By D. Bruzzese, A. Irpino (auth.), Dr. Simone Borra, Professor Roberto Rocci, Professor Maurizio Vichi, Professor Dr. Martin Schader (eds.)

ISBN-10: 3540414886

ISBN-13: 9783540414889

ISBN-10: 3642594719

ISBN-13: 9783642594717

This quantity incorporates a choice of papers awarded on the biannual assembly of the class and information research team of Societa Italiana di Statistica, which was once held in Rome, July 5-6, 1999. From the initially submitted papers, a cautious evaluate strategy resulted in the choice of forty five papers provided in 4 components as follows: type AND MULTIDIMENSIONAL SCALING Cluster research Discriminant research Proximity constructions research and Multidimensional Scaling Genetic algorithms and neural networks MUL TIV ARIA TE info research Factorial tools Textual info research Regression types for info research Nonparametric equipment SPATIAL AND TIME sequence facts research Time sequence research Spatial facts research CASE experiences foreign FEDERATION OF type SOCIETIES The foreign Federation of category Societies (IFCS) is an company for the dissemination of technical and clinical details referring to type and knowledge research within the large feel and in as huge a number functions as attainable; based in 1985 in Cambridge (UK) from the subsequent clinical Societies and teams: British category Society -BCS; category Society of North the USA - CSNA; Gesellschaft fUr Klassifikation - GfKI; jap type Society -JCS; class staff of Italian Statistical Society - CGSIS; Societe Francophone de class -SFC. Now the IFCS comprises additionally the next Societies: Dutch-Belgian class Society - VOC; Polish category Society -SKAD; Associayao Portuguesa de Classificayao e Analise de Dados -CLAD; Korean category Society -KCS; Group-at-Large.

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Gifi, A. (1990) Nonlinear multivariate analysis. New York: Wiley. Gnanadesikan R, Kettenring J. , Ldwehr, 1. M. (1982) Projection plots for displaying clusters. In Statistics ad Probability: Essays in Honor of C. R. Rao (G. Kalliapur, P. R. Krishnaiah & 1. K. Ghosh, eds), North-Holland, Amsterdam, 269-80. , Cucumel G. (1987) Consensus en classification: une revue bibliographique. Mathematiques et Sciences Humaines, 100, 109-128. MacQueen, J. (1967) Some methods for classification and analysis of multivariate observations.

Let X=[Xip] be a (n x k) two-way two-mode (objects by variables) data matrix, regarding the k-variate profiles of n objects. Without loss of generality we suppose that variables are standardized, in order to exclude, in the application of classifications, problems connected with different units of measurements of variables. For the convenience of the reader the terminology used in this paper is listed here: n,k I ={o(, ... ,on}; V={V(, ... ,Vk} p={p\, ... ,Pc } Q={Q\, ... ,Qm} U=[uy] V=[vpd C=[CjI] number of objects, and number of variables to be classified; set of n objects to be classified; set of k variables to be classified; partition of I into C classes, where Pj is the jth class of P; partition of V into m classes, where Qt is the /th class of Q; n x c membership function matrix, assuming values in [0, 1], specifying for each object 0i its membership to class Pj' Matrix U, in this case, identifies a fuzzy classification of objects.

M; (fuzzy variable classification) (4) (4') p==I, ... ,k; (variable partitioning) (5) p=l, ... ,k; (variable covering) (5') p=l, ... ,k; (variable packing) 1=1 or m ~>pl ~ 1 1=1 (5") 46 Several classification problems are defined by combining constraints program [PI]; some relevant cases are listed below: ill the (i) [PI] subject to (2), (3), (4) and (5) identifies a hard partition of both objects and variables; (ii) [PI] subject to (2'), (3), (4') and (5) identifies a fuzzy partition both of objects and variables; (iii) [PI] subject to (2), (3), (4') and (5) identifies a hard partition of objects and a fuzzy partition of variables; (iv) [PI] subject to (2), (3), (4') and (5') identifies a hard partition of objects and a fuzzy covering of variables; (v) [PI] subject to (2'), (3'), (4') and (5') identifies a fuzzy covering both of objects and variables; (vi) [PI] subject to (2'), (3), (4) and (5) identifies a fuzzy partition of the objects and a hard partition of the variables; (vii)[PI] subject to (2'), (3'), (4) and (5) identifies a fuzzy covering of the objects and a hard partition of the variables.

### Advances in Classification and Data Analysis by D. Bruzzese, A. Irpino (auth.), Dr. Simone Borra, Professor Roberto Rocci, Professor Maurizio Vichi, Professor Dr. Martin Schader (eds.)

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