Showing papers on "Mahalanobis distance published in 1979"

Numerical evaluation of cytologic data: II. Comparison of profiles.

Abstract: Results of cytologic studies are often presented as profiles of some type. The numerical characterization of these profiles may be statistically compared using methods of multivariate analysis. This article describes the determination of the statistically significant differences between portions of profiles, the computation of the Mahalanobis distance measure between profiles and the use of the chi-square statistic as a measure of the typicality of a profile. Fully worked numerical examples suitable for execution on a pocket calculator are given.

Reconnaissance Geologic Mapping in Chagai Hills, Baluchistan, Pakistan, by Computer Processing of Landsat Data

Abstract: A Landsat spectral classification map of the Chagai Hills, Baluchistan, Pakistan, has been produced by computer processing of Landsat-1 digital data. A supervised classification algorithm was used which employed the Mahalanobis distance as a maximum-likelihood discriminant. A Landsat geologic map has been interpreted from the spectral classification by use of a set of interpretation rules specifically formulated for the Chagai Hills. The Landsat geologic map shows an overall close agreement with a photogeologic map produced by the Hunting Survey Corp. Areas of disagreement have been studied and evaluated as to the reasons for and validity of the discrepancies. Each pixel of the Landsat data was classified as one of the preselected pixel populations which represent chosen surface types within the Chagai Hills. Pixel populations generated from the control areas of each of the mapped surface types were represented as "characteristic lines" in the Landsat four-dimensional color space. A characteristic line is defined as the line which parallels the pixel population's principal component and passes through the population's center of gravity. The characteristic lines were used to thin out surface types to which the pixel being tested could not be reasonably classified. The Mahalanobis distance classification discriminant was based on the position of a test pixel within the density distributions of the populations. The individual pixel classificat ons were smoothed by reclassifying the central pixel of a 3 × 3 array on the basis of the classification information contained in all nine pixels. A discriminant similar to one of a tightly constrained parallelepiped was used to classify hydrothermal alteration. The alteration classifications were smoothed by considering only those areas where two or more pixels of a 3 × 3 array were classified as altered. Approximately 100 areas classified as hydrothermally altered were located on the Landsat geologic map. Four of these are known to be altered rock. Two of the known areas of alteration were used as control areas; the correct classification of the other two increases the confidence in the alteration classifications across the Chagai Hills.

Mahalanobis distance and variable selection to optimize dose response

Abstract: A battery of statistical techniques are combined to improve detection of low-level dose response. First, Mahalanobis distances are used to classify objects as normal or abnormal. Then the proportion classified abnormal is regressed on dose. Finally, a subset of regressor variables is selected which maximizes the slope of the dose response line. Use of the techniques is illustrated by application to mouse sperm damaged by low doses of x-rays.

A quantitative estimate of the possibility of confusion of Japanese phonemes

Abstract: The problem of quantitatively estimating the possibility of auditory confusion in Japanese phonemes is discussed. Using Mahalanobis' distance, the range of fluctuation in a phoneme is derived by grouping monosyllables into phoneme units. In the case of the stop consonant, over 80 percent of our estimates proved to have good correspondence with the actual data, and it was made clear that the direction of confusion could be estimated.

Concordance in Variable-Subset Discriminant Analysis

Abstract: Subsequent to the identification of a set of variables that best discriminate between two populations, there might still exist nonstatistical reasons for further exploration of a specific subset in terms of its relative discriminating ability. This requires a more f exible criterion than the usual one based on tests of equality of the Mahalanobis distances. A measure of the extent to which a set and a specific subset of variables agree in the discriminant analysis problem, under multivariate normal assumptions, is proposed. This measure is the probability of concordance in classification and its value is shown to be high when the subset of variables suggest large separation between the two populations. A justification for the use of the subset of variables can be derivedfrom a hlgh probability of concordance and the non-statistical considerations discussed in the text. In the two-population (II; i - 1, 2) discriminant analysis problem based on a p-variate normal density, the hypothesis testing techniques intended to result in possible variable reduction are presented in texts such as Kshirsagar's (1972). The methods involve the comparison of the p-variate Mahalanobis distance with that of a specific subset q(q < p). The rejection of the hypothesis of equal distances dictates the use of the p variables in the classification procedure. However, there might be nonstatistical reasons for further exploration of the subset in terms of its relative discriminating ability. For instance, in critical care medical research, the variables that best differentiate between survivors and non-survivors are often realized using both invasive and non-invasive techniques. But the invasive techniques frequently interfere with the condition of the patient (Weil and Shubin 1967). In other research areas, some variables might be prohibitively expensive to measure on a routine basis although their inclusion might increase the probabilities of correct classification. Hence, there exists a real need for a flexible criterion, based on relative discriminating ability, that can be used for the comparison of a set of variables with a specific subset. In this article we present a measure of the degree to which a set and a specific subset of variables agree in the classification of an individual (object) into any one of two populations.