Data Analysis, Classification and the Forward Search: by Roberto Baragona, Salvatore Vitrano (auth.), Prof. Sergio

By Roberto Baragona, Salvatore Vitrano (auth.), Prof. Sergio Zani, Prof. Andrea Cerioli, Prof. Marco Riani, Prof. Maurizio Vichi (eds.)

This quantity includes revised types of chosen papers offered on the biennial assembly of the category and knowledge research workforce (CLADAG) of the Italian Statistical Society, which used to be held in Parma, June 6-8, 2005. Sergio Zani chaired the medical Programme Committee and Andrea Cerioli chaired the neighborhood Organizing Committee. The clinical programme of the convention incorporated 127 papers, forty two in spe­ cialized periods, sixty eight in contributed paper periods and 17 in poster classes. additionally, it used to be attainable to recruit 5 awesome and across the world well known invited audio system (including the 2004-2005 President of the overseas Fed­ eration of class Societies) for plenary talks on their present learn paintings. one of the really good classes, have been prepared by way of Wolfgang Gaul with 5 talks by way of contributors of the GfKl (German type Society), and one through Jacqueline J. Meulman (Dutch/Flemish type Society). hence, the convention supplied loads of scientists and specialists from domestic and overseas with an enticing discussion board for dialogue and mutual trade of data. the subjects of all plenary and really expert classes have been selected to slot, within the broadest attainable feel, the challenge of CLADAG, the purpose of that is "to additional methodological, computational and utilized learn in the fields of category, facts research and Multivariate Statistics". A peer-review refereeing method ended in the choice of forty six prolonged papers, that are contained during this book.

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From the view points of functional data analysis, we assume that we have p-dimensional functions corresponding to n objects. We denote the functions for n objects depending on a variable t as Z{t) = {zi{t)}{i = 1, 2 , . . , n). It is realistic that values Z{tj){j = 1, 2 , . . , m) are given. We restrict ourselves Graphical Representation of Functional Clusters and MDS 33 to two dimensional functional data and to the one dimensional domain. The number of clusters k is prespecified as a user parameter.

2 Graphical Representations of Functional Clustering The purpose of cluster analysis is to find relatively homogeneous clusters of objects based on measured characteristics. Sometimes, we divide methods of cluster analysis into two groups: hierarchical clustering methods and nonhierarchical clustering methods. Hierarchical clustering refers to the formation of a recursive clustering of the objects data: a partition into two clusters, each of which is itself hierarchically clustered. , n}, where Sij is the dissimilarity between objects i and j , and n is the size of the objects.

2 Selected Results According to the J [/MP-criterion the optimal number of clusters for the d a t a at hand is 37. The G K M algorithm also results in a 37-cluster solution, where sets of 174 to 394 individual consumer profiles are assigned to 15 meaningful clusters with centroids ^ 1 , . . ,^15. Moreover, 22 outliers are assigned to single-object clusters. Applying the SGNN algorithm with auax = 81 ( = L) results in a neural network t h a t comprises 14 prototypes ^ 1 , . . , ^14.

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