Robust rank-one matrix completion with rank estimation

Matrix completion aims at estimating the missing entries of a low-rank and incomplete data matrix. It frequently arises in many applications such as computer vision, pattern recognition, recommendation system, and data mining. Most of the existing methods face two problems. Firstly, the data matrix in real world is often disturbed by noise. Noise may change the date structure of the incomplete matrix, thereby degrade the performance of matrix completion algorithms. Secondly, some existing methods need to preset a reasonable rank as input, and the value of rank will affect the performance of the algorithms. Therefore, we proposed a robust rank-one matrix completion method with rank estimation in this pa-per. To mitigate the influence of noise, we divide the incomplete and noisy data matrix into two parts iteratively: low-rank and sparse parts. Besides, we use a weighted rank-one matrix pursuit algorithm to approximate the low-rank part of the data matrix, and the rank of the matrix can be estimated with the adaptive weight vector. The performance of the proposed method is demonstrated by experiments on both synthetic datasets and image datasets. The experimental results demonstrate the performance of the proposed method with incompleted matrices distrubed by sparse noise.(c) 2023 Elsevier Ltd. All rights reserved.

Automated summary

Matrix completion aims to estimate the missing entries of a low-rank and incomplete data matrix. Existing methods face problems with noise disturbance and the need for presetting a reasonable rank value. Therefore, this paper proposes a robust rank-one matrix completion method that divides the incomplete and noisy data matrix into two parts, approximates the low-rank part using a weighted rank-one matrix pursuit algorithm, and estimates the rank of the matrix using an adaptive weight vector. Experimental results demonstrate the performance of the proposed method for incomplete matrices disturbed by sparse noise.