Since dictionaries can be large then one can use sparse random projections to sketch them at low computational cost.This is what today's paper does:
Efficient Dictionary Learning via Very Sparse Random Projections by Farhad Pourkamali-Anaraki, Stephen Becker, Shannon M. Hughes
Performing signal processing tasks on compressive measurements of data has received great attention in recent years. In this paper, we extend previous work on compressive dictionary learning by showing that more general random projections may be used, including sparse ones. More precisely, we examine compressive K-means clustering as a special case of compressive dictionary learning and give theoretical guarantees for its performance for a very general class of random projections. We then propose a memory and computation efficient dictionary learning algorithm, specifically designed for analyzing large volumes of high-dimensional data, which learns the dictionary from very sparse random projections. Experimental results demonstrate that our approach allows for reduction of computational complexity and memory/data access, with controllable loss in accuracy.
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