scispace - formally typeset
Search or ask a question
Topic

Mahalanobis distance

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


Papers
More filters
Journal ArticleDOI
TL;DR: A method for estimating the Mahalanobis distance between two multivariate normal populations when a subset of the measurements is observed as ordered categorical responses and asymptotic properties of the proposed estimator are developed.
Abstract: We present a method for estimating the Mahalanobis distance between two multivariate normal populations when a subset of the measurements is observed as ordered categorical responses. Asymptotic properties of the proposed estimator are developed. Two examples are discussed.

77 citations

Journal ArticleDOI
TL;DR: In this paper, the expectation-maximization (EM) algorithm for Gaussian mixture modeling is improved via three statistical tests that have an increased capability to find the underlying model, while maintaining a low execution time.
Abstract: In this paper, the expectation-maximization (EM) algorithm for Gaussian mixture modeling is improved via three statistical tests. The first test is a multivariate normality criterion based on the Mahalanobis distance of a sample measurement vector from a certain Gaussian component center. The first test is used in order to derive a decision whether to split a component into another two or not. The second test is a central tendency criterion based on the observation that multivariate kurtosis becomes large if the component to be split is a mixture of two or more underlying Gaussian sources with common centers. If the common center hypothesis is true, the component is split into two new components and their centers are initialized by the center of the (old) component candidate for splitting. Otherwise, the splitting is accomplished by a discriminant derived by the third test. This test is based on marginal cumulative distribution functions. Experimental results are presented against seven other EM variants both on artificially generated data-sets and real ones. The experimental results demonstrate that the proposed EM variant has an increased capability to find the underlying model, while maintaining a low execution time.

77 citations

Journal ArticleDOI
TL;DR: The results show that the early stage failure of cooling fan caused by bearing generalized-roughness faults can be detected successfully, and the different unbalanced electrical faults of induction motor can be classified with a higher accuracy by Mahalanobis-Taguchi system.
Abstract: A health index, Mahalanobis distance (MD), is proposed to indicate the health condition of cooling fan and induction motor based on vibration signal. Anomaly detection and fault classification are accomplished by comparing MDs, which are calculated based on the feature data set extracted from the vibration signals under normal and abnormal conditions. Since MD is a non-negative and non-Gaussian distributed variable, Box-Cox transformation is used to convert the MDs into normal distributed variables, such that the properties of normal distribution can be employed to determine the ranges of MDs corresponding to different health conditions. Experimental data of cooling fan and induction motor are used to validate the proposed approach. The results show that the early stage failure of cooling fan caused by bearing generalized-roughness faults can be detected successfully, and the different unbalanced electrical faults of induction motor can be classified with a higher accuracy by Mahalanobis-Taguchi system. Such works could aid in the reliable operation of the machines, the reduction of the unexpected failures, and the improvement of the maintenance plan.

77 citations

Journal ArticleDOI
TL;DR: In this paper, the Mahalanobis distance is shown to be an appropriate measure of distance between two elliptic distributions having different locations but a common shape, which extends a result long familiar in multivariate analysis to a class of nonnormal distributions.
Abstract: SUMMARY The Mahalanobis distance is shown to be an appropriate measure of distance between two elliptic distributions having different locations but a common shape. This extends a result long familiar in multivariate analysis to a class of nonnormal distributions. It can also be used to show that the sample version of the Mahalanobis distance is appropriate under both estimative and predictive approaches to estimation for the family of multivariate normal distributions differing only in location.

77 citations

Journal ArticleDOI
17 Dec 2015-Entropy
TL;DR: The proposed “FRFE + WTT + TSVM” method is superior to 20 state-of-the-art methods and introduced an advanced classifier: twin support vector machine (TSVM).
Abstract: Aim: To detect pathological brain conditions early is a core procedure for patients so as to have enough time for treatment. Traditional manual detection is either cumbersome, or expensive, or time-consuming. We aim to offer a system that can automatically identify pathological brain images in this paper. Method: We propose a novel image feature, viz., Fractional Fourier Entropy (FRFE), which is based on the combination of Fractional Fourier Transform (FRFT) and Shannon entropy. Afterwards, the Welch’s t-test (WTT) and Mahalanobis distance (MD) were harnessed to select distinguishing features. Finally, we introduced an advanced classifier: twin support vector machine (TSVM). Results: A 10 × K-fold stratified cross validation test showed that this proposed “FRFE + WTT + TSVM” yielded an accuracy of 100.00%, 100.00%, and 99.57% on datasets that contained 66, 160, and 255 brain images, respectively. Conclusions: The proposed “FRFE + WTT + TSVM” method is superior to 20 state-of-the-art methods.

76 citations


Network Information
Related Topics (5)
Cluster analysis
146.5K papers, 2.9M citations
79% related
Artificial neural network
207K papers, 4.5M citations
79% related
Feature extraction
111.8K papers, 2.1M citations
77% related
Convolutional neural network
74.7K papers, 2M citations
77% related
Image processing
229.9K papers, 3.5M citations
76% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
2023208
2022452
2021232
2020239
2019249