Consensus en classification : une revue bibliographique

Leclerc, Bruno; Cucumel, Guy

Mathématiques et sciences humaines, Tome 100 (1987), pp. 109-128.

I - Le Probleme MATHEMATIQUE DE L'AGREGATION : articles ou livres de base. Arrow, K.J., (1951) : Social Choice and Individual Values, New York, Wiley.

Bandelt, H.J., Barthelemy, J.P., (1984) : "Medians in Median Graphs", Discrete Applied Mathematics, 8, 131-142. | MR | Zbl

Barbut, M., (1961) : "Médiane, distributivité, éloignements", repr. (1980), Mathématiques et Sciences humaines, 70, 5-31. | Numdam | MR | Zbl

Barthelemy, J.P., (1979b) : "Propriétés métriques des ensembles ordonnés. Comparaison et agrégation des relations binaires", Thèse, Université de Besançon.

Barthelemy, J.P., Janowitz, M.F., (1988): "Axioms for Consensus Rules" (titre provisoire), prépublication.

Barthelemy, J.P., Monjardet, B., (1980) : "Ajustement et résumé de données relationnelles : les relations centrales", in E. Diday et al., eds., Data Analysis and Informatics, Amsterdam, North-Holland.

Barthelemy, J.P., Monjardet, B., (1981) : "The Median Procedure in Cluster Analysis and Social Choice Theory", Mathematical Social Sciences, 1, (3), 235-268. | MR | Zbl

Barthelemy, J.P., Monjardet, B., (1988) : "The Median procedure in data analysis : new results and open problems", in H.H. Bock (ed.), Classification and Related Methods of Data Analysis, Amsterdam, North-Holland. | MR

Borda, J.C., (1784) : Mémoire sur les élections au scrutin ; histoire de l'Académie Royale des Sciences pour 1781, Paris.

Condorcet, M.J.A. (1785) : Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix, Paris.

Day, W.H.E., (1988) : "Consensus methods as tools for data analysis ", in H.H. Bock (ed.), Classification and Related Methods of Data Analysis, Amsterdam, North-Holland. | MR

Guilbaud, G.Th., (1952) : "Les théories de l'intérêt général et le problème logique de l'agrégation", Economie Appliquée, 5, 501-551, repr. (1968) in Eléments de la Théorie des Jeux, Paris, Dunod.

Janowitz, M.F., (1988) : "Induced Social Welfare Functions", Mathematical Social Sciences, (to appear). | MR | Zbl

Leclerc, B., (1988a) : "Consensus Applications in the Social Sciences ", in H.H. Bock (ed.), Classification and Related Methods of Data Analysis, Amsterdam, North-Holland.

Leclerc, B., (1988b) : Medians and Majorities in Semimodular Lattices, rapport CMS-P031, Paris, Centre d'Analyse et de Mathématique Sociales.

Marcotorchino, F., Michaud, P., (1980) : Optimisation en analyse de données relationnelles, in E. Diday et al., eds., Data Analysis and Informatics, Amsterdam, North-Holland, 655-670. | Zbl

Michaud, P., Marcotorchino, F., (1979) : "Modèles d'optimisation en analyse de données relationnelles", Mathématiques et Sciences humaines, 67, 7-38. | Numdam | Zbl

Mirkin, B.G., (1974) : Group Choice (en russe), Trad. anglaise (1979), P. Fisburn, ed., Washington, Winston.

Monjardet, B., (1980) : "Théorie et applications de la médiane dans les treillis distributifs finis", Annals of Discrete Mathematics, 9, 87-91. | MR | Zbl

Monjardet, B., (1987) : "Arrowian Characterizations of Latticial Fédération Consensus Functions", Rapport CMS-P030, Paris, Centre d'Analyse et de Mathématique Sociales.

Young, H.P., Levenglick, A., (1978) : "A Consistent Extension of Condorcet's Election Principle", SIAM Journal on Applied Mathematics, 35, 285-300. | MR | Zbl

Adams, E.N., III (1972) : "Consensus Techniques and the Comparison of Taxonomic Trees", Systematic Zoology, 21, 390-397.

Adams, E.N., III (1986) : "N-Trees as Nestings : Complexity, Similarity and Consensus, J. of Classification 3, n°2, 299-317. | MR | Zbl

Barthelemy, J.P., (1976) : Sur les éloignements symétriques et le principe de Pareto, Math. Sci. hum. 56, 97-125. | Numdam | MR | Zbl

Barthelemy, J.P., (1977a) : A propos des partitions centrales sur un ensemble non nécessairement fini, Statistique et Analyse des données 3, 54-62.

Barthelemy, J.P., (1977b) : Comparaison et agrégation des partitions et des préordres totaux, C.R. Acad. Sci. Paris, A-285, 985-987. | MR | Zbl

Barthelemy, J.P., (1979b) : "Propriétés métriques des ensembles ordonnés. Comparaison et agrégation des relations binaires". Thèse, Université de Besançon.

Barthelemy, J.P., (1988a) : Comments on "Aggregations of Equivalence Relations", by P.C. Fishburn and A. Rubinstein, à paraître dans le Journal of Classification. | Zbl

Barthelemy, J.P., (1988b) : Thresholded consensus for n-trees, à paraître dans J. of Classification. | MR | Zbl

Barthelemy, J.P., Leclerc, B., Monjardet, B., (1984a) : "Ensembles ordonnés et taxonomie mathématique ", in Orders : Description and Roles, eds. M. Pouzet and D. Richard, Annals of Discrete Mathematics, 23, Amsterdam, North-Holland, 523-548. | MR | Zbl

Barthelemy, J.P., Leclerc, B., Monjardet, B., (1984b) : "Quelques aspects du consensus en classification ", in Data Analysis and Informatics III, eds. E. Diday et al., Amsterdam, North-Holland, 307-316. | MR | Zbl

Barthelemy, J.P., Leclerc, B., Monjardet B., (1986): On the Use of Ordered Sets in Problems of Comparison and Consensus of Classifications, J. of Classification 3, n°2, 187-224. | MR | Zbl

Barthelemy, J.P., Mcmorris, F.R., (1986) : "The Median Procedure for n-trees", J. of Classification 3, n°2, 329-334. | MR | Zbl

BOCK, H.H., ed. (1988) : Classification and Related Methods of Data Analysis, Amsterdam, North-Holland. | MR | Zbl

Celeux, G., (1984): Approximation rapide et interprétation d'une partition centrale pour les algorithmes de partitionnement. Rapport INRIA n°301, INRIA, Rocquencourt.

Constantinescu, M., Sankoff, D., (1986) : Tree Enumeration Modulo a Consensus, J. of Classification 3, n°2, 349-356. | MR | Zbl

Day, W.H.E., (1986a) : Foreword : Comparison and Consensus of Classifications, J. of Classification 3, n°2,183-185.

Day, W.H.E., Mcmorris, F.R., (1985) : "A Formalization of Consensus Index Methods", Bulletin of Mathematical Biology, 47, 215-229. | MR | Zbl

Diday, E., (1988) : Compatibility and Consensus in Numerical Taxonomy, Rapport de Recherches, Rocquencourt, INRIA, à paraître.

Finden, C.R., Gordon, A.D., (1985) : "Obtaining Common Pruned Trees", J. of Classification 2, 255-276.

Fishburn, P.C., Rubinstein, A., (1986) : Aggregation of Equivalence Relations, J. of Classification 3, 61-65. | MR | Zbl

Gordon, A.D., (1980) : On the Assessment and Comparison of Classifications, in R.Thomassone (ed.), Analyse des Données et Informatique, Amsterdam, North-Holland, 193-218.

Gordon, A.D., (1986) : Consensus Supertrees : the synthesis of rooted trees containing overlapping sets of labeled leaves, J. of Classification 3, n°2, 335-348. | MR | Zbl

Gordon, A.D., (1987) : A review of Hierarchical Classification, J. of the Royal Statist. Soc., (series A), 150,119-137. | MR | Zbl

Grotschel, M., Wakabayashi, Y. (1987) : A cutting Plane Algorithm for a Clustering Problem, rapport de recherches n°9, Schwerpunktprogramm der Deutschen Forschungsgemeinschaft, Institut für Mathematik, Universität Augsburg.

Hendy, M., Penny, D. and Henderson, I.M., (1988) : Families of Trees and Consensus, in H.H. Bock (ed.), Classification and Related Methods of Data Analysis, Amsterdam, North-Holland. | MR

Leclerc, B., (1984) : "Efficient and Binary Consensus Functions on Transitively Valued Relations",Mathematical Social Sciences, 8, 45-61. | MR | Zbl

Lerman, I.C., Peter, Ph., (1985) : Elaboration et logiciel d'un indice de similarité entre objets d'un type quelconque. Application au problème du consensus en classification, rapport 262, IRISA, Rennes.

Marcotorchino, F., Michaud, P., (1981) : Heuristic approach to the similarity aggregation problem, Methods of operation research 43, 395-404. | Zbl

Marcotorchino, F., Michaud, P., (1982) : "Agrégation de similarités en classification automatique", Revue de Statistique Appliquée, 30, 21-44. | Numdam | MR | Zbl

Margush, T., Mcmorris, F.R., (1981) : "Consensus n-Trees", Bulletin of Mathematical Biology, 43, 239-244. | MR | Zbl

Mcmorris F.R., Neumann, D.A., (1983) : "Consensus Functions on Trees", Mathematical Social Sciences, 4,131-136. | MR | Zbl

Mcmorris, F.R., (1985) : "Axioms for Consensus Functions on Undirected Phylogenetic Trees", Mathematical Biosciences, 74,17-21. | MR | Zbl

Mirkin, B.G., (1975) : "On the Problem of Reconciling Partitions", in Quantitative Sociology, International Perspectives on Mathematical and Statistical Modelling, New-York, Academic Press, 441-449. | MR

Nelson, G., (1979) : "Cladistic Analysis and Synthesis : principles and definitions, with a historical note on Adanson's Familles des plantes (1763-1764)", Syst. Zool., 28, 1-21.

Neumann, D.A., (1983) : "Faithful Consensus Methods for n-Trees", Math. Biosci., 63, 271-287. | MR | Zbl

Neumann, D.A., Norton, V., (1986a) : On Lattice Consensus Methods, J. of Classification 3, n°2, 225-255. | MR | Zbl

Neumann, D.A., Norton, V., (1986b) : Clustering and Isolation in the Consensus Problem for Partitions", J. of Classification 3, n°2, 281-297. | MR | Zbl

Regnier, S., (1965) : "Sur quelques aspects mathématiques des problèmes de classification automatique", ICC Bulletin, 4, 175-191. Repr. (1983) Mathématiques et Sciences humaines, 82, 13-29. | Numdam | Zbl

Regnier, S., Fernandez De La Vega, W., (1976) : Préhension et interprétation de plusieurs classifications d'un même ensemble de données, rapport ADISH, Paris.

Schader, M., (1981) : Scharfe und unscharfe Klassification qualitative Daten, Athenäum, Känigstein. | MR | Zbl

Schader, M., Tüshaus, U., (1986) : Subgradient methods for analyzing qualitative data, in: W. Gaul and M. Schader, eds., Classification as a tool of Research, Amsterdam, North-Holland. | MR

Sokal, R.R., Rohlf, F.J., (1981) : "Taxonomic Congruence in the Leptopodomorpha Reexamined", Syst. Zool., 30, 309-325.

Stinebrickner, R., (1984a) : "s-Consensus Trees and Indices", Bull. of Math. Biology, 46, 923-935. | MR | Zbl

Stinebrickner, R., (1984b) : "An Extension of Intersection Methods from Trees to Dendrograms", Syst. Zool., 33, 381-386.

Stinebrickner, R., (1986) : "s-Consensus Index Method : an additional axiom, J. of Classification 3, n°2, 319-327. | MR | Zbl

Vach, W., Degens, P.O., (1987) : The System of Common Lower Neighbours of a Hierarchy, Communication à la 1ère Conférence Internationale de la Fédération des Sociétés de Classification, Aix-la-Chapelle. | MR | Zbl

Wakabayashi, Y., (1986) : Aggregation of Binary Relations : algorithmic and polyhedral investigations, thèse, Universität Augsburg. | Zbl

Arabie, P., Boorman, S.A., (1973) : Multidimensional Scaling of Measures of Distance between Partitions, J. of Mathematical Psychology 17, 31-63. | MR

Barthelemy, J.P., (1977b) : Comparaison et agrégation des partitions et des préordres totaux, C.R. Acad. Sci. Paris, A-285, 985-987. | MR | Zbl

Barthelemy, J.P., (1979a) : Caractérisations axiomatiques de la distance de la différence symétrique entre des relations binaires, Math. Sci. hum. 67, 85-113. | Numdam | Zbl

Barthelemy, J.P., Leclerc, B., Monjardet, B., (1984a) : "Ensembles ordonnés et taxonomie mathématique ", in Orders : Description and Roles, M. Pouzet and D. Richard (eds.), Annals of Discrete Mathematics, 23, Amsterdam, North-Holland, 523-548. | MR | Zbl

Barthelemy, J.P., Leclerc, B., Monjardet, B., (1984b) : "Quelques aspects du consensus en classification ", in Data Analysis and Informatics III, E. Diday et al. (eds.), Amsterdam, North-Holand, 307-316. | MR | Zbl

Barthelemy, J.P., Leclerc, B., Monjardet, B., (1986) : On the Use of Ordered Sets in Problems of Comparison and Consensus of Classifications", J. of Classification 3, n°2, 187-224. | MR | Zbl

Bobisud, H.M., Bobisud, L.E., (1972) : "A metric for Classifications", Taxon 21, 607-613.

Boorman, S.A., Arabie, P., (1972) : "Structural Measures and the Methods of Sorting ", in Multidimensional Scaling, vol. 1, Theory and Applications in the Behavioral Sciences, R.N. Shepard, A.K. Romney and S.B. Nerlove (eds.), New-York: Seminar Press, 226-249.

Boorman, S.A., Olivier, D.C., (1973) : "Metrics on Spaces of Finite Trees", J. of Mathematical Psychology 10, 26-59. | MR | Zbl

Colless, (1980) : "Congruence between Morphometric and Allozyme data for Menidia species: a reappraisal", Syst. Zool., 29, 288-299.

Constantinescu, M., Sankoff, D., (1986) : Tree Enumeration Modulo a Consensus, J. of classification 3, n°2, 349-356. | MR | Zbl

Day, W.H.E., (1981) : "The Complexity of Computing Metric Distances Between Partitions", Mathematical Social Sciences, 1, 269-287. | MR | Zbl

Day, W.H.E., (1986b) : Analysis of quartet dissimilarity measures between undirected phylogenetic trees, Syst. Zool., 35, 325-333.

Day, W.H.E., Faith, D.P., (1986) : "A Model in Partial Orders for Comparing Objects by Dualistic Measures", Mathematical Biosciences, 8, 179-192. | MR | Zbl

Day, W.H.E., Mcmorris, F.R., (1985) : "A Formalization of Consensus Index Methods", Bulletin of Mathematical Biology, 47, 215-229. | MR | Zbl

Day, W.H.E., Wells, R.S., (1984) : "Extremes in the Complexity of Computing Metric Distances Between Partitions", IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6, 69-73. | Zbl

Estabrook, G.F., Mcmorris, F.R., Meacham, C.A., (1985) : Comparison of Undirected Phylogenetic Trees Based on Subtrees of four Evolutionary Units, Syst. Zool., 34, 193-200.

Faith, D.P., Belbin, L., (1986) : Comparison of classifications using measures intermediate between metric dissimilarity and consensus similarity, J. of Classification 3, n°2, 257-280. | Zbl

Farris, J.S., (1969) : "A Successive Approximations Approach to Character Weighting", Syst. Zool., 18, 374-385.

Hartigan, J.A., (1967) : "Representation of Similarity Matrices by Trees ", J. Amer. Statist. Ass., 62, 1140-1158. | MR

Hubert, L., Arabie, P., (1985) : Comparing partitions, J. of Classification 2, n°2/3, 193-218.

Hubert, L., Arabie, P., (1986) : Comparing partitions, in W. Goul et M. Schader (eds.), Classification as a Tool of Research, Amsterdam, North-Holland. | MR

Hubert, L.J., Baker, F.B., (1977) : "The Comparison and Fitting of Given Classification Schemes", J. Math. Psychol., 16, 233-253. | MR | Zbl

Leclerc, B., (1981): "Description combinatoire des ultramétriques" Math. Sci. hum, 73,5-37. | Numdam | MR | Zbl

Leclerc, B., (1985a) : "Les hiérarchies de parties et leurs demi-treillis ", Math. Sci. hum., 89, 5-34. | Numdam | MR | Zbl

Leclerc, B., (1985b) : "La comparaison des hiérarchies : indices et métriques", Mathématiques et Sciences humaines, 92, 5-40. | Numdam | MR | Zbl

Margush, T., (1982) : "Distances Between Trees", Discrete Applied Mathematics, 4, 281-290. | MR | Zbl

Mickevich, M.F., (1978) : "Taxonomic congruence", Syst. Zool., 27, 143-158.

Nelson, G., (1979) : "Cladistic Analysis and Synthesis : principles and definitions, with a historical note on Adanson's Familles des plantes(1763-1764) ", Syst. Zool., 28, 1-21.

Nelson, G., Platnick, N., (1981) : Systematics and Biogeography. Cladistics and Vicariance, Columbia University Press, New-York.

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Robinson, D.F., Foulds, L.R., (1981) : "Comparison of Phylogenetic Trees", Math. Biosci., 53, 131-147. | MR | Zbl

Rohlf, F.J., (1982) : "Consensus indices for comparing classifications ", Math. Biosci. 59,131-144. | MR

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Schuh, R.T., Farris, J.S., (1981) : "Methods for investigating taxonomic congruence and their application to the Leptopodomorpha", Syst. Zool. 30, 331-351.

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Sokal, R.R., Rohlf, F.J., (1981) : "Taxonomic Congruence in the Leptopodomorpha Reexamined", Syst. Zool., 30, 309-325.

Stinebrickner, R., (1984a) : "s-Consensus Trees and Indices", Bull. of Math. Biology, 46, 923-935. | MR | Zbl

Stinebrickner, R., (1986) : "s-Consensus Index Method : an additional axiom, J. of Classification 3, n° 2, 319-327. | MR | Zbl

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Acharya B.D., Las Vergnas, M., (1982) : Hypergraphs with Cyclomatic Number Zero, Triangulated Graphs, and an Inequality, J. Combinatorial Theory B, 33, 52-56. | MR | Zbl

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Bertrand, P., Diday, E., (1985) : A visual representation of the compatibility between an order and a dissimilarity index : the pyramids, Computational Statistics Quaterly 2, 31-42. | Zbl

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Brossier, G., (1986) : Problèmes de représentation de données par des arbres., Thèse d'Etat, Université de Rennes II.

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Day, W.H.E., Sankoff, D., (1986) : The computational Complexity of Inferring Phylogenics by Compatibility, Syst. Zool. 35, n°2, 224-229.

Diday, E., (1982) : Croisements, ordres et ultramétriques : applications à la recherche de consensus. Rapport de recherche n°144, INRIA Rocquencourt.

Diday, E., (1983) : Croisements ordres et ultramétriques. Mathématiques et Sciences humaines, n°83, 31-54. | EuDML | Numdam | MR | Zbl

Diday, E., (1984) : "Une représentation visuelle des classes empiétantes : les pyramides". Rapport de recherche n°291, INRIA, Rocquencourt.

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Leclerc, B., (1986) : Caractérisation, construction et dénombrement des ultramétriques supérieures minimales, Statistique et analyse de données, 11, 26-50. | EuDML | Numdam | MR | Zbl

Leclerc, B., (1987) : Arbres minimums communs et compatibilité de données de types variés, Mathématiques et Sciences humaines,98, 41-67. | EuDML | Numdam | MR | Zbl

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Reinert, M., (1987) : Classification descendante hiérarchique et analyse lexicale par contexte. Application au corpus des poésies d'A. Rimbaud, Bull. de Méthodologie Sociologique, 13, 53-90.**

Robinson, W.S., (1951) : A Method for Chronological Ordering of Archaeological Deposits, American Antiquity, 16, 293-301.

Statistique et Analyse des Données 10, n°1 (1985) : numéro spécial sur l'analyse conjointe de plusieurs tableaux de données.

Barthelemy, J.P., Leclerc, B., Monjardet B., (1986) : On the Use of Ordered Sets in Problems of Comparison and Consensus of Classifications, J. of Classification 3, n°2, 187-224. | MR | Zbl

Booth, K.S., Leuker, G.S., (1976) : Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comput. Syst. Sci. 13, 335-379. | MR | Zbl

Day, W.H.E., (1981) : "The Complexity of Computing Metric Distances between Partitions", Mathematical Social Sciences, 1, 269-287. | MR | Zbl

Day, W.H.E., (1983a) : "The Role of Complexity in Comparing Classifications ", Mathematical Biosciences, 66, 97-114. | MR | Zbl

Day, W.H.E., (1983b) : "Computationally Difficult Parsimony Problems in Phylogenetic Systematics", Journal of Theoretical Biology, 103, 429-438. | MR

Day, W.H.E., (1985) : "Optimal Algorithms for Comparing Trees with Labelled Leaves", Journal of Classification, 2, 7-28. | MR | Zbl

Day, W.H.E., Sankoff, D., (1986) : The computational Complexity of Inferring Phylogenics by Compatibility, Syst. Zool. 35, n°2, 224-229.

Day, W.H.E., Wells, R.S., (1984) : "Extremes in the Complexity of Computing Metric Distances between Partitions", IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6, 69-73. | Zbl

Golumbic, M.C., (1980) : Algorithmic graph theory and perfect graphs, Academic Press, New-York. | MR | Zbl

Leclerc, B., (1987) : Arbres minimums communs et compatibilité de données de types variés, Mathématiques et Sciences humaines, 98, 41-67. | EuDML | Numdam | MR | Zbl

Wakabayashi, Y., (1985) : Aggregation of Binary Relations : algorithmic and polyhedral investigations, thèse, Universität Augsburg. | Zbl

Guenoche, A., (1982-1986) : Programmes ABCD (Analyse Booléenne et Combinatoire de Données) : sous-tableaux de Robinson, sériation, arbres de Buneman.

Felsenstein, J., et al., (1980-1986) : Package PHYLIP (Phylogeny Inference Package) : inclut notamment un programme de calcul de hiérarchies consensus.