On the risk of using Renyi's entropy for blind source separation

Pham, Dinh-Tuan;Vrins, Frédéric;Verleysen, Michel
(2008) IEEE Transactions on Signal Processing — Vol. 56, n° 10, p. 4611-4620 (2008)

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Abstract
Recently, some researchers have suggested Rényi’s entropy in its general form as a blind source separation (BSS) objective function. This was motivated by two arguments: 1) Shannon’s entropy, which is known to be a suitable criterion for BSS, is a particular case of Rényi’s entropy, and 2) some practical advantages can be obtained by choosing another specific value for the Rényi exponent, yielding to, e.g., quadratic entropy. Unfortunately, by doing so, there is no longer guarantee that optimizing this generalized criterion would lead to recovering the original sources. In this paper, we show that Rényi’s entropy in its exact form (i.e., out of any consideration about its practical estimation or computation) might lead to not recovering the sources, depending on the source densities and on Rényi’s exponent value. This is illustrated on specific examples. We also compare our conclusions with previous works involving Rényi’s entropies for blind deconvolution.
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Pham, D.-T., Vrins, F., & Verleysen, M. (2008). On the risk of using Renyi’s entropy for blind source separation. IEEE Transactions on Signal Processing, 56(10), 4611-4620. https://doi.org/10.1109/TSP.2008.928109 (Original work published 2008)