# Dictionary-based Tensor Canonical Polyadic Decomposition

## TL;DR

This paper introduces a dictionary-based tensor canonical polyadic decomposition method that enhances interpretability and accuracy in tensor source extraction by enforcing known dictionary constraints, with demonstrated benefits in hyperspectral image unmixing.

## Contribution

It proposes a novel formulation of sparse coding for high-dimensional tensors and explores the benefits of dictionary constraints in tensor decomposition.

## Key findings

- Improved parameter identifiability and estimation accuracy.
- Effective in hyperspectral image unmixing.
- Validated on simulated data and real hyperspectral images.

## Abstract

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.