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2017 2nd International Conference on Software, Multimedia and Communication Engineering (SMCE 2017) 
ISBN: 978-1-60595-458-5 
 
Ratings Distribution Recommendation Model-based Collaborative 
Filtering Recommendation Algorithm 
Tao-tao PAN*, Qin-rang LIU and Chang LIU 
China National Digital Switching System Engineering and Technological R&D Center, Zhengzhou 
450002, China 
*Corresponding author 
Keywords: Collaborative filtering, Similarity, Popular ratings, Rating scale. 
Abstract. In order to solve the problem of the popular item ratings interfering in similarity calculation, 
we proposed the ratings distribution recommendation model. Based on this model, we designed a new 
collaborative filtering algorithm. According to ratings distribution, this algorithm firstly get the 
amount of information carried (The Shannon Entropy). Then, it calculated the rating weights to filter 
into traditional similarity calculation. The experimental results show that the algorithm can 
effectively alleviate the above problem and improve the performance of the algorithm. 
Introduction 
With the development of Internet technology, the problem of information overload is becoming more 
and more serious. It is very difficult for people to get the information they need from the ocean of 
knowledge
[1]
. In this context, the recommendation system arises at the historic moment. According to 
the different methods used in recommendation, recommendation system can be divided into 
content-based recommendation system, collaborative filtering recommendation system and hybrid 
recommendation system. Collaborative filtering algorithm first finds a set of users with similar interests 
and goals of the user as the neighbor users, then according to the neighbor users on the item's rating to 
predict the target user rating and recommendation. Collaborative filtering algorithm is widely used in 
recommendation system because it is not limited by the content of the recommended item
[2]
. 
Despite the great success of collaborative filtering technology in the field of recommender systems, 
there are still serious problems such as data sparsity
[3]
, which affect the performance of 
recommendation system. In order to improve the accuracy of recommendation, scholars have put 
forward some solutions. Huang Chuangguang
[4]
 proposed a method to adaptively select the 
recommended target user group and on the basis of selected subgroups of uncertain neighbor trust as 
method, finally get the neighbor. Kaleli
[5]
 uses the information of the user to get the information 
entropy of the user and the item rating, so as to adjust the choice of the nearest neighbor. The nearest 
neighbor selection is more reasonable by clustering method, in the study of Wang
[6]
. Some scholars 
study from the perspective of similarity calculation. Jang
 [7]
 and Xu
[8]
 used the matrix filling to 
alleviate the sparsity, but the rating filled the subjectivity is too strong. Guo
[9]
 adopt the method of 
matrix decomposition, the decomposition process will lose useful information. Luo
[10] 
is introduced 
to improve the number of common rating similarity calculation accuracy. 
On the basis of previous studies, based on the rating of the individualized trend of value 
distribution, this paper analyzes the following problem: the interference of the popular item ratings to 
the similarity calculation, that is, the distribution probability is greater than the rating of the threshold 
Q rating. The popular ratings represent the public preference of the item. When the user's rating of the 
item is a popular rating, that is, the user's preference for this item belongs to the public preference, the 
significance of this evaluation rating is small, cannot effectively reflect the user's personal preferences. 
On the contrary, it can clearly reflect the user's individual preferences. The traditional similarity 
calculation does not consider the interference of the popular item rating. When the data is sparse, the 
interference is very obvious. 
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In order to solve the above problem, this paper designs a recommendation model based on the 
traditional recommendation model. In the model, the amount of the information of the rating in the 
item is estimated and the weight of the rating is distinguished, so as to reduce the interference to the 
similarity calculation. Based on this model, this paper proposes a collaborative filtering algorithm 
(RDRM-CF), which is based on the distribution model of the rating value distribution. The algorithm 
can effectively filter the interference of the popular item ratings and improve the accuracy of the 
algorithm. 
Related Concepts and Model Design 
Related Concepts and Definitions 
Aiming at the problems existing in the traditional algorithm, this paper defines the concept of "item 
rating heat value". 
（Definitions 1）Item rating heat： Item i in the rating value j (j=1, 2, 3, 4, 5) the frequency of use, 
set to j
id . 
（Definitions 2）Item rating using probability： The heat value of the rating j in the item i 
accounts for the proportion of the sum of all the ratings, set to jip , and 
5
1
1ji
j
p

 . The greater the 
probability of the use of the rating, the greater the interference in the calculation of similarity 
（Definitions 3）Item rating probability vector： In the item, the probability of 5 scoring values 
(1, 2, 3, 5,), which is denoted as 
ip , 
1 2 3 4 5( , , , , )i i i i i ip p p p p p , is a vector, which reflects the personalized 
distribution trend of the rating value. 
（Definitions 4）Item rating information content： The amount of information carried by the 
rating value j in the item i (i.e., Shannon entropy) is set to j
iH . The amount of information is a 
measure of the amount of information in the field of statistics, if the probability of occurrence of the 
event, the less the amount of information, that is, the amount of information is inversely proportional 
to the probability of occurrence. Assuming that the probability of occurrence of an event is p, the 
amount of information for this event is shown in equation (1): 
( ) log( )H X p  (1) 
（Definitions 5） Item rating weight： The weight of the rating j in the item i, which represents 
the degree of credibility of the rating value, is set to jitr .
j
itr and 
j
iH are proportional to the larger the 
j
iH , the greater the 
j
itr . 
（Definitions 6） Item rating weight vector: The weights of the 5 ratings in the item (1, 2, 3, 5) 
were recorded in 
iTr , 
1 2 3 4 5( , , , , )i i i i i iTr tr tr tr tr tr . 
Model Design 
The traditional algorithm does not take into account the interference of the item rating heat value in 
the calculation of similarity, which can not guarantee the reliability of the results of similarity 
calculation. In order to solve the above problem, this paper designs a recommendation model of rating 
value distribution, as shown in figure 1. In the statistics module statistics, the weight of the rating will 
be get. In similarity module the rating weight is embedded into the formula of similarity calculation, 
in order to avoid the interference of the popular item rating. 
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user-item rating 
matrix
Statistical Module
Ratings
Probability of each 
rating in the Item
The Shannon 
entropy of each 
rating in the Item
The weight of 
each rating in the 
Item
The weight vector 
of each Item
Ratings
Similarity
Similarity 
Module
Recom
m
endation M
odule
 
Figure 1. Rating value distribution recommendation model. 
Algorithm Design 
The Statistics of Each Rating Value in the Item 
If there are m users and n items in the system, the rating information can be expressed by the rating 
matrix X. X which represents the user u on the item I rating, with the 1~5 5 grades to express the user'spreference for the item, the user - item rating matrix as shown in formula (2): 
1,1 1,
,1 ,
n
m m n
r r
R
r r
 
 
  
 
 
 (2) 
In the item, the distribution of the rating value presents a personalized trend, that is, the different 
values of the items in the item are different. The introduction of parameter 
 ,u i
t , [1, ]u m  , if ,u ir j ，
{1,,2,3,4,5}j , then , 1u it  , else , 0u it  . The value of the i value of the item j 
j
id as shown in formula 
(3). 
,
1
m
j
i u i
u
d t

 (3) 
Probability Statistics of Each Rating in the Item 
According to the value of the value of the calculation of the probability of heat, the item i rating value 
of the probability of jip , as shown in the formula (4) : 
1 2 3 4 5
j
j i
i
i i i i i
d
p
d d d d d

   
 (4) 
Because the problem of data sparseness can affect the accuracy of the probability calculation of the 
rating value, this paper introduces the adjustment parameter t, t is a certain non negative number, the 
improved formula (4) as shown in formula (5): 
1 2 3 4 5( ) 5
j
j i
i
i i i i i
d t
p
d d d d d t


    
 (5) 
The Amount of Information in Each Item in the Item 
According to the formula (1), it is known that the amount of information of each rating is shown in 
formula (6): 
2log
j j
i iH p  
 
(6) 
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Weight Calculation of Each Rating in the Item 
The core idea of this section is to divide the corresponding weights according to the size of the value 
of the information, in order to filter the interference. The greater the probability of a rating value, the 
smaller the amount of information, the smaller the meaning, so the smaller the value of the rating. The 
formula of the rating value j
itr and its probability 
j
itr is shown in (7): 
1 1 2 1= log , 0
j j j
i i itr k H k p k  
 
 (7) 
At the same time, due to the presence of
1 2 3 4 5( ) 5
j
j i
i
i i i i i
d t
p
d d d d d t


    
. Because of parameter t, 
j
ip is generally in the 0.2 floating up and down. In order to make the weight formula with a uniform 
standard, so that =0.2jip , its weight is 1, the weight formula into formula (8) shown: 
2
2
log
log 5
j
j i
i
p
tr  
 
 (8) 
The weight vector of each rating information in the item i is shown in formula (9): 
1 2 3 4 5( , , , , )i i i i i iTr tr tr tr tr tr (9) 
Similarity Calculation 
The traditional similarity calculation algorithm commonly used methods are the following three types: 
cosine similarity, modified cosine similarity and Pearson correlation coefficient. The similarity 
calculation method is improved based on the correlation coefficient of Pearson. The user u and user V 
use the Pearson correlation coefficient to calculate the similarity as shown in formula (10): 
,
, ,
, ,
2 2
, ,
( )( )
( , )
( ) ( )
i u v
i u v i u v
u i u v i v
I I
u i u v i v
I I I I
r r r r
sim u v
r r r r

 
 

 

 
 (10) 
,u ir , ,v ir , respectively, that the user u, V on the item I rating value. ur , vr , respectively, that the user u, 
the average rating of v. 
uI , vI , respectively, indicating that the user u, v has rating the item. ,u vI said 
the user u, v joint scoring items. The similarity calculation using Pearson correlation coefficient, the 
weight of each default item rating the same, but did not take into account the "interference rating 
value" in the similarity calculation process, the calculation result is not accurate enough. In this paper, 
the item rating value information is used to measure the weight of the different scoring values in the 
item, and the weight of the item rating weight vector iTr . is divided into different weights in the item I 
by iTr . The improved similarity calculation method is shown in formula (11): 
, ,
,
, ,
, ,
, ,
2 2
, ,
( )( )
( , )
( ( )) ( ( ))
u i v i
i u v
u i v i
i u v i u v
r r
u i u v i v i i
I I
r r
i u i u i v i v
I I I I
r r r r tr tr
tsim u v
tr r r tr r r

 
   

   

 
 (11) 
,u ir
itr is the weight of the rating value for the user u in the item i. ,u ir is the weight of the user's v 
rating ,v ir . Use the value of the amount of information to adjust the weights of the different items in 
the item, so that the similarity of the results of higher credibility. 
 
378
Experimental Results and Analysis 
Data Sets and Comparison Algorithms 
Movielens_100K was used in the experiment. Movielens_100K stores 943 users for the 1682 films of 
the 100000 scoring. In the experiment, 20% of the data sets were randomly selected as the test set and 
the other as the training set, and then the performance of the following three algorithms was compared 
with that of the 80% algorithms. 
(1) The traditional collaborative filtering recommendation algorithm (Per-CF) based on the 
similarity of Pearson correlation coefficient; 
(2) Collaborative filtering recommendation algorithm (LFRM-CF) based on low pass filtering 
recommendation model proposed by [11]; 
(3) A collaborative filtering recommendation algorithm (RDRM-CF) proposed in this paper based 
on the rating value distribution recommendation model. 
Evaluation Criterion 
In this paper, the average absolute deviation (MAE) is used as the evaluation standard to evaluate 
the accuracy of the proposed algorithm: 
, ,
1
N
u i u i
i
p q
MAE
N




 (12) 
,u ip , which represents the user's u forecast rating on the item i, ,u iq said the user u the true rating of 
the item i, N said the user u has been the number of items. 
Experiment and Result Analysis 
Experiment 1 Selection of threshold λ and parameter t 
In order to select the appropriate parameter t, MAE is the best. The experiment makes the nearest 
neighbor number N=30, take t=5, 10, 15, 20, 25, 35, 40,50 and observe the value of MAE, the 
experimental results in Movielens_100K data set are shown in Figure 4: 
 
Figure 4. Relationship between t and MAE. 
As can be seen from Figure 4: focus on the Movielens_100K data, for different number of nearest 
neighbors, when t=35, the best RDRM-CF algorithm, several experiments are the best when t=34, so 
the follow-up experiment t=34. 
Experiment 2 The influence of nearest neighbor number on algorithm accuracy 
Change the value of the number of neighbors K, Movielens_100K data sets to compare the 
accuracy of the three algorithms, the experimental results shown in Figure 5. 
 
379
 
 
Figure 5. The relationship between the k and MAE. 
As can be seen from Figure 5: 
(1) The accuracy of the three algorithms increases gradually with the increase of k, and the accuracy 
of the algorithm tends to be stable around k=40. 
(2)The accuracy of RDRM-CF algorithm is higher than the other two algorithms. 
Analysis of experimental results: 
(1) When the number of neighbors increases, the useful information increases, and the accuracy of 
the algorithm is improved. When the number of neighbors is higher than 40, the accuracy of the 
algorithm tends to be stable. Therefore, the k=40. 
(2) Movielens_100K belongs to the high sparse data set, and the interference of the item heat rating 
is very obvious, which leads to the decrease of the accuracy of the similarity calculation. The 
RDRM-CF algorithm through the statistics item rating information value to reasonably classify the 
weight rating and filter the interference of the popular item ratings to the similarity calculation, so 
RDRM-CF algorithm accuracy ratio the other two methods. 
Experiment 3 The influence of sparsity on algorithm accuracy 
In order to further analyze the data set of sparsity effects on RDRM-CF algorithm, the random user 
rating to reduce set different sparsity, focuses on the comparison of three algorithms in 
Movielens_100K data accuracy, the experimental results are shown in figure 6. 
 
Figure 6. The relationship between sparsity and MAE sparsity. 
As can be seen from figure 6: 
With the increase of sparsity, the accuracy of the three algorithms is gradually decreased, but the 
accuracy of the algorithm RDRM-CF is also decreased, but it has been higher than the other two 
algorithms. 
Analysis of experimental results: 
With the increase of the sparsity, the rating information is reduced and the rating of the items is 
decreased rapidly, and the reliability of the result is reduced. At the same time, with the increases of 
sparsity, the interference of the popular item ratings to similarity calculation will be more obvious, 
and the RDRM-CF algorithm can reasonably divide the different weight of ratings, so the 
performance of RDRM-CF has been better than the other two algorithms. 
Conclusion 
Traditional algorithm does not take into account the interference of the popular item rating to the 
similarity calculation, which leads to the low accuracy of recommendation. In order to solve the 
problem, this paper designs a recommendation model of rating distribution. The model can 
reasonably distinguish rating weights of each item value. Based on this model, the RDRM-CF 
380
algorithm is proposed. The experimental results show that the RDRM -CF algorithm improves the 
performance compared with the traditional algorithm. 
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