Mahalanobis distance

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

Learning Bregman Distance Functions for Semi-Supervised Clustering

Abstract: Learning distance functions with side information plays a key role in many data mining applications. Conventional distance metric learning approaches often assume that the target distance function is represented in some form of Mahalanobis distance. These approaches usually work well when data are in low dimensionality, but often become computationally expensive or even infeasible when handling high-dimensional data. In this paper, we propose a novel scheme of learning nonlinear distance functions with side information. It aims to learn a Bregman distance function using a nonparametric approach that is similar to Support Vector Machines. We emphasize that the proposed scheme is more general than the conventional approach for distance metric learning, and is able to handle high-dimensional data efficiently. We verify the efficacy of the proposed distance learning method with extensive experiments on semi-supervised clustering. The comparison with state-of-the-art approaches for learning distance functions with side information reveals clear advantages of the proposed technique.

Power-quality event analysis using higher order cumulants and quadratic classifiers

Abstract: In this paper, we present a novel power-quality (PQ) event detection and classification method using higher order cumulants as the feature parameter, and quadratic classifiers as the classification method. We have observed that local higher order statistical parameters that are estimated from short segments of 50-Hz notch-filtered voltage waveform data carry discriminative features for PQ events analyzed herein. A vector with six parameters consisting of local minimas and maximas of higher order central cumulants starting from the second (variance) up to the fourth cumulant is used as the feature vector. Local vector magnitudes and simple thresholding provide an immediate event detection criterion. After the detection of a PQ event, local maxima and minima of the cumulants around the event instant are used for the event-type classification. We have observed that the minima and maxima for each statistical order produces clusters in the feature space. These clusters were observed to exhibit noncircular topology; hence, quadratic-type classifiers that require the Mahalanobis distance metric are proposed. The events investigated and presented are line-to-ground arcing faults and voltage sags due to the induction motor starting. Detection and classification results obtained from an experimentally staged PQ event data set are presented.

Limitations to mapping habitat-use areas in changing landscapes using the Mahalanobis distance statistic

Abstract: We tested the potential of a GIS mapping technique, using a resource selection model developed for black-tailed jackrabbits (Lepus californicus) and based on the Mahalanobis distance statistic, to track changes in shrubsteppe habitats in southwestern Idaho. If successful, the technique could be used to predict animal use areas, or those undergoing change, in different regions from the same selection function and variables without additional sampling. We determined the multivariate mean vector of 7 GIS variables that described habitats used by jackrabbits. We then ranked the similarity of all cells in the GIS coverage from their Mahalanobis distance to the mean habitat vector. The resulting map accurately depicted areas where we sighted jackrabbits on verification surveys. We then simulated an increase in shrublands (which are important habitats). Contrary to expectation, the new configurations were classified as lower similarity relative to the original mean habitat vector. Because the selection function is based on a unimodal mean, any deviation, even if biologically positive, creates larger Malanobis distances and lower similarity values. We recommend the Mahalanobis distance technique for mapping animal use areas when animals are distributed optimally, the landscape is well-sampled to determine the mean habitat vector, and distributions of the habitat variables does not change.

A Novel Weber Local Binary Descriptor for Fingerprint Liveness Detection

Abstract: In recent years, fingerprint authentication systems have been extensively deployed in various applications, including attendance systems, authentications on smartphones, mobile payment authorizations, as well as various safety certifications. However, similar to the other biometric identification technologies, fingerprint recognition is vulnerable to artificial replicas made from cheap materials, such as silicon, gelatin, etc. Thus, it is especially necessary to distinguish whether a given fingerprint is a live or a spoof one prior to such authentication. In order to solve the problems above, a novel local descriptor named Weber local binary descriptor for fingerprint liveness detection (FLD) has been proposed in this paper. The method consists of two components: the local binary differential excitation component that extracts intensity-variance features and the local binary gradient orientation component that extracts orientation features. The co-occurrence probability of the two components is calculated to construct a discriminative feature vector, which is fed into support vector machine (SVM) classifiers. The effectiveness of the proposed method is intuitively analyzed on the image samples and numerically demonstrated by Mahalanobis distance. Experiments are performed on two public databases from FLD competitions from 2011 and 2013. The results have proved that the proposed method obtains the best detection accuracy among the existing image local descriptors in FLD.