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This paper describes the Jensen-Shannon divergence (JSD) and Hilbert space embedding. With natural definitions making these considerations precise, one finds that the general Jensen-Shannon divergence related to the mixture is the minimum redundancy, which can be achieved by the observer. The set of distributions with the metric /spl radic/JSD can even be embedded isometrically into Hilbert space and the embedding can be identified.
Fuglede et al. (Thu,) studied this question.