François Bavaud

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The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by(More)
General clustering deals with weighted objects and fuzzy memberships. We investigate the group-or object-aggregation-invariance properties possessed by the relevant functionals (effective number of groups or objects, centroids, dispersion, mutual object-group information, etc.). The classical squared Euclidean case can be generalized to non-Euclidean(More)
General models of network navigation must contain a deter-ministic or drift component, encouraging the agent to follow routes of least cost, as well as a random or diffusive component, enabling free wandering. This paper proposes a thermodynamic formalism involving two path functionals, namely an energy functional governing the drift and an entropy(More)
1 Introduction: the relative entropy as an epistemological functional Shannon's Information Theory (IT) (1948) definitely established the purely mathematical nature of entropy and relative entropy, in contrast to the previous identification by Boltzmann (1872) of his " H-functional " as the physical entropy of earlier thermodynamicians (Carnot, Clausius,(More)