Modified hierarchical clustering for sparse component analysis

The under-determined blind source separation (BSS) problem is usually solved using the sparse component analysis (SCA) technique. In SCA, the BSS is usually solved in two steps, where the mixing matrix is estimated in the first step, while the sources are estimated in the second step. In this paper we propose a novel clustering algorithm for estimating the mixing matrix and the number of sources, which is usually unknown. The proposed algorithm is based on incorporating a statistical test with a hierarchical clustering (HC) algorithm. The proposed algorithm is based on sequentially extracting compact clusters that have been constructed by the HC algorithm, where the extraction decision is based on the statistical test. To identify the number of sources, as well as the clusters corresponding to the columns of the mixing matrix, we develop a quantitative measure called the concentration parameters. Two numerical examples are presented to present the ability of the proposed algorithm in estimating the mixing matrix and the number of sources.