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

2022/03/22 by Amaury Durand, Durand, Amaury, François Roueff +5 · 1 citation
Engineering · Mathematics · #Elasticity and Material Modeling #FOS: Electrical engineering #Signal Processing (eess.SP) #Tensor decomposition and applications #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2203.11514

openalex publication_date 2022/03/22 · openalex created_date 2022/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Tensor Decompositions and Applications
• Most Tensor Problems Are NP-Hard
• Tensor Decomposition for Signal Processing and Machine Learning

Cited by

• Generalized Nonnegative Structured Kruskal Tensor Regression

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