New penalized criteria for smooth non-negative tensor factorization with missing entries

TL;DR

This paper explores how smoothness penalties can improve non-negative tensor factorization in the presence of missing data, proposing new criteria and algorithms validated through experiments.

Contribution

It introduces novel penalized criteria with efficient algorithms to handle missing entries in non-negative tensor factorization.

Findings

Smoothness penalties help ensure the existence of an optimum with missing data.

New criteria improve the robustness of tensor factorization.

Numerical experiments validate the effectiveness of the proposed methods.

Abstract

Tensor factorization models are widely used in many applied fields such as chemometrics, psychometrics, computer vision or communication networks. Real life data collection is often subject to errors, resulting in missing data. Here we focus in understanding how this issue should be dealt with for nonnegative tensor factorization. We investigate several criteria used for non-negative tensor factorization in the case where some entries are missing. In particular we show how smoothness penalties can compensate the presence of missing values in order to ensure the existence of an optimum. This lead us to propose new criteria with efficient numerical optimization algorithms. Numerical experiments are conducted to support our claims.