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By Carmela Cappelli, Francesco Mola (auth.), Prof. Dr. Hans-Hermann Bock, Prof. Marcello Chiodi, Prof. Antonino Mineo (eds.)

This quantity includes a number of papers awarded through the biennial assembly of the class and knowledge research workforce (CLADAG) of the Societa Italiana di Statistica which used to be orga­ nized through the Istituto di Statistica of the Universita degli Studi di Palermo and held within the Palazzo Steri in Palermo on July 5-6, 2001. For this convention, and after checking the submitted four­ web page abstracts, fifty four papers have been admitted for presentation. They lined a wide range of themes from multivariate info research, with specified emphasis on category and clustering, computa­ tional records, time sequence research, and functions in a variety of classical or contemporary domain names. A two-fold cautious reviewing technique ended in the choice of twenty-two papers that are offered during this vol­ ume. they communicate both a brand new proposal or technique, current a brand new set of rules, or situation a fascinating software. we now have clustered those papers into 5 teams as follows: 1. type equipment with purposes 2. Time sequence research and comparable tools three. computing device in depth suggestions and Algorithms four. category and information research in Economics five. Multivariate research in technologies. In each one part the papers are prepared in alphabetical order. The editors - of them the organizers of the CLADAG confer­ ence - want to convey their gratitude to the authors whose enthusiastic participation made the assembly attainable and intensely successful.

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Extra resources for Advances in Multivariate Data Analysis: Proceedings of the Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society, University of Palermo, July 5–6, 2001

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And t nThe decrease in impurity in (12) is very similar to the criteria in (4) and (6): the so called anti- end- cut factor (PLPR) is combined with a measure of the dissimilarity between the two distribution of Y in t t. and t n , such a measure depending upon the nature of the response variable (notice that in the quantitative case the difference between the distributions is measured by the distance between the means of Y within the two sub-nodes). Ho respectively we now consider an application to a real data set.

Consider a node t , and suppose it is partitioned into two subgroups t L and t n by split s. In CART the decrease in impurity achieved when passing from t to ti. and t n is defined as: where PL and PR denote the proportion of cases in tt. and in t n . Hdt , s) ex: L1Sdt, s) = eUtL - Yt)2 pL + ('f}tR - Yt)2 pR = PLPR(YtL - YtR)2 (7) Notice that the decrease in impurity in (4) and (6) is given by the difference between total heterogeneity and within nodes heterogeneity, coinciding with the between nodes heterogeneity.

00025 K-A r 1/ 2 4 126 - 17249 QU_A 5 210 -5 203987 Table 5. 00028 160 - 27814 190 -5 - 166982 Situation 2 Fig. 3. Filtered images two sit uat ions, ranging from mod erat e to great difficulty of classificat ion. 100 replications were obtained with identical st atisti cal properti es. The perform ance of t he classifier was measured through the error rat e of classification, which was est imated by th e Mont e Carlo method. The est imated error rat e of classification corresponds to th e average of th e error rat es found for t hese replications.

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