Showing papers on "Mahalanobis distance published in 1983"
01 Jan 1983
TL;DR: Numerical taxonomic techniques serve as data-analytic tools in multivariate and multivariable approaches to GVA--without the controversy attending their use in classification.
Abstract: Geographic variation analysis (GVA) and numerical taxonomy have become intimately related. The analysis of single variables distributed over geographic space preceded the development of modern numerical taxonomy. But with the introduction of multivariate statistical techniques into GVA, the two areas began to approach each other until today they intergrade smoothly. Multivariate analysis for designs of k population samples, each based on p variables, permits the computation of multiple discriminant functions, Mahalanobis’ generalized distance, and canonical variate analysis, among others. Such techniques result in distance matrices among locality samples which can be treated by the techniques of numerical taxonomy. If phenetic resemblances of locality samples correspond to their spatial proximities, the former could be interpreted in terms of their spatial relationships and of the evolutionary processes that operate in the spatial context. Numerical taxonomic techniques also include regional clustering, i.e., phenetic clustering with the clusters subject to additional spatial constraints--a useful technique for GVA. Finally, numerical taxonomic techniques serve as data-analytic tools in multivariate and multivariable approaches to GVA--without the controversy attending their use in classification.
35 citations
TL;DR: In this paper, the characteristics of classical discriminant analysis under the random effects model are investigated, assuming that the elements within any randomly selected population are normally distributed with mean vector μ and common covariance matrix Σ, and that over different populations, the distribution of the population-based and sample-based Mahalanobis distances between two different populations.
Abstract: In this article the characteristics of classical discriminant analysis under the random-effects model are investigated. Assuming that the elements within any randomly selected population are normally distributed with mean vector μ and common covariance matrix Σ, and that over different populations μ has a normal distribution with mean vector ξ and covariance matrix T, the distribution of the population-based and sample-based Mahalanobis distances between two different populations, as well as those between an observation and a randomly selected population, are derived. From these, expressions and bounds are derived for the expected probabilities of misclassification under classical discriminant analysis, applied to two- and multiple population problems respectively, when either the population-based or the sample-based linear discriminant functions are used.
8 citations
01 Nov 1983
TL;DR: It is shown that the moments of the interclass Mahalanobis distance between elements of two d-variate Gaussian populations can be expressed in a simple polynomial form.
Abstract: It is shown that the moments of the interclass Mahalanobis distance between elements of two d-variate Gaussian populations can be expressed in a simple polynomial form. The nth moment is expressible as a polynomial of order n whose variable depends on the mean vectors and eigenvalues of the covariance matrices. A closed-form solution is given for computing the coefficients of the polynomial expressions.
3 citations
14 Apr 1983
TL;DR: In this work several distance classifiers are evaluated for use in text-independent speaker identification and it is found that both the maximum a posteriori probability criterion and the correlation distance measure yield extremely poor results.
Abstract: A survey of research efforts in the area of speaker recognition indicate that for the same choice of speaker-dependent speech parameters the recognition accuracy is significantly affected by the distance measure used. In this work several distance classifiers are evaluated for use in text-independent speaker identification. The four distance measures investigated are the Mahalanobis distance, maximum a posteriori probability, nearest neighbor criterion and the correlation distance measure. It is found that both the maximum a posteriori probability criterion and the correlation distance measure yield extremely poor results. The Mahalanobis distance and the nearest neighborhood criterion yield relatively poor results (error \sim20-30 %) with the former consistently superior to the latter. It is shown that these scores can be improved through a proposed variation of the nearest neighbor method.
1 citations
TL;DR: The method proposed is based on examining distances of all observations from the estimated locations of each sample, extensions of the Mahalanobis distance, where the classical means and covariances are replaced by robust estimates.
Abstract: We consider the problem of comparing samples drawn from several subpopulations when the data are multivariate. The method proposed is based on examining distances of all observations from the estimated locations of each sample. The distances examined are extensions of the Mahalanobis distance, where the classical means and covariances are replaced by robust estimates. The analysis of the distances is done by informal graphical methods. The method is illustrated by an example in which three groups of patients are compared with respect to thirteen variables measuring nerve conduction.