Group sparsity in dimensionality reduction of sparse representation

Group sparsity is extensively used in developing Compressed Sensing recovery algorithms, but it is ignored in dimensionality reduction. In this paper, we define supervised group distance based on group sparsity to measure the similarity between recovered sparse coefficients from Compressed Sensing for signal classification, especially the sparse coefficients intra-class. And a graph embedding dimensionality reduction algorithm is then proposed based on the defined supervised group distance. Experimental results on both synthetic and real-world data demonstrate that the proposed method achieves superior performance on both classification error rate and visualization.