Fast Structured Orthogonal Dictionary Learning using Householder Reflections
This addresses the problem of efficient dictionary learning for researchers and practitioners in signal processing and machine learning, offering an incremental improvement over existing methods.
The paper tackles the structured orthogonal dictionary learning problem by proposing algorithms for dictionaries that are Householder matrices or products of a few Householder matrices, achieving theoretically guaranteed approximate recovery with optimal computational complexity and showing in numerical validation performance similar to or better than existing techniques with much improved computational complexity.
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.