Bernard Fichet

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Given a vector u and a certain subset K of a real vector space E, the problem of l -approximation involves determining an element û in K nearest to u in the sense of the l -error norm. The subdominant * of u is the upper bound (if it exists) of the set [x # K : xOu] (we let xOy if all coordinates of x are smaller than or equal to the corresponding(More)
A metric d on a finite set X is called a Kalmanson metric if there exists a circular ordering of points of X , such that d(y; u) + d(z; v) > d(y; z) + d(u; v) for all crossing pairs yu and zv of . We prove that any Kalmanson metric d is an l1-metric, i.e. d can be written as a nonnegative linear combination of split metrics. The splits in the decomposition(More)
In this paper, we establish that the following fitting problem is NP-hard: given a finite set X and a dissimilarity measure d on X (d is a symmetric function d from X to the nonnegative real numbers and vanishing on the diagonal), we wish to find a Robinsonian dissimilarity dR on X minimizing the l∞-error ||d− dR||∞ = maxx,y∈X{|d(x, y)− dR(x, y)|} between d(More)
A reduced identification system for the genus Serratia is proposed. The usefulness of this system was shown by identification of 720 strains from clinical specimens or natural environment. Computation of "diagnosis ability coefficient" and principal component analysis made it possible to reduce this identification system to 9 tests. Numerical taxonomy(More)
This note deals with three-way dissimilarities only de ned on unordered triples. They are in relationship with two-way dissimilarities via an Lp-transformation and a particular attention is paid to the perimeter model (p = 1). In that case, a six-point condition is established. Following the basic papers of Joly-Le Calve (J. of Classi cation, 1995) and(More)
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