K-Hyperplanes Clustering and Its Application to Sparse Component Analysis

In this paper the K-hyperplanes clustering problem is discussed and we present a K-hyperplanes clustering algorithm, which can be applied to sparse component analysis (SCA) for linear model X=AS+V, where X is a m by T matrix of observation, A is an unknown m by n basis matrix and S is an unknown n by T matrix of sparse sources. The proposed algorithm is suitable for a relaxed case when more than one source signal achieves significant value at any time instant. More precisely, in this paper we propose a new algorithm which is suitable for the case when the (m-1) source signals are simultaneously nonzero for sufficient number of samples, where m is the number of observation. In contrast to the conventional SCA algorithm which is based on the assumption that for each time, there is only one dominant component and others components are not significant. We assume that the sources can be only moderately sparse. However, the complexity of the algorithm is higher than that of the conventional SCA algorithms. We confirmed the validity and good performance of the proposed algorithm by computer simulation.