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A ‘maximum‐path’‐based classification
Author(s) -
Scippacercola Sergio
Publication year - 1999
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/(sici)1526-4025(199910/12)15:4<461::aid-asmb409>3.0.co;2-6
Subject(s) - ultrametric space , path (computing) , basis (linear algebra) , mathematics , minimum spanning tree , path length , spanning tree , linearization , mathematical optimization , algorithm , combinatorics , computer science , discrete mathematics , geometry , nonlinear system , metric space , computer network , programming language , physics , quantum mechanics
The aim of this paper is the classification, by means of the maximum path, of n statistical units described by k variables. The method develops in three steps. In the first step, in the minimum spanning tree, among all possible paths, we identify a path of maximum length that is the basis to define a pre‐order on the n statistical units. In the multidimensional space, the maximum path can be considered as a ‘ walk ’ in the mathematical meaning. In the second step, we provide a linearization of the minimum spanning tree with reference to the maximum path. The points on the lateral edges of the maximum path are shifted into the maximum path itself with regard to the ultrametric distance. In the last step, the maximum path and the lateral edges are the basis to use a criterion of constrained classification with barriers. Finally, the method is applied to sets of multidimensional data. Copyright © 1999 John Wiley & Sons, Ltd.