Matrix completion by deep matrix factorization

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

21 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)34-41
Journal / PublicationNeural Networks
Volume98
Online published3 Nov 2017
Publication statusPublished - Feb 2018

Abstract

Conventional methods of matrix completion are linear methods that are not effective in handling data of nonlinear structures. Recently a few researchers attempted to incorporate nonlinear techniques into matrix completion but there still exists considerable limitations. In this paper, a novel method called deep matrix factorization (DMF) is proposed for nonlinear matrix completion. Different from conventional matrix completion methods that are based on linear latent variable models, DMF is on the basis of a nonlinear latent variable model. DMF is formulated as a deep-structure neural network, in which the inputs are the low-dimensional unknown latent variables and the outputs are the partially observed variables. In DMF, the inputs and the parameters of the multilayer neural network are simultaneously optimized to minimize the reconstruction errors for the observed entries. Then the missing entries can be readily recovered by propagating the latent variables to the output layer. DMF is compared with state-of-the-art methods of linear and nonlinear matrix completion in the tasks of toy matrix completion, image inpainting and collaborative filtering. The experimental results verify that DMF is able to provide higher matrix completion accuracy than existing methods do and DMF is applicable to large matrices.

Research Area(s)

  • Collaborative filtering, Deep learning, Image inpainting, Matrix completion, Matrix factorization