Mahalanobis distance

McLachlan, Geoffrey J.

doi:10.1007/bf02834632

Cited by 321 publications

(152 citation statements)

References 3 publications

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“…The most used measure is Mahalanobis distance (Md) [39] and plays a fundamental role in the data analysis with multiple measurements, finding applications on statistical patterns recognition in archeology, medical diagnosis, or remote sensing [40].…”

Section: Chi-square Transformation (Cst)mentioning

confidence: 99%

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Thresholding Algorithm Optimization for Change Detection to Satellite Imagery

Vázquez-Jiménez¹,

Ramos-Bernal²,

Calcerrada³

et al. 2018

Colorimetry and Image Processing

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To detect changes in satellite imagery, a supervised change detection technique was applied to Landsat images from an area in the south of México. At first, the linear regression (LR) method using the first principal component (1-PC) data, the Chi-square transformation (CST) method using first three principal component (PC-3), and tasseled cap (TC) images were applied to obtain the continuous images of change. Then, the threshold was defined by statistical parameters, and histogram secant techniques to categorize as change or unchanged the pixels. A threshold optimization iterative algorithm is proposed, based on the ground truth data and assessing the accuracy of a range of threshold values through the corresponding Kappa coefficient of concordance.Finally, to evaluate the change detection accuracy of conventional methods and the threshold optimization algorithm, 90 polygons (15,543 pixels) were sampled, categorized as real change/unchanged zones, and defined as ground truth, from the interpretation of color aerial photo slides aided by the land cover maps to obtain the omission/ commission errors and the Kappa coefficient of agreement. The results show that the threshold optimization is a suitable approach that can be applied for change detection analysis.

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Section: Chi-square Transformation (Cst)mentioning

confidence: 99%

“…According to Ridd and Liu [13], the CST detection method was applied to each group of difference images (Dif-PC and Dif-TC) to obtain a single global image that stores the continuous change, represented by the square Md [39,40], determined by the equation:…”

Section: Chi-square Transformation (Cst)mentioning

confidence: 99%

Thresholding Algorithm Optimization for Change Detection to Satellite Imagery

Vázquez-Jiménez¹,

Ramos-Bernal²,

Calcerrada³

et al. 2018

Colorimetry and Image Processing

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“…It can be used to determine whether a sample is an outlier or whether a sample has a similarity with another group or not (McLachlan, 1999). The mathematical definition of Mahalanobis distance is given by equation (1).…”

Section: Theoretical Background Of Mahalanobis Distancementioning

confidence: 99%

Determination of Lung Sound as Normal or Abnormal, Using a Statistical Technique

Liyanage¹,

Siriwardhana²,

Abeyrathne³

et al. 2017

International Conference on Bioscience and Biotechnology

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Abstract:In this study the authors investigate a possibility of objectively differentiating a lung sound as normal or abnormal using a statistical technique. For the study, breath sounds were recorded from 30 nonsmoking, healthy subjects and 7 subjects with respiratory disorders whose external physical symptoms were not shown, using an electronic stethoscope. A 4th order Butterworth bandpass filter removed environment sounds and an Adaptive filter using Least Mean Square algorithm cancelled other body sounds from the recorded sound to obtain only the lung sound. After amplifying a lung sound signal up to the initial recorded amplitude, signal was compared with a standard normal and a standard abnormal lung sound. The comparison was done by calculating the Mahalanobis Distance mean values. The Mahalanobis distance mean values obtained from subjects with respiratory disorders showed considerable deviations from the specific range of values obtained by subjects with normal lung sounds concluding this method is capable of distinguishing between normal and abnormal lung sounds and could developed to noninvasively determine the progress of patients with respiratory disorders.

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“…The well-known Euclidean distance is currently the most frequently used metric space for the established clustering algorithms [1], [2]. Other metric spaces, using the Mahalanobis [3], city block Hamming, Minkowski types of distances, etc., are also widely used in different clustering algorithms for different purposes. It is often the case that clustering algorithms employing divergences, i.e.…”

Section: Introductionmentioning

confidence: 99%

A new type of distance metric and its use for clustering

Angelov

Kangin

et al. 2017

Evolving Systems

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Abstract-In order to address high dimensional problems, a new 'direction-aware' metric is introduced in this paper. This new distance is a combination of two components: i) the traditional Euclidean distance and ii) an angular/directional divergence, derived from the cosine similarity. The newly introduced metric combines the advantages of the Euclidean metric and cosine similarity, and is defined over the Euclidean space domain. Thus, it is able to take the advantage from both spaces, while preserving the Euclidean space domain. The directionaware distance has wide range of applicability and can be used as an alternative distance measure for various traditional clustering approaches to enhance their ability of handling high dimensional problems. A new evolving clustering algorithm using the proposed distance is also proposed in this paper. Numerical examples with benchmark datasets reveal that the direction-aware distance can effectively improve the clustering quality of the k-means algorithm for high dimensional problems and demonstrate the proposed evolving clustering algorithm to be an effective tool for high dimensional data streams processing.

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Mahalanobis distance

Cited by 321 publications

References 3 publications

Thresholding Algorithm Optimization for Change Detection to Satellite Imagery

Thresholding Algorithm Optimization for Change Detection to Satellite Imagery

Determination of Lung Sound as Normal or Abnormal, Using a Statistical Technique

A new type of distance metric and its use for clustering

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