Legendre Decomposition for Tensors

TL;DR

This paper introduces Legendre decomposition, a new nonnegative tensor factorization technique that guarantees uniqueness and minimizes KL divergence, outperforming existing methods in accuracy.

Contribution

The paper proposes a novel Legendre decomposition method for tensors, leveraging information geometry to ensure uniqueness and optimality in reconstruction.

Findings

Legendre decomposition provides more accurate tensor reconstructions.

It guarantees the uniqueness of the factorization.

The method minimizes KL divergence from the input tensor.

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.