The well known fuzzy partition clustering algorithms are most based on Euclidean distance function, which can only be used to detect spherical structural clusters. Gustafson-Kessel (GK) clustering algorithm and Gath-Geva (GG) clustering algorithm, were developed to detect non-spherical structural clusters, but both of them based on semi-supervised Mahalanobis distance needed additional prior in...

When we estimate the Mahalanobis distance of one point from a cluster of points, there are a number of potential sources of error. This is particularly so if the cluster is strongly correlated, which implies that its covariance matrix is ill-conditioned. Here we analyse the magnitude of the errors introduced by round-off, inversion of nearsingular matrices, and empirical estimation of mean and ...

Some of the well-known fuzzy clustering algorithms are based on Euclidean distance function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, the former needs added constraint of fuzzy covariance matrix, the later can only be used for the d...

Consider ribosomal proteins, each with a three-dimensional spatial location. Proteins related to the cofactor phenotype may be randomly or non-randomly distributed within the ribosome. To investigate this question, the Mahalanobis distance is computed between each pair of protein locations, and the optimal pairing is determined by minimizing the sum of the within-pair distances. Since no single...

Asymptotic linearity plays a key role in estimation and testing in the presence of nuisance parameters. This property is established, in the very general context of a multivariate general linear model with elliptical VARMA errors, for the serial and nonserial multivariate rank statistics considered in Hallin and Paindaveine (2002a and b, 2004a) and Oja and Paindaveine (2004). These statistics, ...

We present a novel technique for the automatic formation of vascular trees from segmented tubular structures. Our method combines a minimum spanning tree algorithm with a minimization criterion of the Mahalanobis distance. First, a multivariate class of connected junctions is defined using a set of trained vascular trees and their corresponding image volumes. Second, a minimum spanning tree alg...

We study algorithms for online nonparametric regression that learn the directions along which the regression function is smoother. Our algorithm learns the Mahalanobis metric based on the gradient outer product matrix G of the regression function (automatically adapting to the effective rank of this matrix), while simultaneously bounding the regret —on the same data sequence— in terms of the sp...