A Study Of Matrix Completion For Recommendation System

Recent years, with the rapid development of the internet service (especially the mobile internet service) and the proliferation of portable devices, there is a revolution in both the business model of service providers and consuming behav-ior of ordinary people. Prom service providers point of view, they want to find out their consumers quickly and present them what they are interested in. From the consumers perspective, they want to look out what they need among the mass information on the internet. So for both of them, recommendation system is becoming more and more necessary, and matrix completion is among the key techniques of recommendation system. Matrix completion refers to the process of adding entries for unknown or missing values in a incomplete matrix, which is challenging to be applied to large scale recommendation system. For exam-ple, firstly, for developing robust recommendation system, people hope to design convex matrix completion method recommendation system. However, traditional convex matrix completion methods are very both storage and time inefficient, which make them hardly possible to be applied to large scale recommendation system. Secondly, for large scale recommendation system, tuning parameters on large scale data sets is a both time and labor consuming task, however, previous matrix completion methods could not avoid this as their best tuned parameter on small sub samples could not work well on the original large scale data set. Finally, how to make use of rating data for profiling social network users’ interest is still a challenging work. In this paper, we will discuss the above problems in detail, and the contributions of this paper are summarized as follows.Firstly, we propose first order low rank method for solving convex trace bounding constraint matrix completion problem, which overcomes the storage and time inefficient issues of the previous methods. We propose a robust solution for this problem based on trace-ball optimization, which can creatively change the original trace norm constraint into the problem of low-rank matrix factorization. Therefore, by searching in a ball space defined by the new trace constraint, the rank of new matrix can be self-determined such that the local minimum for ma-trix factorization is the global minimum for the original matrix completion task. Meanwhile, we also study the properties of the model parameter which motivates us to research the second problem.Secondly, in this paper, we propose a scale-invariant parametric matrix fac-torization method for addressing the idea that tuning parameters on small sub-matrix and then use them on the original large scale matrix. Specifically, we can use any of the previous matrix factorization methods to estimate the best work-ing factorization variances parameters on small sampled sub-matrix, and then use them for the proposed method to conduct both effective and efficient matrix fac-torization on original large scale matrix. Extensive experiments also show that the proposed method can achieve good performance on the original large scale matrix with the estimate factorization variances on small sampled sub-matrix.Finally, in this paper, we revisit the problem of profiling users’ interests by utilizing the social rating matrix in the context of social network. We discover the phenomenon that although users’ interests are similar to their followees, there are still differences. Based on this observation, we assume that social users’ overall in-terests can be decomposed into individual interests and shared interests. Besides, we also introduce multi-faceted social relationship in unsupervised way. Then we proposed a novel DisSUP model to capture the user’s overall interests and individual interests, ans also the unsupervised multi-faceted social relation ship between social users. Thirdly, we apply the proposed model to three practical applications, namely social rating prediction, controversial item recommendation and 1-hop influential user identification. Finally, experiments on two big real-world data sets extracted from Douban platform show that our proposed model improves the performance for all the three recommendation tasks.