A Fast Matrix-Completion-Based Approach for Recommendation Systems

TL;DR

This paper introduces PCM, a fast matrix completion method tailored for recommendation systems that efficiently handles changing data dimensions and provides personalized recommendations with high accuracy and speed.

Contribution

The paper presents a novel probability completion model (PCM) that reduces computational complexity and adapts to dynamic preference matrices in recommendation systems.

Findings

PCM outperforms SVT in speed and accuracy.

PCM effectively captures data trends with low-rank similarity matrices.

Experimental results demonstrate higher LCS scores and efficiency for PCM.

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.