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

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 includes a collection of papers awarded on the biannual assembly of the class and knowledge research workforce of Societa Italiana di Statistica, which was once held in Rome, July 5-6, 1999. From the initially submitted papers, a cautious evaluate method resulted in the choice of forty five papers awarded in 4 elements as follows: class AND MULTIDIMENSIONAL SCALING Cluster research Discriminant research Proximity buildings research and Multidimensional Scaling Genetic algorithms and neural networks MUL TIV ARIA TE information research Factorial tools Textual information research Regression versions for facts research Nonparametric tools SPATIAL AND TIME sequence facts research Time sequence research Spatial information research CASE reports foreign FEDERATION OF category SOCIETIES The foreign Federation of type Societies (IFCS) is an supplier for the dissemination of technical and medical details bearing on class and knowledge research within the wide experience and in as huge a variety of purposes as attainable; based in 1985 in Cambridge (UK) from the next medical Societies and teams: British type Society -BCS; type Society of North the USA - CSNA; Gesellschaft fUr Klassifikation - GfKI; eastern class Society -JCS; category workforce of Italian Statistical Society - CGSIS; Societe Francophone de type -SFC. Now the IFCS comprises additionally the next Societies: Dutch-Belgian type Society - VOC; Polish type Society -SKAD; Associayao Portuguesa de Classificayao e Analise de Dados -CLAD; Korean class Society -KCS; Group-at-Large.

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This "result" can be generalised to the case of M classifications and obtain M-m c(i, j) =--;;;-' with m = 0,1, ... , M denoting the number of partitions in which the pair (i,j) belongs to different clusters. e. e. m=O); • c(i,j) decreases as m increases, that is as the number of partitions in which (i,j) belongs to different clusters increases. The Euclidean distance on the other hand is tl(i,j)=2·M(l-c(i,j))=2M. It follows that: • tl(i,j)=O if (i,j) belongs to the same cluster in all of the classifications; • tl(i,j)=2M if (i,j) belongs to different cluster in all of the partitions; • tl(i,j) increases as the number of partitions in which (i,j) belongs to different clusters increases.

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:$; VG--1. so that MG--I :$; MG.

D(G,G), the partitions obtained by applying AA and DA respectively (in the following, A-partition and Dpartition). Let n(A(h,G) n D(k,G») indicate the number of cases which are simultaneously placed in A(h,G), the h-th group of the A -partition, and in D(k,G), the k-th group of the D- partition: this quantity measures the degree of overlapping between A(h,G) and D(k,G)' Moreover, the overlapping between the two partitions can be measured by Lgn(A(g,G) n D(g,G»), and the indices of the clusters of the two partitions are selected in such a way that the overlapping is maximum.

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