# Legendre Decomposition for Tensors

arXiv: https://arxiv.org/abs/1802.04502 · HTML: https://mlsanity.com/paper/1802.04502/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2018.

## Built on by (most cited first, 5 of 5)

- [Many-body Approximation for Non-negative Tensors](https://mlsanity.com/paper/2209.15338/) (2022)
- [Fast Tucker Rank Reduction for Non-Negative Tensors Using Mean-Field Approximation](https://mlsanity.com/paper/2103.02898/) (2021)
- [A Complete Decomposition of KL Error using Refined Information and Mode Interaction Selection](https://mlsanity.com/paper/2410.11964/) (2024)
- [Pseudo-Nonlinear Data Augmentation: A Constrained Energy Minimization Viewpoint](https://mlsanity.com/paper/2410.00718/) (2024)
- [Seeding neural network quantum states with tensor network states](https://mlsanity.com/paper/2506.23550/) (2025)

## Abstract (arXiv)

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.