• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.479-488
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• 1999

Moore and Stubblebine(1981) suggested a chi-square test for multivariate normality based on cell counts calculated from the sample Mahalanobis distances. They derived the limiting distribution of the test statistic only when equiprobable cells are employed. Using conditional limit theorems, we derive the limiting distribution of the statistic as well as the asymptotic normality of the cell counts. These distributions are valid even when equiprobable cells are not employed. We finally apply this method to a real data set.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1191-1200
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under two non-normal distributions.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.203-212
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under two non-normal distributions.

• The Journal of the Acoustical Society of Korea
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• v.29 no.1E
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• pp.45-53
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• 2010

In this paper, we present the use of the Features Weighted Mahalanobis Distance (FWMD) in improving the performance of Likelihood Maximizing Beamforming (Limabeam) algorithm in speech recognition for microphone array. The proposed approach is based on the replacement of the traditional distance measure in a Gaussian classifier with adding weight for different features in the Mahalanobis distance according to their distances after the variance normalization. By using Features Weighted Mahalanobis Distance for Limabeam algorithm (FWMD-Limabeam), we obtained correct word recognition rate of 90.26% for calibrate Limabeam and 87.23% for unsupervised Limabeam, resulting in a higher rate of 3% and 6% respectively than those produced by the original Limabearn. By implementing a HM-Net speech recognition strategy alternatively, we could save memory and reduce computation complexity.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.43 no.1 s.307
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• pp.9-16
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• 2006

RDA(Relational Discriminant Analysis) is a way of finding classifiers based on the dissimilarity measures among the prototypes extracted from feature vectors instead of the feature vectors themselves. Therefore, the accuracy of the RDA classifier is dependent on the methods of selecting prototypes and measuring proximities. In this paper we propose to utilize PRS(Prototype Reduction Schemes) and Mahalanobis distances to devise a method of increasing classification accuracies. Our experimental results demonstrate that the proposed mechanism increases the classification accuracy compared with the conventional approaches for samples involving real-life data sets as well as artificial data sets.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.3
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• pp.1-5
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• 1984

It is investigated that Mahalanobis distances are invariant under a proper transformation and interest MDs are distributed as non-central chi-square while it is well known that intraset MDs are distributed as central chi-square. And their moments have been expressed as simple polynomials whose coefficients satisfy straightforward recursive relations.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.385-392
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• 2000

Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.148-152
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• 1998

Gustafson and Kessel proposed a modified fuzzy c-Means algorithm based of the Mahalanobis distance. Though the algorithm appears more natural through the use of a fuzzy covariance matrix, it needs to calculate determinants and inverses of the c-fuzzy scatter matrices. This paper proposes a fuzzy clustering algorithm using pseudo mahalanobis distance, which is more easy to use and flexible than the Gustafson and Kessel's fuzzy c-Means.

• Journal of Information Processing Systems
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• v.10 no.4
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• pp.589-601
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• 2014

The performance of edge detection often relies on its ability to correctly determine the dissimilarities of connected pixels. For grayscale images, the dissimilarity of two pixels is estimated by a scalar difference of their intensities and for color images, this is done by using the vector difference (color distance) of the three-color components. The Euclidean distance in the RGB color space typically measures a color distance. However, the RGB space is not suitable for edge detection since its color components do not coincide with the information human perception uses to separate objects from backgrounds. In this paper, we propose a novel method for color edge detection by taking advantage of the HSV color space and the Mahalanobis distance. The HSV space models colors in a manner similar to human perception. The Mahalanobis distance independently considers the hue, saturation, and lightness and gives them different degrees of contribution for the measurement of color distances. Therefore, our method is robust against the change of lightness as compared to previous approaches. Furthermore, we will introduce a noise-resistant technique for determining image gradients. Various experiments on simulated and real-world images show that our approach outperforms several existing methods, especially when the images vary in lightness or are corrupted by noise.

• Korean Journal of Plant Resources
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• v.27 no.1
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• pp.89-94
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• 2014

Varietal distances were measured by Mahalanobis's $D^2$ statistics in 190 possible comparisons among twenty varieties of Prunus mume with twelve characters such as seed weight, length, width, and diameter, fruit weight, and number of sepals, petals, pistils, and stigmas, and leaf length and width. A complete linkage cluster analysis based on the Mahalanobis's distance ($D^2$) was attempt. Twenty varieties of Prunus mume were largely classified into five subgroups. Group I, II, III, IV and V included two, four, five, five and four varieties, respectively. Most of the varietal groups were not associated with their geographical origins. Number of stigmas, and leaf length and width among the twelve characters were the largest contributors to the $D^2$ in both intra-and inter groups.