A Proximal Approach for Nonnegative Tensor Decomposition

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• 关键词：Constrained optimization ; Proximal algorithm ; Block alternating minimization ; Nonnegative tensor factorization (NTF)
• 刊名：Lecture Notes in Computer Science
• 出版年：2017
• 出版时间：2017
• 年：2017
• 卷：10169
• 期：1
• 页码：201-210
• 丛书名：Latent Variable Analysis and Signal Separation
• ISBN：978-3-319-53547-0
• 卷排序：10169

文摘

This communication deals with N-th order tensor decompositions. More precisely, we are interested in the (Canonical) Polyadic Decomposition. In our case, this problem is formulated under a variational approach where the considered criterion to be minimized is composed of several terms: one accounting for the fidelity to data and others that can represent not only regularization (such as sparsity prior) but also hard constraints (such as nonnegativity). The resulting optimization problem is solved by using the Block-Coordinate Variable Metric Forward-Backward (BC-VMFB) algorithm. The robustness and efficiency of the suggested approach is illustrated on realistic synthetic data such as those encountered in the context of environmental data analysis and fluorescence spectroscopy. Our simulations are performed on 4-th order tensors.