Adaptive quantile low-rank matrix factorization. (July 2020)

• Record Type: Journal Article
• Authors: Xu, Shuang; Zhang, Chunxia; Zhang, Jiangshe
• Is Part Of: Pattern recognition. Volume 103(2020:Jul.)
• Publication Date: 2020-07
• Subjects: Low-rank matrix factorization -- Mixture of asymmetric Laplace distributions -- Expectation maximization algorithm -- Skew noise; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2020.107310
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: A new low-rank matrix factorization model is raised by modeling noise with a MoAL. The new method AQ-LRMF performs well for various kinds of noise. An EM-based efficient algorithm is provided to estimate the parameters in AQ_LRMF. Our model AQ-LRMF can automatically learn the weight of outliers. AQ-LRMF performs best in capturing local structural information in real images. Abstract: Low-rank matrix factorization (LRMF) has received much popularity owing to its successful applications in both computer vision and data mining. By assuming noise to come from a Gaussian, Laplace or mixture of Gaussian distributions, significant efforts have been made on optimizing the (weighted) L 1 or L 2 -norm loss between an observed matrix and its bilinear factorization. However, the type of noise distribution is generally unknown in real applications and inappropriate assumptions will inevitably deteriorate the behavior of LRMF. On the other hand, real data are often corrupted by skew rather than symmetric noise. To tackle this problem, this paper presents a novel LRMF model called AQ-LRMF by modeling noise with a mixture of asymmetric Laplace distributions. An efficient algorithm based on the expectation-maximization (EM) algorithm is also offered to estimate the parameters involved in AQ-LRMF. The AQ-LRMF model possesses the advantage that it can approximate noise well no matter whether the real noise is symmetric or skew. The core idea of AQ-LRMF lies in solving a weighted L 1 problem with weights being learned from data. The experiments conducted on synthetic and real data sets show that AQ-LRMF outperforms several state-of-the-art techniques. Furthermore, AQ-LRMF also has the superiority over the other algorithms in terms of capturing local structural information contained in real images.