Creating and sharing knowledge for telecommunications

Tsallis kernels on measures

Aguiar, P. ; Figueiredo, M. A. T.

Tsallis kernels on measures, Proc IEEE Information Theory Workshop - ITW, Porto, Portugal, Vol. , pp. - , May, 2008.

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Recent approaches to classification of text, images,
and other types of structured data, launched the quest for positive
definite (p.d.) kernels on probability measures. In particular,
kernels based on the Jensen-Shannon (JS) divergence and other
information-theoretic quantities have been proposed. We introduce
new JS-type divergences, by extending its two building
blocks: convexity and Shannon’s entropy. These divergences
are then used to define new information-theoretic kernels on
measures. In particular, we introduce a new concept of q-
convexity, for which a Jensen q-inequality is proved. Based on
this inequality, we introduce the Jensen-Tsallis q-difference, a
nonextensive generalization of the Jensen-Shannon divergence.
Furthermore, we provide denormalization formulae for entropies
and divergences, which we use to define a family of nonextensive
information-theoretic kernels on measures. This family, grounded
in nonextensive entropies, extends Jensen-Shannon divergence
kernels, and allows assigning weights to its arguments.