A Novel Clustering Algorithm Based upon Learning Automata for Collaborative Filtering

Subject Areas : International Journal of Smart Electrical Engineering

Sara Taghipour ¹ , Javad Akbari Torkestani ^{2 *} , Sara Nazari ³

1 - Department of Computer Engineering, Qom Branch, Islamic Azad University, Qom, Iran.
2 - Department of Computer Engineering, Arak Branch, Islamic Azad University, Arak, Iran.
3 - Department of Computer Engineering, Arak Branch, Islamic Azad University, Arak, Iran.

Received: 2021-09-07 Accepted : 2021-10-29 Published : 2021-11-01

Keywords: Learning Automata, collaborative filtering, Clustering, Recommender Systems,

Abstract :

Collaborative Filtering (CF) is one of the principal techniques applied in Recommender Systems, which uses ratings from similar users to predict interest items to a particular user. The scalability issue is a widespread problem of CF. The clustering technique is a successful approach to address the scalability issue in CF. However, some classic clustering methods cannot find appropriate clusters, which leads to low prediction accuracy. This paper suggests a new clustering algorithm based on the Learning Automata (LA) framework to group users for the CF technique. In this algorithm, a learning automaton is assigned to each user to detect the cluster membership of that user. Learning automatons improve their selection based on the reinforcement signal is received from intra-cluster distances and inter-cluster distances in previous iterations.Experimental results on standard and real datasets show that the proposed algorithm outperforms other compared methods in various evaluation metrics. This approach enhances the prediction accuracy and effectively deals with the scalability problem.

Full-Text:



3                                International Journal of Smart Electrical Engineering, Vol.10, No.1, Winter 2021                      ISSN: 2251-9246        

EISSN: 2345-6221

 

pp. 1:6

 

A Novel Clustering Algorithm Based upon Learning Automata for Collaborative Filtering 

Sara Taghipour 1 , Javad Akbari Torkestni 2, Sara Nazari 3

1Department of Computer Engineering, Qom Branch, Islamic Azad University, Qom, Iran, [e-mail]

2Department of Computer Engineering, Arak Branch, Islamic Azad University, Arak, Iran, [e-mail]

3Department of Computer Engineering, Arak Branch, Islamic Azad University, Arak, Iran, [e-mail]

 

 

Abstract

Collaborative Filtering (CF) is one of the main approaches in Recommender Systems, which utilizes ratings from similar users to predict favorite items to a specific user. The scalability issue is a widespread problem of CF. The clustering technique is a successful approach to address the scalability issue in CF. However, some classic clustering methods cannot find appropriate clusters that result in low prediction accuracy. This paper suggests a new clustering algorithm based on the Learning Automata (LA) framework to group users for the CF technique. In this algorithm, each user is equipped with a learning automaton; the mission of each automaton is to find the proper cluster for the user. Learning automatons scatter the users randomly into clusters then, they gradually improve their selection by the feedback received from the intra-cluster distances and inter-cluster distances. Experiments on standard and popular datasets prove that the proposed algorithm achieves better results compared to other methods in different evaluation metrics. This approach enhances the accuracy of prediction and effectively deals with the scalability issue.

Keywords: Recommender Systems, Collaborative Filtering, Clustering, Learning Automata

Article history: Received 20-Apr-2021; Revised 01-May-2021; Accepted 15-May-2021.

© 2021 IAUCTB-IJSEE Science. All rights reserved

 

1.       Introduction

 

The Recommender Systems (RS) uses the overloading information to attract customers. RS generates meaningful recommendations to users for items that are attractive to them [4]. Amazon.com Recommender System[1], Facebook Friend Recommendations, Netflix Recommendation [2], Google News Personalization System[3] are examples of RS in the real world. 

Generally, the RS is categorized into three principal methods: Collaborative Filtering [5], Content-based Filtering [6], and Hybrid method [7]. Collaborative Filtering makes predictions to a specific user based on the ratings of their similar neighbors. Content-based Filtering methods utilize the properties of users and items in addition to explicit ratings. These two methods are often combined in Hybrid methods [8, 9].

Collaborative Filtering (CF) is successful recommendation method in practice [10, 11]. In CF, for a specific user, the missing rating on an item is estimated by ratings that were previously given by similar users. The scalability issue is one of the challenges in the CF that has negatively affected the prediction accuracy of CF [4, 5, 12, 13].

The clustering techniques are used to cope with the scalability and sparsity issues in the CF method. Generally, a cluster-based CF includes three steps. First, user clusters have been constructed by a clustering algorithm. Second, similar users are identified by the similarity measure in each cluster. Finally, the ratings of neighbors are applied to estimate the missing ratings. Clustering users can effectively partition the rating database thus, alleviate the scalability and sparsity issues; To identify similar users for a specific user, smaller clusters instead of the entire database are investigated [5, 11, 12, 14, 15].

Recent works [16-18] show that by applying more advanced clustering methods to alleviate the scalability issue, the prediction accuracy of recommendations can be preserved even outperform the other CF approaches. Koohi tries to alleviate the sparsity issue by clustering users with a fuzzy method and applying it in user-based CF. It shows that fuzzy clustering works well in comparison with KMeans clustering [1]. A novel evolutionary clustering algorithm has been presented by Chen to catch the similar interest between users in CF [16]. In [19], improving the scalability of CF has been achieved by using genetic algorithms to cluster users. K-means clustering algorithms in CF have been investigated by Zahra. The work investigates different centroid selection strategies in the k-means clustering method for CF [20].

Learning Automata (LA) is a reinforcement learning approach that learns by rewarding desired actions and punishing undesired actions. On the other hand, it learns based on feedback received from the system feedback [21]. However, LA has been applied in recommender systems [22, 23], social networks [24, 25], retrieval information [26]; it has not been proposed for clustering in CF methods.

In this study, we have presented a novel clustering algorithm that employed the learning automata method to group users in CF; it has called LAC. The proposed method intends to enhance the quality of clusters by learning automata and thereby increase the accuracy of the prediction. Here, each user is equipped with a learning automaton; the mission of each automaton is to find the proper cluster for the assigned user. The process of the proposed clustering algorithm has been accomplished by the repetition of the following steps. First, each of the learning automatons randomly chooses a cluster based on their action probability vector; a cluster configuration has appeared. Next, to check the current cluster configuration, the reinforcement signal has been determined by the Silhouette value (intra-cluster distances and inter-cluster distances) for each user. Finally, the automaton rewards or punishes the latest action based on the reinforcement signal. In the presented algorithm, the reinforcement signal is calculated based on the Silhouette value that is a measure of how similar a user is to the assigned cluster (cohesion) compared to other clusters (separation).

   The efficiency of our method is assessed through simulation experiments on two real datasets, MovieLens 100K (denoted as Movie 100K) and MovieLens 1M (denotes as Movie 1M). Our method is compared with frequently used CF methods: user-based CF, KMeans CF, and FCM CF (Fuzzy C-means CF). The obtained results show that it is higher than others in accuracy metrics.

The rest of this paper is structured as follows. In section 2, we present the basic concepts of CF, the introduction of learning automata, and related work. In Section 3, our clustering algorithm (LAC) is described in detail. Collaborative Filtering based on the LAC algorithm (LAC-CF) is explained in Section 4. The experimental evaluation results are disclosed in Section 5. Section 6 is the conclusion.

2.        Literature Review

In this part, a concise presentation to the CF is provided. Next, since the proposed technique is based upon Learning Automata to form clusters of users, we will introduce a brief theory of this technique. Finally, related work will be explained.

A.       Collaborative Filtering Recommender Systems:

Collaborative Filtering (CF) is the successful method in RS. for making recommendations; the CF method has been employed in successful online businesses such as Netflix, Amazon, and Lastfm to recommend services and items to their customers [10, 18]. Ratings of n users on m items that are collected in a rating matrix are input data for CF; the rating matrix is sparse because of numerous missing ratings. The CF method could be categorized into model-based methods and memory-based. The principle of model-based CF is to produce a model from the database; it uses the learned model to predict missing ratings. The main property of the memory-based CF is that the rating matrix is explicitly applied to predict missing ratings. Two categories of memory-based CF are user-based CF and item-based CF. The basis of user-based CF is that a user likes those items that its similar users like. For finding similar users, the similarity value between users in the database is calculated by similarity measures then the most similar N users to user u are selected as neighbors of user u. Finally, predicting missing rating for user u is concluded of average ratings of neighbors. Three popular similarity measures for CF are Cosine-based, Adjusted cosine-based, and Pearson correlation-based [2-5] that described below. In Table 1, the symbols used in the following formula are reported. The formula for Cosine-based similarity is as equation (1):

 

 

 

 

Symbol and meaning

)1(

 

The formula for Adjusted-cosine similarity is as equation (2):

Meaning	Symbol
Set of items rated by user u
Set of items rated by user v
User u’s rating for item i
User v’s rating for item i
The average rating by user u
The average rating by user v
The average rating for item i
User u’s predicted rating on item i
Neighbors of user u

The formula for Pearson correlation similarity is as equation (3):

(2)

After detecting the neighbors of user u, we can take into account the ratings of neighbors on item i to estimate the probable rating of user u on new item i; by equation (4). 

(3)

Where  is the estimated rating of user u for item i, and b is a user of the neighbor set.

B.        Learning Automata Theory

 Learning automatons (LAs) are decision-taking elements applied in a random environment [6-8]. Each automaton picks a particular action from its action set. The actions are picked according to a specific probability distribution which is updated based on the environment feedback to the recent actions. This learning process is repeated until the optimal action is found so that the average reward received from the environment is maximized or the average penalty is minimized.

In the present study, we use variable structure learning automata which are defined by a quadruple [α, β, P, T] where

·       is the set of actions of LAs. Index r is the number of actions.

·        is the received signal from the environment called reinforcement signal. in a P-model environment .

·        is the set of action probability vectors. (pi is the probability of action i)

·       T is the learning algorithm, T[p(n), α(n), β(n)], where revises LAs actions probability vector. If T is a linear operator, the learning algorithm is called linear. Otherwise, the learning algorithm is called nonlinear.

The main theory in learning algorithm T is that If the learning automaton chooses action αi in the nth iteration and receives a favorable response from the environment, algorithm T rewards the action and increases its probability, and decreases the probability of other actions by equation (5). It is worth mentioning that always the sum of probability of actions for each automaton is equal to 1.

If the learning automaton chooses action αi in the nth iteration and receives an unfavorable response from the environment, algorithm T decreases the probability of the action and increases the probability of other actions by equation (6).  

(4)

If a=b, the learning algorithm is called linear reward-penalty (LRP), if a >b, the learning algorithm is called linear reward-epsilon-penalty (), and if b=0 the learning algorithm is called linear reward-inaction (LRI).

C.       Related work:

Many studies have been done to deal with the scalability problem by clustering without scarifying the accuracy of prediction in CF. Clustering of users can effectively partition the rating database and thereby improve the scalability in CF and provide comparable prediction accuracy as the basic CF approach [9, 10]. In this context, most of the papers used KMeans as a basic clustering technique in CF. Recent works have been employed advanced clustering techniques to achieve higher accuracy of prediction in CF. Koohi applies fuzzy clustering to the sparse dataset in user-based CF for improving the prediction process of user-based CF. The result has shown that fuzzy clustering works well in comparison with KMeans clustering (Koohi and Kiani 2016) [1]. In the paper[11], a Genetic algorithm has been applied for clustering recommender system dataset to address the scalability issue of the system. An evolutionary clustering algorithm has been investigated by Chen to find out the similar interest between users in CF. In the paper, the users and items are considered as network nodes. The evolutionary clustering algorithm is used for network nodes and clusters of users are formed. Then, user-based collaborative filtering methods are performed in each cluster. improved accuracy shows the effectiveness of clustering in CF[12]. Learning Automata (LA) algorithms have been used in different domains in recommender systems. Rezvanian introduced the learning automata approach for the social network [13, 14]. In the web recommender system, Akbari [15] proposed a method to arrange the web documents in a search engine by using a LA algorithm to train the search engine. Forsati [16] tried to learn the behavior of users by distributed learning automata. It used the learned patterns to recommends pages to the current user. To the best of our knowledge, presenting and applying a learning automata algorithm to cluster users in CF is a new effort in the recommender system.

3.       The Proposed Algorithm(LAC)

In this section, a new clustering method based upon learning automata is introduced to cluster users in recommender systems to put similar users in the same group; it is called LAC.

This method provides the clusters of users as input for user-based CF. The flowchart of the LAC is shown in Fig. 1, and the pseudocode for our algorithm is given in Fig. 2. As shown in Fig. 1, the proposed clustering algorithm contains four main steps: parameter setting, action selection operation, reinforcement signals computation, and probability vectors update operation. Each of these steps is described in Sections A, B, C, and D.

A.       Parameter setting

The parameters required for all steps of the algorithm are defined, including the number of clusters, Learning automaton assignment, action-set formation, actions probability vector, stop criteria. Let Ai be the learning automaton is assigned to user i. The mission of Ai is to detect the cluster membership of user i. the number of learning automatons is equal to the number of users. The action-set of learning automaton Ai has included K distinct actions; each corresponds to one cluster. K indicates the number of clusters. The initial action probability vector that shows the choice probability of every action is set to the same value; it means that each user might be clustered at K possible cluster with the same probability. Stop criteria is the maximum allowed number of iterations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 1.       Flowchart of LAC algorithm

B.       Action selection process:

A learning automaton (Ai) randomly chooses one of K actions based on its probability vector (Pi); selecting one of K actions by Ai means selecting one of the K clusters for user i. The selected action is called RCi. This selection process has been implemented by roulette wheel selection. All learning automatons have performed the selection step in parallel and thus K clusters of users have formed; a random cluster configuration has been generated. To assess the current cluster configuration, the reinforcement signals have to be determined by the next step.

C.       Reinforcement Signal:

Reinforcement signals have been calculated to show how the latest actions of learning automatons were good. Then based on the result, the algorithm punishes or rewards these selected actions. 

To produce a reinforcement signal, we calculate the Silhouette value for each point in the current cluster configuration. Silhouette value (si) is a measure that estimates how user i is similar to the assigned cluster (cohesion) compared to other clusters (separation). The value near 1for si means that the assigned cluster was suitable for user i. On the other hand, the value -1 for si means that the assigned cluster was not suitable for that user [32].

 

 

 

 

Silhouette value for the  user, si, is defined as:

	(5)
	(6)

In equation (7), the parameter ai is the average similarity values from user i to the other users in the same cluster and bi is the minimum average similarity values from user i to users in a different cluster. In our algorithm, to produce a reinforcement signal for user i, the user with the best Silhouette value in each cluster is detected and considered as the Leather of that cluster. Then, the cluster that its Leather has the least Euclidean distance with user i is considered as appropriate cluster (ACi). Finally, for user i, appropriate cluster (ACi) and learning automaton cluster assignment (RCi) are compared and if they were the same, the reinforcement signal is set 0 otherwise 1.

D.       Probability vectors update operation:

The action probability vector of each automaton is updated by the learning algorithm. The action probability vector is updated based on the reinforcement signal that is obtained from the previous step (section C). The learning automaton decrease or increase the chance of selecting current action for later iterations by updating the probability vector. If the corresponding reinforcement signal receives the reward signal (reinforcement signal=0), the automaton will update its probability vector by equation (5); otherwise, it receives a penalty signal (reinforcement signal=1), and the automaton will update its probability vector by equation (6).

4.       The proposed collaborative filtering based on LAC (LAC-CF)

To overcome the scalability issue and produce higher prediction accuracy, we introduce a new collaborative filtering recommender system called the LAC-CF. LAC-CF builds on top of the proposed learning automata clustering (LAC). Once the clusters have been founded by the LAC algorithm, predicting missing ratings will be initiated. The pseudo-code of CF based on LAC is shown in Fig. 3. It contains three main steps: Finding clusters using LAC (Algorithm. 1), calculating the similarity between users in their respective clusters, and predicting missing ratings for unrated items. Remarkably, the calculating similarity of users is performed only within the same cluster (not for all users in the dataset). Therefore, the approach can be more efficient.

 

 

 

(7)

Algorithm1. Pseudocode of clustering based on Learning Automata in RS (LAC)

Input: user-item rating matrix                  n, K //numbers of users, numbers of clusters Output: clusters of users () Assumptions:    Let Ai be the learning automaton corresponding to user i Begin =           //initial LAs Probability vector =0            = 0      =0              WHILE (t < tmax)        //All LAs select an action based on their probability vector For each user, i,     = random cluster based on  End        // Reinforcement signal () is computed for each LA For each user i  = find an appropriate cluster End For each user i  If ==              = 0   else              = 1    End if End for      // Update probability vector under reinforcement signal For each user i        If = 0              Update  by equation (5)       Else if  =1              Update  by equation (6)      End if End for    t = t + 1   END WHILE End Fig. 2.       The pseudocode of the LAC algorithm         Fig. 3.       The pseudocode of the LAC-CF algorithm         5.       Experiment and evaluation In this section, the datasets and the evaluation metrics are described. The results of the proposed algorithm are assessed in some experiments. All experiments are run on a PC with Intel processor Core i7 @ 2.5 GHz and 8 GB RAM using MATLAB software (version 2017) running on the Windows platform. A.       Dataset Two popular recommender systems datasets, MovieLens 100K; denoted as Movie 100K and MovieLens 1M; denoted as Movie 1M (https://grouplens.org/datasets/movielens/) are used to evaluate the proposed algorithm. Movie 100K is a movie rating dataset with 943 users, 1,682 movies, and 100,000 ratings. Movie 1M contains a movie rating dataset with 6,040 users, 3,900 movies, and 1,000,209 ratings. Rating scores are in the range of 1 to 5. For each dataset, 80% of the ratings are used for training sets, and the remaining 20% is used for testing sets. B.       Evaluation metrics The two most popular metrics to evaluate the performance of recommender systems are Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). Note that lower MAE and RMSE values demonstrate more accurate predictions and implying the better performance of RS.      The parameter m points to the number of ratings that are to be predicted,   is the real rate,  is the predicted rate, u points to a user, and i to an item. C.       Experimental results In this section, the accuracy of the proposed LAC-based CF (denoted as LAC-CF) is compared with, three of the existing frequent approaches: User-based CF, user-based CF with KMeans clustering (KMeans-CF), and user-based CF with Fcm clustering (Fcm-CF). The results of the evaluation of algorithms in terms of prediction accuracy metrics, MAE and RMSE, have been compared. The results in Figs 5-8 display that the suggested algorithm achieves lower MAE and RMSE than others. In our experiment, the number of clusters is given 3, 5, 8, 10, and 20 clusters. In simulations, the number of the nearest neighbors is set as 5, 10, 20, 30, 40, 50, and 100. To decide between similarity measures for the simulation phase, we have tested three popular and widely-used similarity measures and then analyzed the quality of the results.     Fig. 4.       comparison of similarity methods: cosine, Pearson correlation, and adjusted cosine   Fig. 4 depicts the results of comparing cosine (CS), Pearson correlation-based (PS), and adjusted cosine (ACS) similarity methods. It demonstrates that the Pearson correlation-based metric has provided a higher accuracy value than two others in all collaborative filtering algorithms used at this job: user-based CF, KMeans-CF, Fcm-CF, and LAC-CF. Thus, the Pearson correlation-based similarity method has been selected as the similarity method to conduct experiments. Fig. 5 compares the MAE and RMSE of the presented LAC-CF method against the compared methods for the different number of neighbors on Movie 100K. The result shows that the proposed method outperforms the other approaches due to the accurate clustering algorithm. Figs. 6 and 8 depict the MAE and RMSE of the LAC-CF against the two cluster-based methods, KMeans CF and Fcm CF. They show the results for the various numbers of clusters on the dataset Movie 100K and Movie 1M, respectively. In Fig.6, it is demonstrated that the different clustering algorithms obtained the lowest MAE and RMSE on the condition that the number of clusters is equal to 8 in Movie 100K. In Fig. 8, when the number of clusters is equal to 10 in Movie 1M, the LAC-CF algorithm gained the best results. In Fig. 7, the number of neighbors on Movies 1M is changed and the result of methods is obtained. The results show that LAC-CF gains better results than other methods.         Fig. 5.        The MAE, RMSE in various nearest neighbors on Movie 100K     Fig. 6.       The MAE, RMSE in the different number of clusters on Movie 100K.       Fig. 7.        The MAE, RMSE in various nearest neighbors on Movie 1M.   Fig. 8.       The MAE, RMSE in the different number of clusters on Movie 1M.     6.       Conclusion and suggestions In this study, we have presented a novel clustering algorithm (LAC) that employed the learning automata method to group users in CF. We present a collaborative filtering recommender system called the LAC-CF approach. Our approach employs the LAC algorithm as a clustering algorithm to generate clusters of users with similar interests. 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