Mahalanobis distance

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

Variational Inference for Mahalanobis Distance Metrics in Gaussian Process Regression

Abstract: We introduce a novel variational method that allows to approximately integrate out kernel hyperparameters, such as length-scales, in Gaussian process regression. This approach consists of a novel variant of the variational framework that has been recently developed for the Gaussian process latent variable model which additionally makes use of a standardised representation of the Gaussian process. We consider this technique for learning Mahalanobis distance metrics in a Gaussian process regression setting and provide experimental evaluations and comparisons with existing methods by considering datasets with high-dimensional inputs.

Variants of cepstrum based speaker identity verification

Abstract: Analysis parameters and various distance measures are investigated for a template matching scheme for speaker identity verification (SIV). Two parameters are systematically varied-the length of the signal analysis window, and the order of the linear predictive coding/-cepstrum analysis. Computational costs associated with the choice of parameters are also considered. The distance measures tested are the Euclidean, inverse variance weighting, differential mean weighting, Kahn's simplified weighting, the Mahalanobis distance, and the Fisher linear discriminant. Using the equal error rate (EER) of pairwise utterance dissimilarity distributions, performance is estimated for prespecified and (a simulation of) user-determined input vocabulary. Performance varies significantly across vocabulary, and average performance is approximately 5% EER for the better algorithms on telephone speech. >

A New Procedure of Clustering Based on Multivariate Outlier Detection

Abstract: Clustering is an extremely important task in a wide variety of ap- plication domains especially in management and social science research. In this paper, an iterative procedure of clustering method based on multivariate outlier detection was proposed by using the famous Mahalanobis distance. At rst, Mahalanobis distance should be calculated for the entire sample, then using T 2 -statistic x a UCL. Above the UCL are treated as outliers which are grouped as outlier cluster and repeat the same procedure for the remaining inliers, until the variance-covariance matrix for the variables in the last cluster achieved singularity. At each iteration, multivariate test of mean used to check the discrimination between the outlier clusters and the inliers. Moreover, multivariate control charts also used to graphically visual- izes the iterations and outlier clustering process. Finally multivariate test of means helps to rmly establish the cluster discrimination and validity. This paper employed this procedure for clustering 275 customers of a famous two- wheeler in India based on 19 dierent attributes of the two wheeler and its company. The result of the proposed technique conrms there exist 5 and 7 outlier clusters of customers in the entire sample at 5% and 1% signicance level respectively.

Determining the Suitability and Accuracy of Various Statistical Algorithms for Satellite Data Classification

Abstract: Land use and land cover (LULC) data is very important for determining the nature and mechanism of different land surface, hydrological processes. The production of land use land cover map, using an image classification is one of the most common applications of remote sensing. However, image classification is a complex process that may be affected by many factors including spatial resolution, classifier used, training sets, etc. This paper briefly reviews the suitability of different methods of classification that are commonly used and their impact on classification accuracy. Three different supervised classification techniques (Maximum likelihood, Mahalanobis Distance, and Minimum Distance) were applied in Kashmir valley for the classification of the IRS LISS-III (2008) image in thirteen different LULC classes; agriculture, aquatic vegetation, barren land, built-up, exposed rock, forest, horticulture, pastures, plantation, riverbed, scrub land, snow, and water. The classified maps where then visually compared with each other and the accuracy of classified map was assessed using the reference data sets which consisted of a large number of ground samples collected in each land cover category. The overall accuracy for Maximum likelihood classifier was 89%, for Mahalanobis distance was 54% and for Minimum distance was 48%. It was observed that the Maximum likelihood method gave the best results and good agreement between classes extracted from the classified maps and field observations. Mahalanobis distance method has overestimated agriculture land, plantation and built-up. Minimum distance method overestimated overestimated water, built-up and horticulture and underestimated agriculture. The selection of a suitable classification method is significant for improving classification accuracy.

Image staining and differential diagnosis of ultrasound scans based on the Mahalanobis distance

Abstract: The covariance matrices associated with each state of health or disease from a previous study are used as the basis of an image staining display technique for aid in quantitative differential diagnosis. A state of health or disease is chosen by the clinician: this selects the covariance matrix from the data base. A region of interest (ROI) is then scrolled through an abdominal B-scan. For each position of the ROI a point in the four-dimensional feature space is calculated. A natural measure of the distance of this point from the center of mass (multivariate mean) of the disease class is calculated in terms of the covariance matrix of this class; this measure is the Mahalanobis distance. The confidence level for acceptance or rejection of the hypothesized disease class is obtained from the probability distribution of this distance, the T/sup 2/ probability law. This confidence level is color coded and used as a color stain that overlays the original scan at that position. The variability of the calculated features is studied as a function of ROI size, or the spatial resolution of the color coded image, and it is found that for an ROI in the neighborhood of 4 cm/sup 2/ most of the variability due to the finite number of independent samples (speckles) is averaged out, leaving the "noise floor" associated with inter- and intra-patient variability. ROIs on the order of 1 cm/sup 2/ may result with technical advances in B-scan resolution. A small number of points on organ boundaries are entered by the user, to fit with arcs of ellipses to be used to switch between organ (liver and kidney) data bases as the ROI encounters the boundary. By selecting in turn various state-of-health or state-of-disease databases, such images of confidence levels may be used for quantitative differential diagnosis. The method is not limited to ultrasound, being applicable in principle to features obtained from any modality or multimodality combination. >