Combining Swarm with Gradient Search for Maximum Margin Matrix Factorization
Maximum Margin Matrix Factorization is one of the very popular techniques of collaborative filtering. The discrete valued rating matrix with a small portion of known ratings is factorized into two latent factors and the unknown ratings are estimated by th
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School of Computer and Information Sciences, University of Hyderabad, Hyderabad, India [email protected], [email protected], [email protected], [email protected] 2 Central University of Rajasthan, Ajmer, India
Abstract. Maximum Margin Matrix Factorization is one of the very popular techniques of collaborative filtering. The discrete valued rating matrix with a small portion of known ratings is factorized into two latent factors and the unknown ratings are estimated by the resulting product of the factors. The factorization is achieved by optimizing a loss function and the optimization is carried out by gradient descent or its variants. It is observed that any of these algorithms yields near-global optimizing point irrespective of the initial seed point. In this paper, we propose to combine swarm-like search with gradient descent search. Our algorithm starts from multiple initial points and uses gradient information and swarm-search as the search progresses. We show that by this process we get an efficient search scheme to get near optimal point for maximum margin matrix factorization.
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Introduction
Recommender Systems (RS) are tools and techniques for providing suggestions for items to be used by a user. Recommender systems analyse patterns of users’ interest in various products and provide a personalized recommendation to suit the users taste. A good personalized recommendation can provide a new dimension in e-commerce particularly for entertainment products like movies, music, TV shows, and books. Broadly speaking, the techniques of the recommender system are classified into Content Based filtering and Collaborative filtering [9]. Latent factor model is one of the important approaches in Collaborative filtering and it tries to explain the rating of an item by a user in terms of latent factors of users and of items. Separating out the user factors and item factors from the set of ratings is accomplished through matrix factorization (MF), which is a one of the most successful realizations of Collaborative filtering. A user-item rating matrix is factorized into user-latent factor and item-latent factor matrix. The product of these two factor matrices is made to be consistent with the observed ratings and unobserved ratings are estimated. This is achieved computationally by minimizing a loss function [9]. c Springer International Publishing Switzerland 2016 R. Booth and M.-L. Zhang (Eds.): PRICAI 2016, LNAI 9810, pp. 167–179, 2016. DOI: 10.1007/978-3-319-42911-3 14
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K.H. Salman et al.
Matrix factorization method has recently become very popular for recommender system and among different matrix factorization techniques, Maximum Margin Matrix Factorization (MMMF) [19] is reported to be the most suitable for factorizing a rating matrix. Algorithmically, given few entries of the rating matrix, it is to determine two latent factor matrices U and V such that the product U V T is optimal with respect to some criterion function for the set of observed ratings. The set of observed ratings is very small
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