Advances in Data Science and Classification: Proceedings of by J. Douglas Carroll, Anil Chaturvedi (auth.), Professor

By J. Douglas Carroll, Anil Chaturvedi (auth.), Professor Alfredo Rizzi, Professor Maurizio Vichi, Professor Dr. Hans-Hermann Bock (eds.)

The publication presents new advancements in class and knowledge research, and provides new issues that are of relevant curiosity to trendy statistics. specifically, those comprise category conception, multivariate information research, multi-way facts, proximity constitution research, new software program for class and information research, and functions in social, monetary, clinical and different sciences. for lots of of those subject matters, this booklet presents a scientific cutting-edge written by means of most sensible researchers on the planet. This e-book will function a beneficial creation to the realm of type and information research for study staff and help the move of latest advances in info technology and category to a variety of functions.

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Additional info for Advances in Data Science and Classification: Proceedings of the 6th Conference of the International Federation of Classification Societies (IFCS-98) Università “La Sapienza”, Rome, 21–24 July, 1998

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K. uk Abstract: Much of the classification literature ignores notions of probability. In our view, this is due in part to a dominant tendency in the early days of computers for developing heuristic clustering algorithms and in part due to long traditions in classification outside the statistical/probabilistic orbit, of which biological taxonomy and book classification are primary examples. Statisticians have rightly stressed the role of probabilistic concepts in formulating classification problems and in interpreting classifications but we believe that they are wrong in suggesting, as they sometimes seem to, that other approaches are unsatisfactory.

Dk is constituted by the k subgroups Ci of points such that the sum of the Lebesgue measures of their disjoint convex hulls H(Ci ) is minimum (1 ~ i ~ k) (Hardy and Rasson (1982); Hardy (1983)). The hypervolume clustering criterion is thus defined as W(P, k) = k L m(H(Ci )) i = I where P is a partition of the observed points into k clusters, H(Ci ) is the convex hull of the points belonging to Ci and m(H(Ci )) is the m-dimensional Lebesgue measure of that convex hull. 3. Methods to determine the number of clusters The first six indices - those whose performance was best in Milligan and Cooper's (1985) study - are the the Calinski and Harabasz (1974) method (MI)' the J index (Duda and Hart (1973)) (M2)' the C index (Hubert and Levin (1975)) (M3)' the 'Y index (Goodman and Kruskal (1954)) (M4), the Beale (1969) test (M5)' and the Cubic Clustering Criterion (M6) (Sarle, 1983).

References: BEALE, E. M. L. (1969): Euclidean cluster analysis. Bulletin of the International Statistical Institute, 43, 2, 92-94. , and HARABASZ, J. (1974): A dendrite method for cluster analysis. Communications in Statistics, 3, 1-27. E. (1973): Pattern Classification and Scene Analysis. Wiley, New York. A. H. (1954): Measures of association for crossclassifications. Journal of the American Statistical Association, 49, 732-764. D. (1997): How many clusters? An investigation of five procedures for detecting nested cluster structure, in Proceedings of the IFCS-96 Conference, Kobe (in print).

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