Statistical geometry and classification: Tools for each other
type: Item
instance of: scholarly article
zbMATH Open document ID: 1001.62006
author: Didier Jacquemin
author: J. P. Rasson
publication date: 2002-11-26T00:00:00Z
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62H30
zbMATH DE Number: 1577763
zbMATH Keywords: classification
zbMATH Keywords: discriminant rules
zbMATH Keywords: statistical geometry
zbMATH Keywords: convex hull
zbMATH Keywords: convex support
zbMATH Keywords: partitioning
MaRDI profile type: Publication
title: Statistical geometry and classification: Tools for each other
review text: This paper shows some relationships between statistical geometry and classification rules. The first conclusion given is that whatever area one is considering, it is always an expansion of the convex hull of the sample from its centroid. Part two of the paper describes some aspects of classification and discrimination for convex clusters, such as the partitioning problem, the maximum likelihood solution to the clustering problem with corresponding discriminant rules and statistical geometry as a rule. In Part three it is shown how to estimate the inside-outside version of the convex support of a uniform distribution using the classical approach and discriminant analysis.NEWLINENEWLINENEWLINEPart four demonstrates how classification and discriminant analysis for nonconvex clusters work. The partitioning problem is reformulated, and then the maximum likelihood solution to the clustering problem and corresponding discriminant rules are given. Finally an open problem on the estimation of the nonconvex support of a uniform distribution is presented. Graphical examples illustrate the problems handled in the paper. Exact mathematical proofs are not given for most problems.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00040].
description: scientific article