New Convergence and Performance Measures for Blind Source Separation Algorithms

Neural learning algorithms developed for blind separation of mixed source signals give rise to a Global Separating-Mixing (GSM) matrix that can be used to measure the performance of the unmixing system. In the case of the instantaneous linear noiseless mixing model, we consider the GSM as a transformation operator and show that it is equivalent to a combined stretching and rotation in the signal space. The extent of rotation is obtained using a polar decomposition method and can be taken as a measure of convergence to the problem solution. We also propose a new performance index (E3) that can be used to measure the performance of algorithms used in blind separation problems. The index E3 is more precise than the commonly used E1 and E2 indices and is normalized to the interval {0,1}. Experimentations using artificially generated supergaussian Laplacian signals have been performed using a fast ICA algorithm and considering a wide range of the number of mixed sources. Using the proposed E3 measure, we present experimental results on the dependence of algorithm performance on the number of mixed signals.