Mixing Matrix Estimation Based on Directional Fuzzy C-means and K-means

In underdetermined blind source separation with unknown number of sources, it is a challenging problem to estimate the mixing matrix precisely. Two major drawbacks of existing methods are that they cannot estimate the number of sources correctly under ill-conditioned conditions (namely, the directions of some mixed vectors are close) and they are susceptible to outliers. To deal with these issues, a mixing matrix estimation method based on directional fuzzy C-means (DFCM) and K-means is proposed. First, the observation signals are pre-clustered by DFCM, such that we can: 1) determine the number of sources by the convergence point of the clustering validity index; 2) eliminate outliers according to the membership matrix; 3) determine the initial clustering points of K-means. Finally, K-means is used to achieve mixing matrix estimation based on the pre-determined number of sources and the initial clustering points. The simulation results suggest that the proposed method has superior performance of mixing matrix estimation.