François Bavaud

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General clustering deals with weighted objects and fuzzy memberships. We investigate the groupor 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)
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 deterministic 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)
The long term goal of this research is to develop a program able to produce an automatic segmentation and categorization of textual sequences into discourse types. In this preliminary contribution, we present the construction of an algorithm which takes a segmented text as input and attempts to produce a categorization of sequences, such as narrative,(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)
A fuzzy partition assigns to each among n objects a distribution over a categories. Elementary linear algebraic methods permit to introduce and investigate concepts and properties such as a) variance and inertia decomposition; b) coarseand fine-graining (nestedness); c) iteration of fuzzy partitions; d) stability of a group in regard to another partition;(More)
Exchange matrices represent spatial weights as symmetric probability distributions on pairs of regions, whose margins yield regional weights, generally well-specified and known in most contexts. This contribution proposes a mechanism for constructing exchange matrices, derived from quite general symmetric proximity matrices, in such a way that the margin of(More)