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 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)
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)
Classical factorial treatments applied on words-documents counts matrices (such as Correspondence Analysis (FCA), Latent Semantic Indexing (LSI), as well as non-linear generalizations of FCA (NLCA)) can be described in the framework of kernels associated to Support Vector Machines (SVM). This paper exposes the relationships between those formalisms, and(More)