# Learning Mixtures of Separable Dictionaries for Tensor Data: Analysis and Algorithms

## TL;DR

This paper introduces a novel approach for learning sparse tensor representations through mixtures of separable dictionaries, providing theoretical guarantees and efficient algorithms for both batch and online learning.

## Contribution

It generalizes separable dictionary learning by proposing mixture models, deriving identifiability conditions, and developing algorithms for practical tensor data analysis.

## Key findings

- Proposed mixture dictionary model improves tensor data representation.
- Derived conditions ensure local identifiability of the learned dictionaries.
- Algorithms demonstrate effectiveness in numerical experiments.

## Abstract

This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing the separable dictionary learning model. Two different approaches for learning mixture of separable dictionaries are explored and sufficient conditions for local identifiability of the underlying dictionary are derived in each case. Moreover, computational algorithms are developed to solve the problem of learning mixture of separable dictionaries in both batch and online settings. Numerical experiments are used to show the usefulness of the proposed model and the efficacy of the developed algorithms.