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Mahalanobis distance

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


Papers
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Journal ArticleDOI
TL;DR: The Euclidean distance between syntactically linked words in sentences predicts, under ideal conditions, an exponential distribution of the distance between linked words, a trend that can be identified in real sentences.
Abstract: We study the Euclidean distance between syntactically linked words in sentences. The average distance is significantly small and is a very slowly growing function of sentence length. We consider two nonexcluding hypotheses: (a) the average distance is minimized and (b) the average distance is constrained. Support for (a) comes from the significantly small average distance real sentences achieve. The strength of the minimization hypothesis decreases with the length of the sentence. Support for (b) comes from the very slow growth of the average distance versus sentence length. Furthermore, (b) predicts, under ideal conditions, an exponential distribution of the distance between linked words, a trend that can be identified in real sentences.

131 citations

Proceedings ArticleDOI
05 Feb 2015
TL;DR: This research aims at studying the performance of k-nearest neighbor classification when applying different distance measurements including Euclidean, Standardized Euclideans, Mahalanobis, City block, Minkowski, Chebychev, Cosine, Correlation, Hamming, Jaccard, and Spearman.
Abstract: This research aims at studying the performance of k-nearest neighbor classification when applying different distance measurements. In this work, we comparatively study 11 distance metrics including Euclidean, Standardized Euclidean, Mahalanobis, City block, Minkowski, Chebychev, Cosine, Correlation, Hamming, Jaccard, and Spearman. A series of experimentations has been performed on eight synthetic datasets with various kinds of distribution. The distance computations that provide highly accurate prediction consist of City block, Chebychev, Euclidean, Mahalanobis, Minkowski, and Standardize Euclidean techniques.

131 citations

Book ChapterDOI
01 Apr 1990
TL;DR: A tracking approach that combines a prediction and a matching steps is presented that will be illustrated in several experiments that have been carried out considering noisy synthetic data and real scenes obtained from the INRIA mobile robot.
Abstract: This paper describes the development and the implementation of a line segments based token tracker. Given a sequence of time-varying images, the goal is to track line segments corresponding to the edges extracted from the image being analyzed. We will present a tracking approach that combines a prediction and a matching steps. The prediction step is a Kalman filtering based approach that is used in order to provide reasonable estimates of the region where the matching process has to seek for a possible match between tokens. Correspondence in the search area is done through the use of a similarity function based on Mahalanobis distance between attributs carefully chosen of the line segments. The efficiency of the proposed approach will be illustrated in several experiments that have been carried out considering noisy synthetic data and real scenes obtained from the INRIA mobile robot.

131 citations

Journal ArticleDOI
TL;DR: A new framework for computing the Euclidean distance and weighted distance from the boundary of a given digitized shape is presented and an algorithm that calculates the geodesic distance transform on surfaces is presented.
Abstract: A new framework for computing the Euclidean distance and weighted distance from the boundary of a given digitized shape is presented. The distance is calculated with sub-pixel accuracy. The algorithm is based on a equal distance contour evolution process. The moving contour is embedded as a level set in a time varying function of higher dimension. This representation of the evolving contour makes possible the use of an accurate and stable numerical scheme, due to Osher and Sethian [22]. The relation between the classical shape from shading problem and the weighted distance transform is presented, as well as an algorithm that calculates the geodesic distance transform on surfaces.

131 citations

01 Jan 2009
TL;DR: In this article, a generalization of the k-median problem with respect to an arbitrary dissimilarity measure D was studied, and a linear time (1+†)-approximation algorithm was given for the problem.
Abstract: We study a generalization of the k-median problem with respect to an arbitrary dissimilarity measure D. Given a finite set P of size n, our goal is to find a set C of size k such that the sum of errors D(P,C) = P p2P minc2C ' D(p,c) “ is minimized. The main result in this paper can be stated as follows: There exists a (1+†)-approximation algorithm for the k-median problem with respect to D, if the 1-median problem can be approximated within a factor of (1+†) by taking a random sample of constant size and solving the 1-median problem on the sample exactly. This algorithms requires time n2 O(mk log(mk/†)) , where m is a constant that depends only on † and D. Using this characterization, we obtain the first linear time (1+†)-approximation algorithms for the k-median problem in an arbitrary metric space with bounded doubling dimension, for the Kullback-Leibler divergence (relative entropy), for the Itakura-Saito divergence, for Mahalanobis distances, and for some special cases of Bregman divergences. Moreover, we obtain previously known results for the Euclidean k-median problem and the Euclidean k-means problem in a simplified manner. Our results are based on a new analysis of an algorithm of Kumar, Sabharwal, and Sen from FOCS 2004.

130 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
2023208
2022452
2021232
2020239
2019249