Abstract: For the problem of underdetermined blind source separation of sparse sources, the estimation of the mixing matrix is crucial. To improve the estimation performance, a combined cluster analysis algorithm  is proposed. Firstly, the short-time Fourier transform is used to transform the observed signal in the time domain into a sparse signal in the frequency domain, and the normalization of the observed data is used to transform the linear clustering of sparse signal into the compact clustering in the frequency domain. Secondly, the affinity propagation (AP) clustering is used to search the neighborhood of each observed data to automatically form the number of data classes and corresponding key data. Finally, the results of AP clustering are used as the initial values of the K-means algorithm, and the clustering center of each class data is further modified. The simulation results shows that the combined cluster algorithm  can effectively improve the estimation accuracy of the underdetermined mixing matrix. Another advantage of the combined method is that it overcomes the drawbacks of the classic K-means algorithm that needs to know the number of sources and is very sensitives to the initial partition of the data.

Key words: underdetermined blind source separation, sparse representation, mixing matrix estimation, affinity propagation, K-means