Advances in Classification and Data Analysis by D. Bruzzese, A. Irpino (auth.), Dr. Simone Borra, Professor

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

This quantity incorporates a choice of papers offered on the biannual assembly of the class and information research team of Societa Italiana di Statistica, which used to be held in Rome, July 5-6, 1999. From the initially submitted papers, a cautious assessment method resulted in the choice of forty five papers offered 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 information research Regression types for info research Nonparametric equipment SPATIAL AND TIME sequence facts research Time sequence research Spatial facts research CASE stories overseas FEDERATION OF type SOCIETIES The overseas Federation of class Societies (IFCS) is an supplier for the dissemination of technical and medical details bearing on type and information research within the extensive feel and in as vast quite a number purposes as attainable; based in 1985 in Cambridge (UK) from the subsequent clinical Societies and teams: British class Society -BCS; type Society of North the US - CSNA; Gesellschaft fUr Klassifikation - GfKI; jap type Society -JCS; class crew of Italian Statistical Society - CGSIS; Societe Francophone de class -SFC. Now the IFCS comprises additionally the next Societies: Dutch-Belgian type Society - VOC; Polish category Society -SKAD; Associayao Portuguesa de Classificayao e Analise de Dados -CLAD; Korean type Society -KCS; Group-at-Large.

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These two step procedures, called "tandem analysis" or "tandem clustering", have been warned against by several authors (Arabie and Hubert, 1994, De Soete e Carrol, 1994), because the first few components or factors of X do not necessarily define a subspace that is the most informative about the cluster structure in the data but on the contrary it may obscure or mask the taxonomic information in X. These warnings suggest the third approach to directly classify units on the basis of each group of variables.

Nil) + (nk. l)-(ni. -nj{)-(nk. n-n,l-ni. Jnilnkl [n-n,l-2(ni. -nil +nk. -nkl) ] i=1 k=i+1 i=1 The number of comparisons considered is: Finally we obtain the isolation of the cluster gl for one qualitative variable: A similar procedure can be applied to calculate 0i gl) for an ordinal or a quantitative variable. Having fixed the number of groups L, the classification algorithm starts from an initial partition and then tries to move the units from one group to another until the criterion (11) converges.

Referring now to a G-structure, C(I,G), ... G), a measure of the within-groups S. Borra et al. ), Advances in Classification and Data Analysis © Springer-Verlag Berlin Heidelberg 2001 36 dispersion is VG = Lg Vg,G = Lg ~ n(C(g,G»)Vq(C(g,G»' By construction, it is always VG0:$; VG:$; VI, VI being a measure of the total dispersion. A possible measure of the quality of the G-structure is then MG = (VI - VG)/JtI. Moreover, if the groups are obtained following a hierarchical (divisive or agglomerative) procedure, it is VG:$; VG--1.

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