Showing papers on "Mahalanobis distance published in 1987"

Near-Infrared Spectrum Qualification via Mahalanobis Distance Determination

Abstract: The use of near-infrared reflectance analysis (NIRA) for the quantitation of components of complex mixtures is well established. The lack of qualitative feedback in this approach is a major drawback. In view of this, it is believed that qualitative evaluation of the sample spectrum is also necessary for routine application of the NIRA technique. A method for qualifying a spectrum for application of a quantitative equation is described. The method involves generation of a quantitative equation, followed by the development of a qualitative equation based on the Mahalanobis distance algorithm, which is used to determine if the spectrum is suitable for analysis. This approach is demonstrated for the determination of lincomycin in an agricultural premix. The determination of proper control limits on the Mahalanobis distance is discussed. The improvement in precision obtained with the use of spectral selection is reviewed.

The Euclidean distance classifier: an alternative to the linear discriminant function

Abstract: The sample linear discriminant function (LDF) is known to perform poorly when the number of features p is large relative to the size of the training samples, A simple and rarely applied alternative to the sample LDF is the sample Euclidean distance classifier (EDC). Raudys and Pikelis (1980) have compared the sample LDF with three other discriminant functions, including thesample EDC, when classifying individuals from two spherical normal populations. They have concluded that the sample EDC outperforms the sample LDF when p is large relative to the training sample size. This paper derives conditions for which the two classifiers are equivalent when all parameters are known and employs a Monte Carlo simulation to compare the sample EDC with the sample LDF no only for the spherical normal case but also for several nonspherical parameter configurations. Fo many practical situations, the sample EDC performs as well as or superior to the sample LDF, even for nonspherical covariance configurations.

Estimation of signal to noise ratio using mahalanobis distance

Abstract: In this paper, we propose some alternative estimatiors to that given by C. G. Khatri and C. R. Rao (1985), for estimating Signal to Noise ratio. Using Pitman Nearness, Condition for prefering one estimator over the other is estabilished. It is shown numerically that estimators corresponding to Entropy loss function are better more oftern than those corresponding to Squared Error loss.

An evaluation of the M-statistic in human odontomorphometric distance analyses

Abstract: The usefulness of the M-statistic in odontomorphometric distance analyses was evaluated against a battery of more traditional metrics, which included Mahalanobis' D2, Penrose's shape metric, the Manhattan distance and Delta. Odontometric data used for the analyses were derived from 202 Paraguayan Lengua Indians and 125 contemporary caucasoids. Efron's Bootstrap procedure was used to evaluate the statistical accuracy of the different metrics, when each was applied to the same populations. Additionally, metric stability in the face of reduced sample size, statistical bias resulting from over- and underestimation, and the effects of standardization, were investigated. Our results indicated that Penrose's shape metric rather that the recently introduced M-statistic was the most reliable metric evaluated. Penrose's shape remained the most reliable when sample size was artificially reduced and when raw data were used. Interestingly, Mahalanobis' generalized distance emerged as the least reliable statistics, especially when used on small sample sizes.

Metric Considerations in Clustering: Implications for Algorithms

Abstract: Given measurements on p variables for each of n individuals, aspects of the problem of clustering the individuals are considered. Special attention is given to models based upon mixtures of distributions, esp. multivariate normal distributions. The relationship between the orientation(s) of the clusters and the nature of the within-cluster covariance matrices is reviewed, as is the inadequacy of transformation to principal components based on the overall (total) covariance matrix of the whole (mixed) sample. The nature of certain iterative algorithms is discussed; variations which result from allowing different covariance matrices within clusters are studied.