K-EVD clustering and its applications to sparse component analysis

Abstract

In this paper we introduce a simple distance measure from a mdimensional point a hyper-line in the complex-valued domain. Based on this distance measure, the K-EVD clustering algorithm is proposed for estimating the basis matrix A in sparse representation model X = AS + N. Compared to existing clustering algorithms, the proposed one has advantages in two aspects: it is very fast; furthermore, when the number of basis vectors is overestimated, this algorithm can estimate and identify the significant basis vectors which represent a basis matrix, thus the number of sources can be also precisely estimated. We have applied the proposed approach for blind source separation. The simulations show that the proposed algorithm is reliable and of high accuracy, even when the number of sources is unknown and/or overestimated. © Springer-Verlag Berlin Heidelberg 2006.