A valuation of state of object based on weighted Mahalanobis distance

Krusińska, Ewa

doi:10.1016/0031-3203(87)90066-5

Cited by 15 publications

(6 citation statements)

References 6 publications

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“…Further, in the system for the computerized respiratory disease consulting unit it is planned to use pre-prepared algorithms so that there is no difference from the computational point of view what methods they contain. T h e system being set up in Wroclaw [7] will also be enhanced b y the robust analogues of the methods for comprehensive evaluation of the condition of the patients (degree of illness in disease) introduced b y Krusinska [ 8 ] and used by Krusinska and Liebhart [S] to assess the condition of people sufl'ering from obstructive airways disease.…”

Section: Discussionmentioning

confidence: 99%

Robust multivariate methods in laboratory techniques and in assisting medical diagnosis

Krusińska

Liebhart

1990

Medical Informatics

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The usefulness of robust multivariate methods in medical applications, for example, the indirect estimation of total lung capacity by robust regression and the assistance of medical diagnosis in obstructive airways disease using robust discriminant functions, is discussed. The results of robust methods that consist in downweighting the influence of the multivariate outliers are compared with the outcomes of classical procedures. The advantages of modern robust algorithms are proved in the present study. It is planned to include the methods in the system for the computerized consulting unit for respiratory diseases that is being set up in Wrocław.

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Section: Discussionmentioning

confidence: 99%

Robust multivariate methods in laboratory techniques and in assisting medical diagnosis

Krusińska

Liebhart

1990

Medical Informatics

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“…Some available criteria that have been used in previous studies for distinguishing between useful and poor variables are rule performance criteria (Krusińska 1987;Snapinn and Knoke 1989;Ganeshanandam and Krzanowski 1989), group separation criteria (McKay and Campbell 1982;Krzanowski 1983;Daudin and Bar-Hen 1999), model goodness-of-fit criteria such as AIC and BIC (Daudin 1986) and other criteria including R 2 , Hotelling's T 2 and Wilk's (see Rencher 1993). Choice among these criteria depends on the initial aims of the classification rule, but rule performance and group separation criteria are generally popular.…”

Section: Introductionmentioning

confidence: 98%

Variable selection in discriminant analysis based on the location model for mixed variables

Mahat

Krzanowski

Hernández

2007

ADAC

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Non-parametric smoothing of the location model is a potential basis for discriminating between groups of objects using mixtures of continuous and categorical variables simultaneously. However, it may lead to unreliable estimates of parameters when too many variables are involved. This paper proposes a method for performing variable selection on the basis of distance between groups as measured by smoothed Kullback-Leibler divergence. Searching strategies using forward, backward and stepwise selections are outlined, and corresponding stopping rules derived from asymptotic distributional results are proposed. Results from a Monte Carlo study demonstrate the feasibility of the method. Examples on real data show that the method is generally competitive with, and sometimes is better than, other existing classification methods.

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“…6-7] to the general location model [19] and derived a distance that specializes to the Mahalanobis distance in the absence of nominal variables. Krusin´ska [9] proposed a weighted Mahalanobis distance for mixed data as the weighted sum of the Mahalanobis distance for continuous variables and a Mahalanobis-type distance for discrete variables introduced by Kurczyn´ski [13]. More recently, Bedrick et al [4] derived a Mahalanobis distance for the mixed ordinal and continuous data using the grouped continuous model [2].…”

Section: Introductionmentioning

confidence: 98%

“…In discriminant analysis, for example, the classification rule based on the classical Fisherian linear discriminant function for classifying an observation into one of two or more distinct multivariate normal populations reduces to a comparison of so-called Mahalanobis distances (e.g., [16, p. 31]). This approach is a common one in pattern recognition (e.g., [9]). Whereas distance measures for continuous data are well developed [21], those for mixed discrete and continuous data are less so because of the lack of a standard model for such data.…”

Section: Introductionmentioning

confidence: 99%

A generalized Mahalanobis distance for mixed data

Leon

Carrière

2005

Journal of Multivariate Analysis

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A distance for mixed nominal, ordinal and continuous data is developed by applying the Kullback-Leibler divergence to the general mixed-data model, an extension of the general location model that allows for ordinal variables to be incorporated in the model. The distance obtained can be considered as a generalization of the Mahalanobis distance to data with a mixture of nominal, ordinal and continuous variables. Moreover, it includes as special cases previous Mahalanobis-type distances developed by Bedrick et al. (Biometrics 56 (2000) 394) and Bar-Hen and Daudin (J. Multivariate Anal. 53 (1995) 332). Asymptotic results regarding the maximum likelihood estimator of the distance are discussed. The results of a simulation study on the level and power of the tests are reported and a real-data example illustrates the method. r

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A valuation of state of object based on weighted Mahalanobis distance

Cited by 15 publications

References 6 publications

Robust multivariate methods in laboratory techniques and in assisting medical diagnosis

Robust multivariate methods in laboratory techniques and in assisting medical diagnosis

Variable selection in discriminant analysis based on the location model for mixed variables

A generalized Mahalanobis distance for mixed data

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