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978-1-7281-0003-6/19/$31.00 ©2019 IEEE
A new collaborative approach to solve the gray-
sheep users problem in recommender systems
Abdellah EL FAZZIKI
University of Sidi Mohammed Ben
Abdellah, Fez, Morocco
abdellah.elfazziki@usmba.ac.ma
Youssouf EL ALLIOUI
LS3M, FPK, USMS University, B.P.:
145, 25000, Khouribga, Morocco
yelallioui@gmail.com
Ouafae EL AISSAOUI
University of Sidi Mohammed Ben
Abdellah, Fez, Morocco
ouafae.elaissaouil@usmba.ac.ma
Mohammed BENBRAHIM
University of Sidi Mohammed Ben
Abdellah, Fez, Morocco
mohammed.benbrahim@usmba.ac.ma
Yasser EL MADANI EL ALAMI
ENSIAS, University of Mohammed V
Rabat, Morocco
y.alami@um5s.net.ma
Abstract—Recommender systems aim to help users to find
items that fit their requirements and preferences. In that field,
the collaborative filtering (CF) approach is considered as a
widely used one. There are two main approaches for CF:
memory-based and model-based. Both of the two approaches
are based on the use of users' ratings to predict the top-N
recommendation for the active user. Despite its simplicity and
efficiency, The CF approach stills suffer from many drawbacks
including sparsity, gray sheep and scalability. The aim of this
work is to deal with the gray sheep problem, by proposing a
novel collaborative filtering approach. This novel approach
aims to enhance the accuracy of prediction by turning the users
whose preferences disagree with the target user, into new
similar neighbors. For instance, if a user X is dissimilar to a user
Y then the user
Ź
X is similar to the user Y.
To evaluate the performance of the proposed approach, we have
used two datasets including MovieLens and FilmTrust. The
Experimental results show that our approach outperforms
many traditional recommendation techniques.
Keywords—Recommender system, gray-sheep problem,
Collaborative filtering, Opposite neighbors, Similarity Measure
I. I
NTRODUCTION
Recommender system are intelligent software that have
the ability to recommend items to users by considering their
preferences [1]. The main goal of recommender systems is to
help users in such situations of information overload by
providing them items that suit their requirements. Such
systems aim to filter incoming streams of information by
enabling passing the relevant ones to the user and blocking the
irrelevant ones [2]. Recommender systems have been widely
used in different domains such as movies [3], music [4]
libraries [5] and e-commerce [6].
Due to the increasing use of recommender systems, many
technical approaches to build such systems have been
proposed. According to [7], there are three main types of
recommender systems: collaborative filtering (CF) [8],
content-based [9] and hybrid recommender systems [10].
According to [11], collaborative filtering is the most widely
applied approach on the web, while the other approaches are
less frequently employed.
CF aims to predict for an unrated item the rating than
might be given by the target user, based on the users' ratings.
There are two main approaches for CF: memory-based and
model-based, where the memory-based approaches are often
classified into two main categories, the user-based and the
Item-based, where the first one is based on the users who share
the same preferences, while the second one is based on the
items that are most similar to the target item.
Despite its advantages, CF stills face many challenges and
problems that affect the accuracy of recommendations.
Among those challenges, there is the Gray sheep which refers
to users who have unusual tastes and don’t share similar
preferences with other users [12]. Therefore, it is so hard to
find neighbors. Scalability is another major issue that appears
when the size of the data set being enormously huge. It
becomes difficult to compute similarities when more and more
users and items are added to the database. Also, the sparsity
problem occurs when users are very active, but they don't rate
the available items. Thus, the user-item matrix is extremely
sparse, which can decrease the accuracy, since the similarity
measures is computed based on the ratings given by users [13].
In this paper, we address the problem of grey sheep
associated with CF by proposing a novel approach that aims
to find fictive neighbors for a given user, in order to ameliorate
the prediction accuracy. The principle consists in converting
the users whose tastes differ from the target user, into
neighbors. The underlying assumption of our approach is that
if a user X has an opposite opinion of a user Y, then, the user
¬X has the same opinion as the user Y. Our approach will
increase the number of similar neighbors, which makes the
similarity measures results more significant and then improve
the prediction efficiency.
The rest of this paper is organized as follows: Section 2
gives an overview of the collaborative filtering baseline
approach. Section 3 describes our proposed approach and the
original contribution of this work. The experiments and results
are presented in section 4; Finally, Section 5 presents our
conclusions and future works.
II. B
ACKGROUND
CF techniques aim to predict items for a user based on a
set of preferred items that were previously rated by other
users. There are two types of ratings. Either the users are
explicitly asked to rate items using a rating scale [14], or the
ratings can be inferred implicitly by analyzing the user's
behaviors while using a website such as the history of
purchases [15]. The users' ratings are gathered in a matrix
called the rating matrix which consists of a table where each
row represents a user, each column represents a specific item,
and the number at the intersection of a row and a column
represents the user’s rating value. This matrix is the basic
input in collaborative filtering used to build effective
prediction models and users’ profiles [16].
CF algorithms are categorized into two main approaches:
model-based and memory-based techniques. The first one
aims to build a model based on a training dataset of ratings,
and then use that model to predict unobserved ratings and
make recommendations. There are many machine learning
algorithms that can be used to build a model such as,
clustering techniques [17], dimensionality reduction methods
[18], support vector machines, neural networks [19]. Memory-
based CF is considered as the earliest CF approach [20]. This
approach utilizes the entire rating matrix to generate a
prediction. In Memory-based CF there are two main
algorithms: the item-based CF and the user-based CF. Both of
them aim to select the k-nearest neighbors using a similarity
measure, and based on the selected neighbors the prediction
can be computed. In what follows, we will focus our study on
the user-based approach.
A. User-based approqch Recommendation tasks
The user based approach requires three mains steps as
presented in the below figure:
Fig. 1. Memory-Based CF process
1) Data representation
To build a recommender system using a user based
approach, it is required firstly to create a user-item rating
matrix, where rows represent the users and columns the items
and the intersections between them represent the ratings. In
many cases, the users don't rate items regularly, which causes
the sparsity problem. One way to solve this problem is by
filling the missing values with the average user’s ratings.
2) Neighborhood formation
In user-based approaches, the prediction of a user rating
on an item is based on the ratings given to that item by the
nearest neighbors. So a set of nearest neighbors has to be
selected using a similarity measure between users [21]. One
commonly used similarity metric is the Pearson correlation
coefficient that can be computed using the following formula :
ݏ݅݉
ǡ
ൌ
σ൫
ೌೕ
ି
ೌ
ത
ത
ത
൯൫
್ೕ
ି
್
ത
ത
ത
ത
൯
ೕసభ
ටσ൫
ೌೕ
ି
ೌ
ത
ത
ത
൯
మ
σ൫
್ೕ
ି
್
ത
ത
ത
ത
൯
మ
ೕసభ
ೕసభ
(1)
3) Predictions generation
After selecting the k-nearest neighbors who have already
rated the target item, their ratings can be used by a prediction
function to compute the rating value that can be given by the
target user. The prediction can be generated using the
following formula:
௦ǡ
ൌݎҧ
௦
σሺ
ǡ
ି
ത
ത
ത
ሻכ௦
ೞǡ
ೖ
సభ
σห௦
ೞǡ
ห
ೖ
సభ
(2)
The above function can be used to compute the predicted
ratings for all items that have not yet been seen by a user, and
based on the prediction values the Top-N recommended items
can be determined. As can be noticed, the prediction function
uses the KNN technique where K represents the number of
closest neighbors.
B. Evaluation metrics
After building any prediction model, it is necessary to
evaluate its performance in making predictions. In
recommender systems, there are two commonly used
evaluation metrics: the MAE (mean absolute error) and the
RMSE (root mean squared error). The MAE is a measure of
average absolute differences between observed and predicted
ratings. The lower the MAE, the better the model is.
ܯܣܧ ൌ
σห
ೞǡ
ି
ೞǡ
ห
ሺೞǡሻ
ே
(3)
The Root Mean Squared Error (RMSE) measures the
average magnitude error made by the prediction function
while predicting a user’s rating. It’s the square root of the
average of squared residuals. Residuals are the difference
between the actual ratings and the predicted ratings. The lower
the RMSE, the better the model.
ܴܯܵܧ ൌට
σ൫
ೞǡ
ି
ೞǡ
൯ଶ
ሺೞǡሻ
ே
(4)
From the above-described steps, we can notice that the
user-based approach is so easy to implement and give good
recommendations, but despite these advantages, there are
many drawbacks within this approach that affect its efficiency
such as sparsity, scalability and the gray sheep problem. In the
gray sheep problem, it is a hard task to find neighbors for a
user whose taste is unique. In this case, the results obtained
from the similarity measure function show a very low
correlation. Thus the prediction can't be done. In the next
section, we will present a proposed approach to solve this
problem.
III. O
UR
A
PPROACH
As mentioned in the previous section, the user-based
approach uses a similarity measure to compute similarities
between users and then select the nearest neighbors for a given
user. The computed similarities can be positive or negative.
The users whose similarities are positive are well correlated
with the target user, therefore, their ratings can be used to
make a prediction. In the gray sheep case, it is difficult to
select neighbors and make a prediction, since most users have
low or negative correlations. The figure 2 below presents an
example of a gray sheep situation which occurs in user-based
approach
Fig. 2. Example of gray sheep situation in user-based techniques
The purpose of this work is to deal with the gray sheep
problem by proposing an approach that aims to increase the
size of the neighbors to use their ratings while computing the
prediction function and then improving the recommendations.
The idea of our approach is to exploit the users whose
preferences are different from the target user, by turning them
into neighbors. This idea will help to infer new fictive
Data representation Neighborhood formation Predictions generation
Dissimilar Similar
Active user
neighbors whose similarity values with the active user are
close to 1. Therefore, inferred users will enhance the density
of the active user neighborhood. Consequently, additional
insight will be provided to the recommender engine to make
useful recommendations.
The following figure (figure 3) presents our proposed
approach that includes an additional step called Rating Matrix
augmentation that comes before determining the active user's
neighbors.
Fig. 3. Proposed Memory Based CF Process
Rating matrix augmentation step aims to add new rows in
the rating matrix. Each row represents a new inferred user
whose ratings are opposite to the real one. The opposite ratings
can be deducted using the following formula:
We denote R the ݉ ×݊ rating matrix where m is the
number of users and n represents the number of items. The
entry ݎ݆ܽ refers to the rating given by user a for an item j.
Max and Min represent, respectively, the high and the low
value in a given numeric scale.
For example, in a 5-scale rating which ranges from 1 to 5,
if a user a provided ݎ݆ܽ= 5 as a rating for an item j, then, the
inferred rating of user ¬ܽ for the item j will be ¬ݎܽ݅=1.
TABLE I. E
XAMPLE OF AN OPPOSITE RATING
M
ATRIX IN A
5
POINT
SCALE
Users
Items
i1 i2 i3 i4 i5 i6 i7
ܽ 5 3 2 4
ܽ 1 3 4 2
The above table shows an example of opposite ratings on
a 5-point scale using the previous formula. As can be noticed,
the number 3 doesn't change after applying the formula. In
fact, it represents a neutral rating.
Fig. 4. Example of an active user neighborhood after users inference phase
The above figure shows an example of the fictive
neighbors that can be resulted after applying the neighborhood
formation step on the fictive users. As we can ntice, red
squares represent the new fictive neighbors. The inferred
neighbors are likely to be positively correlated with the target
user.
IV. E
XPERIMENTATION AND
R
ESULTS
To evaluate the performance of our proposed approach we
used the MovieLens and FilmTrust datasets. The main
objective is to compare the performance of the proposed
approach with the User Based Collaborative Filtering
approach using real-world datasets. In this section, we first
present a brief description of the used datasets. Second, we
present the evaluation procedure and the specification test
environment. Then the results of the comparison study are
presented to determine the most performant approach.
A. Datasets collection
The experiments were performed on two commonly used
datasets: MovieLens and FilmTrust. Both are academic
research projects of web-based movie recommender systems.
MovieLens is a 5-point scale rating dataset that ranges
from 1 (means bad) to 5 (means excellent). It consists of 1682
movies, 943 users and 100,000 ratings.
FilmTrust dataset consists of 1856 users, 2092 movies and
759922 ratings. It was collected from a movie recommender
systems website based on a social network which includes
ratings and reviews. Ratings are numeric values on a 5-point
scale between 0.5 and 4 stars.
B. Experiments
To evaluate our approach, we did several experiments
using MovieLens and FilmTrust datasets. To compute the
validation metrics we used a 10-fold cross-validation technic.
We launched these experiments on a laptop computer with an
Intel i5 at 2.4GHz and 8 GB RAM.
Fig. 5. MAE comparison using FilmTrust dataset
Fig. 6. MAE comparison using MovieLens dataset
Data representation Ratings matrix
Augmentation
Neighborhood
formation
Predictions
generation
Similar
Active user
Dissimilar
Figures 6 and 7 display for each dataset, the results
obtained after comparing our proposed approach named
Augmented User-Based Collaborative Filtering approach
(AUBCF) and the UBCF. The figures depict a comparison on
MAE where the horizontal axis is the number of users in the
neighborhood. It increases from ͳͲ to ͳͲͲ at the interval of
ͳͲ. In figure 7, we can see the MAE of our approach and the
baseline technique, are inversely proportional to the
neighborhood size. We can see that our approach has lower
MAE than the baseline approach. In figure 6 we see that our
approach keeps a regular decreasing manner for the MAE
while the baseline approach decreases until ܰൌ͵Ͳ then it
remains stable until ܰൌͲ where MAE starts increasing.
Overall, we can conclude that our approach provides better
performance than the baseline approach in both datasets.
V. C
ONCLUSION
&
PERSPECTIVES
Collaborative filtering is a widely used approach in
recommender systems that stills suffer from many drawbacks,
including the gray sheep problem. In this paper, we have
proposed a novel collaborative filtering approach to deal with
that problem. The proposed approach aims to infer new fictive
neighbors for the active user based on users who have shown
dissimilar tastes and preferences. In order to test our
algorithm, we compared it with UBCF as a baseline approach.
The comparison was done based on two datasets including
FilmTrust and MovieLens. The obtained results showed that
our approach outperforms the UBCF and improves the
accuracy of predictions in the case of gray sheep problems. In
future work, we would like to investigate the hybridization of
our approach with various machine learning techniques, to
enhance the accuracy of recommendations.
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