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Title Consensus theories, an oriented survey
Author MONJARDET Bernard, HUDRY Olivier
Keywords Aggregation rule, Arrowian result, Complexity, Consensus theory, Distance, Lower valuation, Median semilattice, Médiane, Restricted domain, Tournament solution
Topic None
Abstract This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly - but not exclusively - concentrated on the most significant results obtained, sometimes with other researchers, by a team of French researchers who are or were full or associate members of the Centre d'analyse et de mathématique sociale (CAMS).
Number 190, Summer 2010, special issue: Theories and uses. Tribute issue to Bruno Leclerc
Language  English
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Title Maximum of the transfer distance to a given partition
Author CHARON Irène, HUDRY Olivier, DENOEUD-BELGACEM Lucile
Keywords Distance, Partitions, Transferts
Topics Classification - Clustering - Partitioning, Combinatorics, Discrete Mathematics, Distances
Abstract In this paper, we study a distance defined over the partitions of a finite set. Given two partitions P and Q, this distance, called the transfer distance, is defined as the minimum number of transfers of an element from one class to another, required to transform P into Q or equivalently Q in P. We give some formulae for the maximum distance value between a given partition and any partition, then the maximum distance value between a given partition and a partition with an upper-bounded number of classes.
Number 179, Fall 2007
Language   French
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Title Arch graphs
Author LECLERC Bruno
Keywords 2-tree, Algorithm, Cycle, Distance, Graph, Tree, Tree encoding
Topics Algorithms - Algorithmic Theory, Distances, Graphs, Trees
Abstract An arch-graph may be obtained from a simple edge by successive addings of 3-paths, grafted on their extremities. Equivalently, it admits no subgraph of which every vertex has degree at least three, and is maximal with this property, for a fixed number of vertices. It is known that a tree distance may be summarized by 2n-3 of its entries, conveniently chosen. Arch graphs with n vertices correspond to such sets of entries. They include the graphs of the so-called 2-tree type. We study these graphs, and the k-arch graphs and k-trees which naturally generalize them. It is recalled how a tree metric or function is associated to a valued arch graph, and the properties of this correspondence are investigated.
Number 157, Spring 2002
Language   French
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Title Clustering unlabelled words with statistical methods
Author BEAUJARD Christel, JARDINO Michèle
Keywords Classement, Distance, Language modeling, Mapping, Optimization, Statistics
Topics Classification - Clustering - Partitioning, Distances, Linguistics, Optimization
Abstract Our goal is to develop robust language models for speech recognition. These models have to predict a word knowing its history. Although the increasing size of electronic text data, all the possible word sequences of a language cannot be observed. A way to generate these non encountered word sequences is to map words in classes. The class-based language models have a better coverage of the language with a reduced number of parameters, a situation which is favourable to speed up the speech recognition systems. Two types of automatic word classification are described. They are trained on word statistics estimated on texts derived from newspapers and transcribed speech. These classifications do not require any tagging, words are classified according to the local context in which they occur. The first one is a mapping of the vocabulary words in a fixed number of classes according to a Kullback-Leibler measure. In the second one, similar words are clustered in classes whose number is not fixed in advance. This work has been performed with French training data coming from two domains, both different in size and vocabulary.
Number 147, Fall 1999, special issue: Classification
Language   French
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