A clustering method based on the \(L_ 1\)-norm
type: Item
instance of: scholarly article
title: A clustering method based on the \(L_ 1\)-norm
zbMATH Open document ID: 0624.62058
DOI: 10.1016/0167-9473(87)90058-2
author: Krzysztof Jajuga
published in: Computational Statistics and Data Analysis
publication date: 1987-01-01T00:00:00Z
review text: \textit{G. H. Ball} and \textit{D. J. Hall} [A clustering technique for summarizing multivariate data. Behavioral Science 12, 153-165 (1967)] developed the ISODATA clustering method based on Euclidean distance. In this paper a version of the ISODATA method based on the \(L_ 1\)-norm is given. It is proved that the optimal location parameter vectors for each class of observations are median vectors. An iterative algorithm to obtain the classification of observations and the optimal location parameter vectors is given. The results of Monte Carlo studies of the performance of this method for bivariate normal and bivariate Laplace distributions are presented. Some comparisons of this method and the classical ISODATA method are made.
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 65C99
zbMATH DE Number: 4013783
zbMATH Keywords: L1-norm
zbMATH Keywords: ISODATA clustering method
zbMATH Keywords: optimal location parameter vectors
zbMATH Keywords: median vectors
zbMATH Keywords: iterative algorithm
zbMATH Keywords: classification
zbMATH Keywords: Monte Carlo studies
zbMATH Keywords: bivariate normal
zbMATH Keywords: bivariate Laplace distributions
MaRDI profile type: Publication
full work available at URL: 0167-9473(87)90058-2
OpenAlex ID: W2073149227
cites work: Q5585021
description: scientific article; zbMATH DE number 4013783