, Drama, Fantasy, Film-
Noir, Horror, Musical, Mystery, Romance, Sci-Fi,
Thriller, War, Western and other special information of
movies.

B. Evaluation Metrics

We use the Mean Absolute Error (MAE) metrics to
measure the prediction quality of our proposed approach
with other collaborative filtering methods. If prediction
ratings set of N users is
corresponding true ratings set is
defined as:
N
=∑
12
,
{
{ , n n
,,,}
, MAE is
N
m mm
?
, and
12
,}
N
n
?
1
||
ii
i
mn
MAE
N
=
−
(5)
Lower the MAE, higher the precision of prediction
and recommendation.

C. Experimental Results

Firstly, we need some regulations in experiments: if
the prediction
1P < , choose 1 as the result, else if
choose 5 as the result. We do the experimental evaluation
as follows.
a) Neighborhood size effect
The neighborhood size has a significant effect on the
prediction quality. We performed an experiment where
we varied the number of neighbors by step of 5 from 10 to
50. The results are shown in Fig.1, from which we can
observe that in the beginning, as the number of neighbors
is increasing, the MAE is lower, but after 30 neighbors
are selected, there is no considerable improvement in
quality, so we select 30 as our optimal choice of
neighborhood size.

5P > ,

Fig. 1. Neighborhood size’s impact on MAE.

b) Comparison
We select 300 users ratings from datasets, and from
which we select 100, 200, 300 users respectively as
training set. As to the active users, we vary the number of
rated items provided by the active users from 5, 10, 15, to
20, and give the name of Given5, Given10, Given15 and
Given20. Set neighborhood size as 30, the result can be
seen in Table 1, Fig.2, Fig.3 and Fig.4, in which CFIP is
our proposed approach, UPCC is user-based CF, IPCC is
item-based CF and EMDP is the method proposed in [16]
(parameters value in this method are set as
30
γ =
, 25
δ =
,
0.4
ηθ==
).

TABLE I
MAE COMPARISONS WITH OTHER METHODS

Training
Set
IPCC 0.892
UPCC 0.876
EMDP 0.834
CFIP
0.829
IPCC 0.855
UPCC 0.844
EMDP 0.833
CFIP
0.825
IPCC 0.851
UPCC 0.840
EMDP 0.828
CFIP
0.797


0.7
λ =
,
Methods Given5 Given10 Given15 Given20
ML_100
0.850
0.846
0.826
0.818
0.834
0.822
0.820
0.813
0.829
0.816
0.816
0.778
0.838
0.831
0.813
0.804
0.821
0.816
0.811
0.786
0.813
0.809
0.802
0.757
0.826
0.812
0.790
0.771
0.812
0.808
0.781
0.753
0.807
0.800
0.774
0.719
ML_200
ML_300

Fig. 2. MAE comparison with other methods with Training Users=100.



Fig. 3. MAE comparison with other methods with Training Users=200.

Page 5

Fig. 4. MAE comparison with other methods with Training Users=300.

From the table and figures, we observe that our new
approach significantly improves the recommendation
quality of collaborative filtering, and outperforms UPCC,
IPCC and EMDP. We also find that the larger the
numbers of training users and active users’ rated items
are, the more accurate the prediction is.
c) Impact on new user
We randomly select some users from training set, and
wipe off their all rating records. Then they are same as
new user. Via computation the item’s ComRV to generate
the recommendation for them. We set these recommended
items a rating prediction as 4 and set N in Top-N as 20,
then compare with their true ratings in the test set and
calculate the MAE. It is about 0.952, which proves this
novel measure is an effective way of recommending for
new users.


V. CONCLUSIONS AND FUTURE WORK

In this paper, we try a novel strategy of missing data
making up, which alleviates the sparsity problem by
making every two users have more common rated items.
Furthermore, we propose an item’s popularity weight in
similarity computation. And in the recommendation step,
dealing with new user problem, we give a new evaluation
about items, which is Composite Recommendation Value.
Based on it, it’s simple and effective to find the proper
items for new users. Through the experimental analysis,
our approach proves to be an outstanding way in CF. It
outperforms other existing CF methods in accuracy of
recommendation. And it also does a good job when up to
new users. Our proposed approach can be applied not
only in movie or IPTV program recommendation, but also
in E-commerce, such as recommender systems for online
bookstore.
For future work, we will conduct more research on
following parts: (1) How to describe and sort the items
resource with better methods, for example, metadata
technology. Then we can compute the correlation between
items more accurately. (2) How to capture users’ feedback
in direct or indirect ways for better understanding users’
interests and better recommendation quality.

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