Sparsity analysis originates from the researches of neurobiology on visual perception. It has been proved that the responses of the neurons in human low-level and mid-level vision system to the outside signals are highly sparse, includingpopulation sparseness and lifetime sparseness. Recently, inspired by the researches on neurobiology, more attentions have been paid on application of sparsity analysis in signal processing and pattern recognition. In this paper, we discuss sparsity analysis of the patterns and its application in recognition. There are two key points involved with the researches, the rest point is sparsity analysis of patterns, and there are two aspects within this point, that's sparse decomposition for pattern representation and sparse decomposition for dictionary learning. The second key point lies in the application of sparsity analysis in recognition. In this paper, we apply the algorithm for character and face recognition. Classfication is based on the reconstruction residual error, then sparsity analysis and its application in recognition are combined via actual problem. Our work is presented as following: Firstly, in actual recognition system, people often face the problem of large number of categories or training samples. Directly using sparse representation leads to difficulties in computation and unstable results. So we propose a local sparse coding algorithm to cope with this situation, and we apply the proposed algorithm for character recognition. Combined with template matching, a two steps strategy is proposed for degraded character recognition and handwritten digit character recognition. Experimental results show that the proposed algorithm can not only promote the accuracy but save computation costs. Secondly, inspired by former researches, we find that not only single sample suffered from large noises but also samples from the same class suffered from difference which makes the samples clustered separately. The clustered samples destroy the assumption of sparse representation which believes that strong correlations exist within one class. So, we propose a robust principal component analysis algorithm based on clustering to analysis the principal components within the pattern via low-rank matrix recovery. In the recognition process, we combine sparse representation and principal component analysis together to represent the samples. Experiments on handwritten digit and face recognition show that the proposed algorithm wor...
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