Multi-weight Matrix Completion with Arbitrary Subspace Prior Information

by   Hamideh Sadat Fazael Ardakani, et al.

Matrix completion refers to completing a low-rank matrix from a few observed elements of its entries and has been known as one of the significant and widely-used problems in recent years. The required number of observations for exact completion is directly proportional to rank and the coherency parameter of the matrix. In many applications, there might exist additional information about the low-rank matrix of interest. For example, in collaborative filtering, Netflix and dynamic channel estimation in communications, extra subspace information is available. More precisely in these applications, there are prior subspaces forming multiple angles with the ground-truth subspaces. In this paper, we propose a novel strategy to incorporate this information into the completion task. To this end, we designed a multi-weight nuclear norm minimization where the weights are such chosen to penalize each angle within the matrix subspace independently. We propose a new scheme for optimally choosing the weights. Specifically, we first calculate an upper-bound expression describing the coherency of the interested matrix. Then, we obtain the optimal weights by minimizing this expression. Simulation results certify the advantages of allowing multiple weights in the completion procedure. Explicitly, they indicate that our proposed multi-weight problem needs fewer observations compared to state-of-the-art methods.



There are no comments yet.


page 1

page 2

page 3

page 4


Multi-weight Nuclear Norm Minimization for Low-rank Matrix Recovery in Presence of Subspace Prior Information

Weighted nuclear norm minimization has been recently recognized as a tec...

Nonconvex Matrix Completion with Linearly Parameterized Factors

Techniques of matrix completion aim to impute a large portion of missing...

Optimal Exploitation of Subspace Prior Information in Matrix Sensing

Matrix sensing is the problem of reconstructing a low-rank matrix from a...

Matrix Completion with Prior Subspace Information via Maximizing Correlation

This paper studies the problem of completing a low-rank matrix from a fe...

Categorical Matrix Completion

We consider the problem of completing a matrix with categorical-valued e...

A Greedy Algorithm for Matrix Recovery with Subspace Prior Information

Matrix recovery is the problem of recovering a low-rank matrix from a fe...

Robust Matrix Completion State Estimation in Distribution Systems

Due to the insufficient measurements in the distribution system state es...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.