A novel geometric multiscale approach to structured dictionary learning on high dimensional data

Abstract

Adaptive dictionary learning has become a hot-topic research field during the past decade. Though several algorithms have been proposed and achieved impressive results, they are all computationally intensive due to the lack of structure in their output dictionaries. In this paper we build upon our previous work and take a geometric approach to develop better, more efficient algorithms that can learn adaptive structured dictionaries. While inheriting many of the advantages in the previous construction, the new algorithm better utilizes the geometry of data and effectively removes translational invariances from the data, thus able to produce smaller, more robust dictionaries. We demonstrate the performance of the new algorithm on two data sets, and conclude the paper by a discussion of future work.