Underdetermined mixing matrix estimation based on joint density-based clustering algorithms

Abstract

In underdetermined blind source separation (UBSS), the estimation of the mixing matrix is crucial because it directly affects the performance of UBSS. To improve the estimation accuracy, this paper proposes a joint clustering analysis method based on density based spatial clustering of applications with noise (DBSCAN) and clustering by fast search and find of density peaks (CFSFDP). In the reprocessing, the observed signals in the time domain are transformed into sparse signals in the frequency domain through a short time Fourier transform (STFT), and single-source-point (SSP) detection is used to enhance the linear clustering characteristic of signals. In addition, to facilitate the use of density-based clustering analysis, mirroring mapping is used to transform the linear clustering into compact clustering on the positive half unit circle (or sphere). For the estimation of the underdetermined mixing matrix (UMM), the DBSCAN algorithm is first used to search for high-density data points, and automatically find the number of clusters and the cluster centers; then, the CFSFDP algorithm is used to search the density peaks of the data clusters, so as to further modify the cluster centers. Because each cluster center corresponds to a column vector of the mixing matrix, the proposed algorithm can estimate the UMM through cluster analysis. The simulation results show that the proposed algorithm can not only improve the estimation accuracy of the UMM, but also provide a more robust estimator. In addition, the joint clustering method also makes up for the shortcomings of the CFSFDP algorithm that requires human intervention.