New Penalized Criteria for Smooth Non-Negative Tensor Factorization With Missing Entries

• Published in: IEEE transactions on signal processing Vol. 72; pp. 2233 - 2243
• Main Authors: Durand, Amaury, Roueff, Francois, Jicquel, Jean-Marc, Paul, Nicolas
• Format: Journal Article
• Language: English
• Published: New York IEEE 2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Communication networks; Computer Science; Computer vision; Convergence; CP decomposition; Criteria; Data collection; Factorization; Mathematical analysis; Missing data; missing values; Non-negative tensor decomposition; Optimization; PARAFAC; Psychometrics; Research and development; Signal and Image Processing; Signal processing algorithms; Smoothness; Splines (mathematics); tensor completion; Tensors; Vectors; Tensor completion; CP decomposition; Smoothness; Missing values; Non-negative tensor decomposition; PARAFAC
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2024.3392357

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 non-negative 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 leads us to propose new criteria with efficient numerical optimization algorithms. Numerical experiments are conducted to support our claims.