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arXiv · 1912.00600

A Fast Matrix-Completion-Based Approach for Recommendation Systems

Meng Qiao·Zheng Shan·Fudong Liu·Wenjie Sun
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Abstract

Matrix completion is widely used in machine learning, engineering control, image processing, and recommendation systems. Currently, a popular algorithm for matrix completion is Singular Value Threshold (SVT). In this algorithm, the singular value threshold should be set first. However, in a recommendation system, the dimension of the preference matrix keeps changing. Therefore, it is difficult to directly apply SVT. In addition, what the users of a recommendation system need is a sequence of personalized recommended results rather than the estimation of their scores. According to the above ideas, this paper proposes a novel approach named probability completion model~(PCM). By reducing the data dimension, the transitivity of the similar matrix, and singular value decomposition, this approach quickly obtains a completion matrix with the same probability distribution as the original matrix. The approach greatly reduces the computation time based on the accuracy of the sacrifice part, and can quickly obtain a low-rank similarity matrix with data trend approximation properties. The experimental results show that PCM can quickly generate a complementary matrix with similar data trends as the original matrix. The LCS score and efficiency of PCM are both higher than SVT.

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Meng Qiao, Zheng Shan, Fudong Liu, Wenjie Sun. 2019-12-02. A Fast Matrix-Completion-Based Approach for Recommendation Systems. https://arxiv.org/abs/1912.00600

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