Legendre Decomposition for Tensors

Abstract

We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an input tensor. We empirically show that Legendre decomposition can more accurately reconstruct tensors than other nonnegative tensor decomposition methods.

12 pages, 6 figures, accepted to the 32nd Annual Conference on Neural Information Processing Systems (NIPS 2018)

References in corpus (4)

• Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
• On Tensors, Sparsity, and Nonnegative Factorizations
• Equivalence of restricted Boltzmann machines and tensor network states
• Information Decomposition on Structured Space

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• Fast Tucker Rank Reduction for Non-Negative Tensors Using Mean-Field Approximation
• Hierarchical Probabilistic Model for Blind Source Separation via Legendre Transformation