Learning Latent Features with Pairwise Penalties in Low-Rank Matrix Completion

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

1 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)4210-4225
Journal / PublicationIEEE Transactions on Signal Processing
Volume68
Online published8 Jul 2020
Publication statusPublished - 2020
Externally publishedYes

Abstract

Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent variables can be exploited by pairwise learning using the graph regularized matrix factorization (GRMF) method. However, existing GRMF approaches often use the squared loss to measure the pairwise differences, which may be overly influenced by dissimilar pairs and lead to inferior prediction. To fully empower pairwise learning for matrix completion, we propose a general optimization framework that allows a rich class of (non-)convex pairwise penalty functions. A new and efficient algorithm is developed to solve the proposed optimization problem, with a theoretical convergence guarantee under mild assumptions. In an important situation where the latent variables form a small number of subgroups, its statistical guarantee is also fully considered. In particular, we theoretically characterize the performance of the complexity-regularized maximum likelihood estimator, as a special case of our framework, which is shown to have smaller errors when compared to the standard matrix completion framework without pairwise penalties. We conduct extensive experiments on both synthetic and real datasets to demonstrate the superior performance of this general framework.

Research Area(s)

  • matrix factorization, non-convex pairwise penalty, pairwise learning

Citation Format(s)

Learning Latent Features with Pairwise Penalties in Low-Rank Matrix Completion. / Ji, Kaiyi; Tan, Jian; Xu, Jinfeng et al.
In: IEEE Transactions on Signal Processing, Vol. 68, 2020, p. 4210-4225.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review