Mahalanobis distance

About: Mahalanobis distance is a research topic. Over the lifetime, 4616 publications have been published within this topic receiving 95294 citations.

A strategy on constructing core collections by least distance stepwise sampling

Abstract: A strategy was proposed for constructing core collections by least distance stepwise sampling (LDSS) based on genotypic values. In each procedure of cluster, the sampling is performed in the subgroup with the least distance in the dendrogram during constructing a core collection. Mean difference percentage (MD), variance difference percentage (VD), coincidence rate of range (CR) and variable rate of coefficient of variation (VR) were used to evaluate the representativeness of core collections constructed by this strategy. A cotton germplasm collection of 1,547 accessions with 18 quantitative traits was used to construct core collections. Genotypic values of all quantitative traits of the cotton collection were unbiasedly predicted based on mixed linear model approach. By three sampling percentages (10, 20 and 30%), four genetic distances (city block distance, Euclidean distance, standardized Euclidean distance and Mahalanobis distance) combining four hierarchical cluster methods (nearest distance method, furthest distance method, unweighted pair-group average method and Ward’s method) were adopted to evaluate the property of this strategy. Simulations were conducted in order to draw consistent, stable and reproducible results. The principal components analysis was performed to validate this strategy. The results showed that core collections constructed by LDSS strategy had a good representativeness of the initial collection. As compared to the control strategy (stepwise clusters with random sampling strategy), LDSS strategy could construct more representative core collections. For LDSS strategy, cluster methods did not need to be considered because all hierarchical cluster methods could give same results completely. The results also suggested that standardized Euclidean distance was an appropriate genetic distance for constructing core collections in this strategy.

Regionalization in geology by multivariate classification

Abstract: The concept of multivariate classification of “geological objects” can be combined with the concept of regionalized variables to yield a procedure for typification of geological objects, such as rock units, well records, or samples. Numerical classification is followed by subdivision of the area of investigation, and culminates in a regionalization or mapping of the classification onto the plane. Regions are subdivisions of the map area which are spatially contiguous and relatively homogeneous in their geological properties. The probability of correct classification of each point within a region as being part of that region can be assessed in terms of Bayesian probability as a space-dependent function. The procedure is applied to subsurface data from western Kansas. The geologic properties used are quantitative variables, and relationships are expressed by Mahalanobis' distances. These functions could be replaced by other metrics if qualitative or binary data derived from geological descriptions or appraisals were included in the analysis.

Mahalanobis distance and its application for detecting multivariate outliers

Abstract: While methods of detecting outliers is frequently implemented by statisticians when analyzing univariate data, identifying outliers in multivariate data pose challenges that univariate data do not. In this paper, after short reviewing some tools for univariate outliers detection, the Mahalanobis distance, as a famous multivariate statistical distances, and its ability to detect multivariate outliers are discussed. As an application the univariate and multivariate outliers of a real data set has been detected using R software environment for statistical computing.