Underdetermined BSS Based on <Emphasis Type="Italic">K</Emphasis>-means and AP Clustering

Underdetermined blind source separation (UBSS) is a hard problem to solve since its mixing system is not invertible. The well-known “two-step approach” has been widely used to solve the UBSS problem and the most pivotal step is to estimate the underdetermined mixing matrix. To improve the estimation performance, this paper proposes a new clustering method. Firstly, the observed signals in the time domain are transformed into sparse signals in the frequency domain; furthermore, the linearity clustering of sparse signals is translated into compact clustering by normalizing the observed data. And then, the underdetermined mixing matrix is estimated by clustering methods. The K-means algorithm is one of the classical methods to estimate the mixing matrix but it can only be applied to know the number of clusters in advance. This is not in accord with the actual situation of UBSS. In addition, the K-means is very sensitive to the initialization of clusters and it selects the initial cluster centers randomly. To overcome the fatal flaws, this paper employs affinity propagation (AP) clustering to get the exact number of exemplars and the initial clusters. Based on those results, the K-means with AP clustering as initialization is used to precisely estimate the underdetermined mixing matrix. Finally, the source signals are separated by linear programming. The experimental results show that the proposed method can effectively estimate the mixing matrix and is more suitable for the actual situation of UBSS.