Binary Matrix Completion Using Unobserved Entries

03/13/2018
by   Masayoshi Hayashi, et al.
0

A matrix completion problem, which aims to recover a complete matrix from its partial observations, is one of the important problems in the machine learning field and has been studied actively. However, there is a discrepancy between the mainstream problem setting, which assumes continuous-valued observations, and some practical applications such as recommendation systems and SNS link predictions where observations take discrete or even binary values. To cope with this problem, Davenport et al. (2014) proposed a binary matrix completion (BMC) problem, where observations are quantized into binary values. Hsieh et al. (2015) proposed a PU (Positive and Unlabeled) matrix completion problem, which is an extension of the BMC problem. This problem targets the setting where we cannot observe negative values, such as SNS link predictions. In the construction of their method for this setting, they introduced a methodology of the classification problem, regarding each matrix entry as a sample. Their risk, which defines losses over unobserved entries as well, indicates the possibility of the use of unobserved entries. In this paper, motivated by a semi-supervised classification method recently proposed by Sakai et al. (2017), we develop a method for the BMC problem which can use all of positive, negative, and unobserved entries, by combining the risks of Davenport et al. (2014) and Hsieh et al. (2015). To the best of our knowledge, this is the first BMC method which exploits all kinds of matrix entries. We experimentally show that an appropriate mixture of risks improves the performance.

READ FULL TEXT

page 25

page 27

research
11/22/2014

PU Learning for Matrix Completion

In this paper, we consider the matrix completion problem when the observ...
research
07/24/2018

Collective Matrix Completion

Matrix completion aims to reconstruct a data matrix based on observation...
research
01/24/2018

Matrix Completion with Nonconvex Regularization: Spectral Operators and Scalable Algorithms

In this paper, we study the popularly dubbed matrix completion problem, ...
research
07/02/2015

Categorical Matrix Completion

We consider the problem of completing a matrix with categorical-valued e...
research
01/10/2014

Online Matrix Completion Through Nuclear Norm Regularisation

It is the main goal of this paper to propose a novel method to perform m...
research
10/23/2017

Sequential Matrix Completion

We propose a novel algorithm for sequential matrix completion in a recom...
research
06/07/2023

Exploiting Observation Bias to Improve Matrix Completion

We consider a variant of matrix completion where entries are revealed in...

Please sign up or login with your details

Forgot password? Click here to reset