Underdetermined mixing matrix estimation based on artificial bee colony optimization and single-source-point detection

It is difficult to solve the problem of underdetermined blind source separation (UBSS) since the mixing system is not invertible. Therefore, estimating the underdetermined mixing matrix becomes the most crucial step in the well-known “two-step approach”. To improve the estimation performance, this paper proposes a novel clustering analysis method combining artificial bee colony (ABC) optimization with single-source-point (SSP) detection. The observed signals in the time domain are first transformed into sparse signals in the time-frequency domain by a short time Fourier transform (STFT). And the SSP detection is performed to enhance the sparsity of the signals, and the linear clustering of sparse signal is also converted into compact clustering by mirroring mapping in order to find the corresponding clustering centers in the dense data piles. The clustering centers correspond to the column vectors of the mixing matrix, so the mixing matrix can be estimated by cluster analysis. In the estimation process, the global search capability of the ABC algorithm is fully utilized. Based on the linear clustering characteristics of sparse signals, a new search strategy combining deterministic search with stochastic search is used for bee colony to alleviate the contradiction between the population diversity and the convergence speed of the algorithm. Considering the fact that the ABC algorithm has poor local exploitation capacity, a local search strategy based on Levy flight is also used to further search the neighborhood of the current optimal solution, which can significantly improve the local exploitation performance of the algorithm. The simulation results show that the proposed method can not only estimate the underdetermined mixing matrix (and the source signals) more accurately, but also provide a more robust estimator.