Fast Structured Orthogonal Dictionary Learning using Householder Reflections

TL;DR

This paper introduces efficient algorithms for structured orthogonal dictionary learning, focusing on Householder matrices, with theoretical guarantees and improved computational complexity validated through numerical experiments.

Contribution

It presents novel algorithms for Householder-based orthogonal dictionary learning with theoretical guarantees and demonstrates superior computational efficiency.

Findings

The algorithms achieve approximate recovery with optimal complexity.

Numerical results show comparable or better performance than existing methods.

The techniques work well in sample-limited scenarios.

Abstract

In this paper, we propose and investigate algorithms for the structured orthogonal dictionary learning problem. First, we investigate the case when the dictionary is a Householder matrix. We give sample complexity results and show theoretically guaranteed approximate recovery (in the $l_{\infty}$ sense) with optimal computational complexity. We then attempt to generalize these techniques when the dictionary is a product of a few Householder matrices. We numerically validate these techniques in the sample-limited setting to show performance similar to or better than existing techniques while having much improved computational complexity.