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This paper describes several important methods for the blind source separation of audio signals in an integrated manner. Two historically developed routes are featured. One started from independent component analysis and evolved to independent vector analysis (IVA) by extending the notion of independence from a scalar to a vector. In the other route, nonnegative matrix factorization (NMF) has been extended to multichannel NMF (MNMF). As a convergence point of these two routes, independent low-rank matrix analysis has been proposed, which integrates IVA and MNMF in a clever way. All the objective functions in these methods are efficiently optimized by majorization-minimization algorithms with appropriately designed auxiliary functions. Experimental results for a simple two-source two-microphone case are given to illustrate the characteristics of these five methods.