Pair-wise Preference Relation based Probabilistic Matrix Factorization for Collaborative Filtering in Recommender System

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Highlights

  • A novel preference relation based collaborative filtering model is proposed.

  • The proposed model can capture both second and higher order user-item interactions.

  • Side information is integrated using matrix co-factorization framework.

  • The proposed model is evaluated using standard ranking measures like NDCG and MAP.

  • The proposed model is compared with the current state-of-the-art related methods.

Abstract

Matrix Factorization (MF) is one of the most popular techniques used in Collaborative Filtering (CF) based Recommender System (RS). Most of the MF methods tend to remove sparsity or predict missing ratings. However, the prime objective of any RS is to generate recommendation of items, where items having higher preferences should be placed at higher positions in the recommendation list. Further, the integration of user and item features ( i.e. Side Information) in any RS model, increases the quality of recommendation. Keeping these in mind, we propose a Probabilistic MF (PMF) model that takes Preference Relation as input (instead of ratings) for generating efficient ranking of items. The user and item side information are integrated into the model using matrix co-factorization technique. Also, user and item neighborhood information (known as second-order interaction among similar users or items) are integrated into the model. The use of PMF enables the proposed method to capture user-item interaction of higher-order. Hence, the proposed RS model can capture all the desired user-item interaction information. Experimental results obtained using two ‘MovieLens’ datasets indicate the superiority in recommendation quality of the proposed model over the recent state-of-the-art MF methods.

Introduction

It has always been a difficult task to choose items or things of our preferences from internet due to information overload. Recommender System(RS) [1], [2], [3], [4] lists out a subset of items that might be useful to us, and thus saves much time. Initially, the use of RS was limited to contents like movies, songs and TV shows, etc. related databases. However, their usages were expanded to other fields like social recommendation [5], [6], book recommendation [7], e-learning recommendation [8] and much more. These days, almost all the websites, especially e-commerce sites, are using some kind of RSs to help users in finding their preferred items. Based on the usage types, RSs are categorized as: Personal RS (for individuals) [2], [9] and Group RS (for a group of users) [10], [11], [12]. The growing popularity of RS makes it a popular research topic these days.

Most of the RSs use one of the two filtering techniques, namely Collaborative Filtering(CF) and Content-Based Filtering(CB). CB model [13], [14] uses item features to build a model using the past experiences of users. Based on the built model, it analyzes the features of new items when they arrive, and then list out recommendations. CB model requires sufficient item features as well as a substantial amount of user-item interactions. However, most of the dataset we use for building RS, are very sparse and it is very difficult to build a user profile for each user. In that case, CF [15], [16], [17] is an effective alternative, which exploits user-item interaction (mostly ratings) and generate prediction of items for a user based on the similarity of preference to other users available in the dataset. Hence, CF is the most commonly used filtering approach in the field of RS. Again, CF is of two types: Memory-Based and Model-Based. Memory-Based CF techniques [18] use neighborhood information, i.e., similarity information among users and/or items, for generating recommendation. Where as, Model-Based CF techniques used to find out user item latent factors (e.g. Matrix Factorization), based on the available users’ preferences, which are later used to predict preference(ratings) of unseen items for any user. According to Liu et al. [19], as memory-based models confined to find neighborhood information among users or items, they can capture only local information. This local information is termed as Local Structure (LS) which refers to second-order interaction among similar users or items. But, model-based CF techniques captures global information by applying latent factor based approach to predict missing ratings. This global information is termed as Global Structure (GS), which refers to the higher-order interaction among all users and items. The RS model that can integrate both LS and GS, produces efficient recommendations [20], [21].

Matrix Factorization (MF) [22] is one of the most explored model-based CF technique for RSs. Use of MF towards RS, gained attention after the NetFlix prize competition,1 because the method proposed by the winning team, was mostly related to MF [23], [24], [25]. Since then, MF-based CF models for RSs improved significantly [26], [27], [28]. MF based RS models can handle sparse data, which is highly desirable for any RS. Probabilistic MF (PMF), initially proposed by Mnih and Salakhutdinov [29], proved to be performing better than the traditional MF procedure, and was used widely later on [30], [31], [32]. However, as discussed earlier, most of these PMF based models capture only GS while LS is ignored. Also, item ordering is not considered in most of the MF-based RS models, as they try to predict missing ratings only. According to recent studies [19], [33], use of Preference Relation (PR) instead of ratings provides better ordering of items in the recommended list. Brun et al. [33] proposed the first PR based approach towards RS, which is based on memory-based CF. Later on, use of PR is extended towards RS using MF and others [19], [34], [35], and more. Hence, in this study we proposed a PR based PMF framework for RSs, that takes PRs of users as input and generates recommendations. The neighborhood information of users and items are also integrated into the model. Further user and item features (known as Side Information) are co-factorized in the PMF framework, to gather users’ preferences towards items. The main contributions of this paper is summarized as:

  • A novel Preference Relation based PMF method is proposed for CF in RS.

  • The proposed model is able to capture both LS and GS of user-item interaction.

  • User and item features(i.e., side information) are integrated using matrix co-factorization framework.

  • The method produces ranking of items, i.e. items having higher preference is placed higher in the list.

The organization of the rest part of this paper is done as follows. Section 2 will discuss a comprehensive survey of the state-of-the-art techniques of PMF based CF and PR based CF, as well as the motivation behind the current work. Following this, Section 3 will discuss the proposed method in detail. Section 4 contains the detailed experimental evaluation of the proposed model, along with comparison among other related models. Finally, Section 5 aggregates the findings of the current research with a future scope.

Section snippets

Related works and motivation

Using probabilistic factor based models [36], [37], the computational complexity of the model reduces significantly. However the major drawbacks of these models is the intractability of exact inference and potentially inaccurate approximation. This section starts with the description regarding MF and their usage towards RS. The probabilistic version of MF and its efficiency towards RS is also described in details. Finally, the motivation behind the current work is presented.

Methodology

This section starts with the problem definition of the proposed research. Next, the factorization method for the proposed model is formulated, which uses both PR and user-item latent feature vectors. This paper uses the PMF framework for CF, but the model uses PRs which also integrates user-item correlation and side information. The recommendation procedure is written step wise with the help of an algorithm.

Experimental results and discussion

This section introduces the datasets used for the experimental work done using the proposed model. This is followed by the discussion of different evaluation measures, which are used to compare the proposed model with the standard MF based models.

Conclusion

The main intention of this work is to improve the ranking quality of the RS. To achieve this end we induced PRs of users into PMF framework. With the use of PR, the higher preferred items are placed at the top of the recommendation list, which is desirable. In addition we also preserve the key aspects of users’ preference by integrating user & item neighborhood information as well as user-item side information. Hence, the proposed model handles all the required user-item interactions. The

CRediT authorship contribution statement

Abinash Pujahari: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing - original draft. Dilip Singh Sisodia: Resources, Software, Supervision, Validation, Visualization, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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