Journal ArticleDOI
Linear Discriminant Analysis: Loss of Discriminating Power When a Variate is Omitted
Reads0
Chats0
TLDR
In this paper, the problem of estimating the reduction of the discriminating power when a single variate from the complete set of p variates is excluded after the discriminant function has been formed is addressed.Abstract:
where a is the probability of misclassification, A' is the iMahalanobis' distance, Pi = (HA g')/o is the normalized difference of the expectations of the ith variate in the populations A and B, and p is the number of variates. However, this procedure requires too much computing. Approximate algorithms have been suggested (Weiner and Dunn [1966]) but they also require large computers. Only in special cases (namely, when the correlation matrix has some specified properties) are more simple techniques to select the best variates available (Cochran [1964]). In some situations a more particular problem is of interest: estimation of the reduction of the discriminating power when a single variate from the complete set of p variates is excluded after the discriminant function has been formed. 2. Let A = ai i be a symmetric square matrix. If we cross out the kth line and the kth column of this matrix, the elements of the new inverse matrix Aiwill be connected with the elements of the matrix A-' by an equality:read more
Citations
More filters
Journal ArticleDOI
Multivariate analysis versus multiple univariate analyses.
Carl J. Huberty,John D. Morris +1 more
TL;DR: In this article, the argument for preceding multiple ANOVAs with MANAs with a multivariate analysis of variance (MANOVA) to control for Type I error is challenged, and several situations are discussed in which multiple ANAs might be conducted without the necessity of a preliminary MANOVA.
Journal ArticleDOI
The Performance of Fisher's Linear Discriminant Function Under Non-Optimal Conditions
TL;DR: In this paper, a review of the published work on the performance of Fisher's linear discriminant function when underlying assumptions are violated is given, and new results are presented for the case of classification using both binary and continuous variables.
Journal ArticleDOI
Computations for Variable Selection in Discriminant Analysis
TL;DR: In this paper, an algorithm for computing statistics for all possible subsets of variables for a discriminant analysis is proposed and a comparison with a stepwise procedure is also presented through two examples.
Journal ArticleDOI
Interpreting Discriminant Functions: A Data Analytic Approach.
TL;DR: Based on a geometric interpretation of MANOVA, new indices called discriminant ratio coefficients are derived which will aid in the identification and interpretation of that subset of variables that essentially contribute to a significant group discrimination.
Journal ArticleDOI
Results in statistical discriminant analysis: a review of the former Soviet union literature
Šarūnas Raudys,Dean M. Young +1 more
TL;DR: In this paper, a succinct overview of important contributions by former Soviet Block researchers to several topics in the discriminant analysis literature concerning the small training-sample size problem is given. But most results derived by former former Soviet Union researchers are unknown to statisticians and statistical pattern recognition researchers in the West.
References
More filters
Book
Statistical Methods for Research Workers
TL;DR: The prime object of as discussed by the authors is to put into the hands of research workers, and especially of biologists, the means of applying statistical tests accurately to numerical data accumulated in their own laboratories or available in the literature.
Journal ArticleDOI
On the Performance of the Linear Discriminant Function
TL;DR: In this paper, the authors consider the role of correlations between variates and show that positive correlations are generally harmful and negative correlations helpful, and conclude that most correlations are positive, while negative correlations are helpful.