Sparse representations using learned dictionaries are being increasingly usedwith success in several data processing and machine learning applications. Theavailability of abundant training data necessitates the development ofefficient, robust and provably good dictionary learning algorithms. Algorithmicstability and generalization are desirable characteristics for dictionarylearning algorithms that aim to build global dictionaries which can efficientlymodel any test data similar to the training samples. In this paper, we proposean algorithm to learn dictionaries for sparse representations from large scaledata, and prove that the proposed learning algorithm is stable andgeneralizable asymptotically. The algorithm employs a 1-D subspace clusteringprocedure, the K-hyperline clustering, in order to learn a hierarchicaldictionary with multiple levels. We also propose an information-theoreticscheme to estimate the number of atoms needed in each level of learning anddevelop an ensemble approach to learn robust dictionaries. Using the proposeddictionaries, the sparse code for novel test data can be computed using alow-complexity pursuit procedure. We demonstrate the stability andgeneralization characteristics of the proposed algorithm using simulations. Wealso evaluate the utility of the multilevel dictionaries in compressed recoveryand subspace learning applications.
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