Mahalanobis distance

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

Three Mahalanobis distances and their role in assessing unidimensionality.

Abstract: Unidimensionality is the hallmark psychometric feature of a well-constructed measurement scale. However, in determining the degree to which a set of items form a unidimensional scale, aberrant item response patterns may distort our investigations. For example, aberrant response patterns may adversely impact interitem covariances which, in turn, can distort estimates of a scale's dimensionality and reliability. In this study, we investigate and compare the utility of three Mahalanobis distance (M-distance) measures in identifying and downweighting aberrant item response patterns. Our findings indicated that a residual-based M-distance measure had the best properties. Specifically, response patterns having greater residual-based M-distances were responsible for observed violations of unidimensionality. When these response patterns were properly downweighted according to this M-distance, the data fitted a one-factor model better and scale reliability increased. The procedures are illustrated using three real data sets.

Automatic Fungal Disease Detection based on Wavelet Feature Extraction and PCA Analysis in Commercial Crops

Abstract: This paper describes automatic detection and classification of v isual symptoms affected by fungal disease. Algorithms are developed to acquire and process color images of fungal disease affected on commercial crops like chili, cotton and sugarcane. The developed algorith ms are used to preprocess, segment, extract and reduce features fro m fungal affected parts of a crop. The feature extract ion is done with discrete wavelet transform (DWT) and features are further reduced by using Principal co mponent analysis (PCA). Reduced features are then used as inputs to classifiers and tests are performed to classify image samples. We have used statistical based Mahalanobis distance and Probabilistic neural network (PNN) classifiers. The average classification accuracies using Mahalanobis distance classifier are 83.17% and using PNN classifier are 86.48%.

A new concept of quantiles for directional data and the angular Mahalanobis depth

Abstract: In this paper, we introduce a new concept of quantiles and depth for directional (circular and spherical) data. In view of the similarities with the classical Mahalanobis depth for multivariate data, we call it the angular Mahalanobis depth. Our unique concept combines the advantages of both the depth and quantile settings: appealing depth-based geometric properties of the contours (convexity, nestedness, rotation-equivariance) and typical quantile-asymptotics, namely we establish a Bahadur-type representation and asymptotic normality (these results are corroborated by a Monte Carlo simulation study). We introduce new user-friendly statistical tools such as directional DD- and QQ-plots and a quantile-based goodness- of-fit test. We illustrate the power of our new procedures by analyzing a cosmic rays data set.

Taxonomic congruence in Eskimoid populations.

Abstract: The study compares distance relationships in Eskimoid populations based on metric and attribute data with linguistic relationships based on structural and lexicostatistical data. Taxonomic congruence and the non-specificity hypothesis are investigated by matrix correlations and by a clustering procedure. The matrix correlation approaches employed are the Pearson product-moment correlation coefficient and the Spearman rank-order correlation coefficient. An unweighted pair-group clustering procedure provides a visual comparison of biological and linguistic relationships. Data consist of 74 craniometric measurements and 28 cranial observations taken on 12 Eskimoid populations. Mahalanobis' D2 and Balakrishnan and Sanghvi's B2 were used to compute the metric and attribute distances, respectively. The results indicate that a strict adherence to the non-specificity hypothesis is untenable. Also, there is better concordance between the sexes for metric distances than for attribute distances, and the metric data are more concordant with linguistic relationships than are the attribute data.

Re‐evaluating the role of the Mahalanobis distance measure

Abstract: It is shown that the sum of squares of the standardised scores of all non-zero principal components (PCs) equals the squared Mahalanobis distance. A new distance measure, the reduced Mahalanobis distance, is explored in which the number of PCs retained is less than the full rank model. It is illustrated by both one-class and two-class classifiers. Linear discriminant analysis can be employed as a soft model, and principal component analysis using the pooled variance-covariance matrix is introduced as an intermediate view between conjoint and disjoint models allowing linear discriminant analysis to be used on these reduced rank models. By choosing the most discriminatory PCs, it can be shown that the reduced Mahalanobis distance has superior performance over the full rank model for discriminating via soft models. Copyright © 2016 John Wiley & Sons, Ltd.