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NMF versus ICA for blind source separation

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Abstract

Blind source separation (BSS) is a problem of recovering source signals from signal mixtures without or very limited information about the sources and the mixing process. From literatures, nonnegative matrix factorization (NMF) and independent component analysis (ICA) seem to be the mainstream techniques for solving the BSS problems. Even though the using of NMF and ICA for BSS is well studied, there is still a lack of works that compare the performances of these techniques. Moreover, the nonuniqueness property of NMF is rarely mentioned even though this property actually can make the reconstructed signals vary significantly, and thus introduces the difficulty on how to choose the representative reconstructions from several possible outcomes. In this paper, we compare the performances of NMF and ICA as BSS methods using some standard NMF and ICA algorithms, and point out the difficulty in choosing the representative reconstructions originated from the nonuniqueness property of NMF.

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Notes

  1. There is actually a study that considers the effect of the nonuniqueness property of NMF to the reconstruction results as it displays the average signal-to-noise values over some trials (Plaza et al. 2012). However the authors do not mention the difficulty in choosing the representative reconstructions.

  2. The auxiliary function for proving the nonincreasing property in any MUR based NMF algorithm is also the Lyapunov function, so that the stability of any MUR based NMF algorithm can be shown directly by using the result presented in Badeau (2010).

  3. MVCNMF has a justification as a BSS method as it looks for estimate source vectors that span a simplex that circumscribes the observed data.

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  1. Computer Science Department, College of Arts and Applied Sciences, Dhofar University, Salalah, Oman

    Andri Mirzal

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Mirzal, A. NMF versus ICA for blind source separation. Adv Data Anal Classif 11, 25–48 (2017). https://doi.org/10.1007/s11634-014-0192-4

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