Showing papers on "Mahalanobis distance published in 1981"
TL;DR: In this paper, influence functions for a variety of parametric functions in multivariate analysis are obtained, including the generalized variance, the matrix of regression coefficients, the noncentrality matrix Σ-1 δ, and the matrix L, which is a generalization of 1-R2, canonical correlations, principal components and parameters that correspond to Pillai's statistic (1955), Hotelling's (1951) generalized To2 and Wilk's Λ (1932).
Abstract: The influence function introduced by Hampe1 (1968, 1973, 1974) is a tool that can be used for outlier detection. Campbell (1978) has obtained influence function for Mahalanobis’s distance between two populations which can be used for detecting outliers in discrim-inant analysis. In this paper influence functions for a variety of parametric functions in multivariate analysis are obtained. Influence functions for the generalized variance, the matrix of regression coefficients, the noncentrality matrix Σ-1 δ in multivariate analysis of variance and its eigen values, the matrix L, which is a generalization of 1-R2 , canonical correlations, principal components and parameters that correspond to Pillai’s statistic (1955), Hotelling’s (1951) generalized To2 and Wilk’s Λ (1932), which can be used for outlier detection in multivariate analysis, are obtained. Delvin, Ginanadesikan and Kettenring (1975) have obtained influence function for the population correlation co-efficient in the bivariate case. It is shown in...
60 citations
TL;DR: A satisfactory and consistent overall classification accuracy was achieved by using the sequential selection algorithms for selecting continuous features by maximizing the Mahalanobis distance at each step of the feature selection process.
7 citations
TL;DR: Mahalanobis distance is an information theoretic metric measure that can be used as an index to investigate the effectiveness of individual inputs in multivariable control systems as mentioned in this paper, and it can also be used to measure the complexity of control systems.
Abstract: Mahalanobis distance, which is an information theoretic metric measure, can be used as an index to investigate the effectiveness of individual inputs in multivariable control systems.
4 citations
TL;DR: In this article, the problem of selecting the best of several normal populations in terms of Mahalanobis distance when population variance-covariance matrices are equal and unknown is discussed.
Abstract: In this paper the problem of selecting the best of several normal populations in terms of Mahalanobis distance (MD) whenpopulation variance-covariance matrices are equal and unknown is discussed. The selection rule enunciated is shown to ap-proximately satisfy the usual requirement of a minimum guaranteed probability of correct selection. Methods of computing tables required for application of the rule are discussed.
4 citations
TL;DR: In this paper, a table look-up maximum likelihood (TMSML) method was proposed to reduce the core memory requirements to store the table and achieve the same results as the conventional maximum likelihood method.
Abstract: A new pattern clasification algorithm named a table look-up maximum likelihood method was developed. It can achieve nearest processing speed as a conventional table look-up method in spite of the identical clasification accuracy with a maximum likelihood method. Hyperellipsoids defined by the same Mahalanobis' distance associated with each categories overlap each other in multidimensional feature space. Look-up tables in the new algorithm can be considered as orthogonal projections of these set of hyperellipsoids to each feature axes. As compared with a conventional table look-up algorithm, this algorithm is more simple, and in addition can remarkably reduce core memory requirements to store the table.Using this new algorithm, a LANDSAT MSS image and a high-altitude color infrared aerial photograph were clasified to examine processing times. The results indicated that these rocessing rates compared with the maximum likelihood method are four and seven times faster respectively.
3 citations
TL;DR: In this paper, distance coefficients among local populations of modern male Japanese were computed on the basis of 33 cranial measurements shown in the text, including D2s, Q-mode correlation coefficients, and PENROSE's size and shape distances.
Abstract: This report provides distance coefficients among local populations of modern male Japanese. MAHALANOBIS' D2s, Q-mode correlation coefficients, and PENROSE'S size and shape distances were computed on the basis of 33 cranial measurements shown in the text.
2 citations
TL;DR: A set of spectral measures and two decision algorithms have been investigated with respect to classification accuracy and robustness to measurement variables and classification accuracy of 80 percent was achieved with tissue classification.
1 citations