Kullback–Leibler relative-entropy has unique properties in cases involving distributions resulting from relative-entropy minimization. Tsallis relative-entropy is a one-parameter generalization of Kullback–Leibler relative-entropy in the nonextensive thermostatistics. In this paper, we present the properties of Tsallis relative-entropy minimization and present some differences with the classica...

We study minimization of a parametric family of relative entropies, termed relative α-entropies (denoted Iα(P,Q)). These arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (KullbackLeibler divergence). Just like relati...

We study minimization of a parametric family of relative entropies, termed relative α-entropies (denoted Iα(P,Q)). These arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (KullbackLeibler divergence). Just like relati...

Automatic facial recognition has many potential applications in different areas of humancomputer interaction. However, they are not yet fully realized due to the lack of an effectivefacial feature descriptor. In this paper, we present a new appearance based feature descriptor,the local directional pattern (LDP), to represent facial geometry and analyze its performance inrecognition. An LDP feat...

We prove that for the relative entropy of faithful normal states φ and ω on the von Neumann algebra M the formula S(φ,ω) = sup{ω(Λ)-logφ(/): h = h*eM] holds. In general von Neumann algebras the relative entropy was defined and investigated by Araki [1, 3]. After Lieb had proved the joint convexity of the relative entropy in the type / case [10] several proofs appeared in the literature and they...