Kernel recursive least squares dictionary learning algorithm

Abstract

An online dictionary learning algorithm for kernel sparse representation is developed in the current paper. In this framework, the input signal nonlinearly mapped into the feature space is sparsely represented based on a virtual dictionary in the same space. At any instant, the dictionary is updated in two steps. In the first step, the input signal samples are sparsely represented in the feature space, using the dictionary that has been updated based on the previous data. In the second step, the dictionary is updated. In this paper, a novel recursive dictionary update algorithm is derived, based on the recursive least squares (RLS) approach. This algorithm gradually updates the dictionary, upon receiving one or a mini-batch of training samples. An efficient implementation of the algorithm is also formulated. Experimental results over four datasets in different fields show the superior performance of the proposed algorithm in comparison with its counterparts. In particular, the classification accuracy obtained by the dictionaries trained using the proposed algorithm gradually approaches that of the dictionaries trained in batch mode. Moreover, in spite of lower computational complexity, the proposed algorithm overdoes all existing online kernel dictionary learning algorithms.