Mahalanobis distance

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

New Trends in Multivariate Diagnosis

Abstract: Taguchi Methods, also called Robust Design, have been successfully applied in many engineering applications to improve the performance of the product/process. These methods are proved to be extremely useful and cost effective. In this paper we will describe how Taguchi Methods are useful in multidimensional system applications. We use Mahalanobis distance (MD) for constructing a measurement scale for the multidimensional systems and the principles of Taguchi Methods for optimizing the system. Therefore, we refer to this procedure as the Mahalanobis-Taguchi-System (MTS). The measures and methods used in MTS are data analytic rather than usual probability based inference. In this paper, a detailed procedure of MTS is explained with two case studies.

A robust background subtraction method for changing background

Abstract: Background subtraction is a useful and effective method for detecting moving objects in video images. Since this method assumes that image variations are caused only by moving objects (i.e., the background scene is assumed to be stationary), however, its applicability is limited. In this paper, we propose a background subtraction method that robustly handles various changes in the background. The method learns the chronological changes in the observed scene's background in terms of distributions of image vectors. The method operates the subtraction by evaluating the Mahalanobis distances between the averages of such image vectors and newly observed image vectors. The method we propose herein expresses actual changes in the background using a multi-dimensional image vector space. This enables the method to detect objects with the correct sensitivity. We also introduce an eigenspace to reduce the computational cost. We describe herein how approximate Mahalanobis distances are obtained in this eigenspace. In our experiments, we confirmed the proposed method's effectiveness for real world scenes.

Incorporating distance constraints into species distribution models

Abstract: Summary 1. Species distribution models (SDM) are increasingly applied as predictive tools for purposes of conservation planning and management. Such models rely on the concept of the ecological niche and assume that distribution patterns of the modelled species are at some sort of equilibrium with the environment. This assumption contrasts with empirical evidence indicating that distribution patterns of many species are constrained by dispersal limitation. 2. We demonstrate that the performance of SDM based on presence-only data can be significantly enhanced by incorporating distance constraints (functions relating the likelihood of species’ occurrences at a site to the distance of the site from known presence locations) to the modelling procedure. This result is highly consistent for a variety of niche-based models (ENFA, DOMAIN and Mahalanobis distance), distance functions (nearest neighbour distance, cumulative distance and Gaussian filter) and taxonomic groups (plants, snails and birds, a total of 226 species). 3. Distance constraints are expected to enhance the accuracy of niche-based models even in the absence of strong dispersal limitation by accounting for mass effects and spatial autocorrelation in environmental factors for which data are not available. 4. While distance-based methods outperformed niche-based models when all data were used, their accuracy deteriorated sharply with smaller sample sizes. Niche-based methods are shown to cope better with small sample sizes than distance-based methods, demonstrating the potential advantage of niche-based models when calibration data are limited. 5. Synthesis and applications. Incorporating distance constraints in SDM provides a simple yet powerful method to account for spatial autocorrelation in patterns of species distribution, and is shown empirically to improve significantly the performance of such models. We therefore recommend incorporating distance constraints in future applications of SDM.

Discriminant analysis in correlation similarity measure space

Abstract: Correlation is one of the most widely used similarity measures in machine learning like Euclidean and Mahalanobis distances. However, compared with proposed numerous discriminant learning algorithms in distance metric space, only a very little work has been conducted on this topic using correlation similarity measure. In this paper, we propose a novel discriminant learning algorithm in correlation measure space, Correlation Discriminant Analysis (CDA). In this framework, based on the definitions of within-class correlation and between-class correlation, the optimum transformation can be sought for to maximize the difference between them, which is in accordance with good classification performance empirically. Under different cases of the transformation, different implementations of the algorithm are given. Extensive empirical evaluations of CDA demonstrate its advantage over alternative methods.

The Influence Function as an Aid in Outlier Detection in Discriminant Analysis

Abstract: The influence function is used to develop criteria for detecting outliers in discriminant analysis. For Mahalanobis' D2, the influence function is a quadratic function of the deviation of the discriminant score for the perturbed observation from the discriminant score for the mean of the corresponding group. A X2 approximation to the null distribution of the influence function values appears to be suitable for graphical representation.