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

arXiv: https://arxiv.org/abs/1903.09284 · HTML: https://mlsanity.com/paper/1903.09284/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2019.

## Built on by (most cited first, 4 of 4)

- [A Guide to Computational Reproducibility in Signal Processing and Machine Learning](https://mlsanity.com/paper/2108.12383/) (2021)
- [Structured Low-Rank Tensors for Generalized Linear Models](https://mlsanity.com/paper/2308.02922/) (2023)
- [Low-Rank Phase Retrieval with Structured Tensor Models](https://mlsanity.com/paper/2202.08260/) (2022)
- [Multi-Dictionary Learning for Low Rank Sparse Coding](https://mlsanity.com/paper/2509.10033/) (2025)

## Abstract (arXiv)

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.