Showing papers on "Linear discriminant analysis published in 1971"
TL;DR: It would seem that use of the maximum likelihood method would be preferable, whenever practical, in situations where the normality assumptions are violated, especially when many of the independent variables are qualitative.
231 citations
TL;DR: In this article, Monte Carlo estimates have been obtained for two quantities of interest in a discriminant analysis involving the usual linear discriminant function, the unconditional probability of correct classification and the expected value of its estimate based on the calculated Mahalanobis distance.
Abstract: Monte Carlo estimates have been obtained for two quantities of interest in a discriminant analysis involving the usual linear discriminant function. The first is the unconditional probability of correct classification; the second is the expected value of its estimate based on the calculated Mahalanobis distance. These two quantities are shown in tables and graphs versus the population Mahalanobis distance. Equal sample sizes of 25, 50, and 100 have been used in forming the discriminant functions; 2, 6, 10, 15, 20, and 30 variates have been used. A comparison is made between the Monte Carlo estimates of the unconditional probability of correct classification and an approximation suggested by Lachenbruch [41].
52 citations
TL;DR: 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:
35 citations
TL;DR: In a schematic concept-formation task, recovery of a priori schematic class membership by Os varied inversely as physical cluster diameter, with concept acquisition across trials evidenced in only the low-cluster-diameter condition.
Abstract: Patterns were computer-generated about two prototypes to form schematic clusters of three diameters about the cluster centroids. In a schematic concept-formation task, recovery of a priori schematic class membership by Os varied inversely as physical cluster diameter, with concept acquisition across trials evidenced in only the low-cluster-diameter condition. For each 0 who failed to classify according to the schema rule, linear discriminant function analysis was applied to his classes. In all cases, O-generated classes were successfully recovered by the physical pattern features used as predictors, the mapping of these classes by the LDF exceeding that by the schema rule in accuracy at all cluster-diameter levels.
34 citations
TL;DR: In this paper, various estimators calculated from the sample used to generate the sample discriminant function have been proposed and compared by using unconditional mean square error as the criterion, where each distribution is univariate normal with common variance.
Abstract: The probability of misclassification inherent in the use of a linear discriminant function is not necessarily known to the experimenter using such a function. Various estimators calculated from the sample used to generate the sample discriminant function have been proposed. The purpose of this paper is to evaluate and to compare several of these estimators by using unconditional mean square error as the criterion. Discussion is restricted to the case where each of the distributions is univariate normal with common variance.
27 citations
TL;DR: In this paper, an asymptotic expansion of the distribution of Z as well as the associated probability of misclassification with respect to the three numbers of degrees of freedom is given.
24 citations
TL;DR: In this paper, the authors used the Bayes decision rule to classify sandstones, greywackes, pelites, limestones, dolomites, and acid-igneous and basicigneous rocks.
Abstract: Classification of sandstones, greywackes, pelites, limestones, dolomites, and acid-igneous and basicigneous rocks, using a literature sample of 183 post-1920 analyses for the 11 major oxides has achieved an 80-percent success rate. The method is based on nonparametric estimation of a probability density function for each category to be classified, using the Bayes decision rule. The method is suitable for use with small training sets and gives much improved results over a linear discriminant function. Classification following data compression using principal components also has given satisfactory recognition rates.
16 citations
TL;DR: Two linkable computer programs have been developed for a special case of nonlinear discriminant analysis because joint normal distributions are postulated, but not equal covariance matrices, which seems to be important to the computer-aided diagnosis.
16 citations
TL;DR: This paper examines the question of how to make a determination of success for discriminant analysis given that the basis for such a judgment lies in estimates of expected error rates, and compares several techniques in a setting of high true probabilities of misclassification.
13 citations
8 citations
01 Jul 1971
TL;DR: The result of recognition experiments for artificial patterns indicates that the proposed nonlinear discriminant function has sufficient rates of classification with a relatively small number of training patterns.
Abstract: A method for constructing a new type of nonlinear discriminant function is proposed, and the capability is evaluated by computer simulation. As the orthogonal basis for this function, a ?-function system is used that is obtained by generalizing the finite Walsh functions to the case of many-valued variables. The discriminant function discussed has the following desired features. It can deal with not only binary patterns, but also many-valued ones. The determination of a weighting vector requires neither storage nor iteration for training patterns. A notion of complexity between pattern classes is introduced to make clear the requirement of the present system for the structure of a pattern space. Examples of separation boundaries for 2-component-pattern classes demonstrate that the discriminant function has a high ability of generalization for new input patterns. The result of recognition experiments for artificial patterns indicates that for various values of the number of pattern components, the number of values taken by a component, and the complexity of pattern classes, the proposed system has sufficient rates of classification with a relatively small number of training patterns.
01 Feb 1971
TL;DR: Huberty et al. as discussed by the authors used the proportion of correct classifications as an index of discriminatory power of each subset of variables selected, and four procedures using indices that order the variables with respect to contribution to discrimination yielded the best results.
Abstract: Huberty, Carl J. On the Variable Selection Problem in Multiple Group Discriminant Analysis. Feb 71 39p.; Paper presented at the Annual Meeting of the American Educational Research Association, Nov York, New York, February 1971 EDRS Price MF-$0.65 HC-$3.29 Cluster Analysis, Correlation, Criteria, tDiscriminant Analysis, `.'actor Analysis, *Mathematical Models, Mathematics, *Multiple Regression Analysis, *Predictor Variables, Research Methodology, *Statistical Analysis, Tests of Significance This study was concerned with various schemes for reducing the numocr of variables in a multivariate analysis. Two sets of illustrative data were used; the numbers of criterion groups were 3 and 5. The proportion of correct classifications was employed as an index of discriminatory power of each subset of variables selected. Of the four procedures using indices that order the variables with respect to contribution to discrimination, the (forward) stepwise procedure yielded the best results. Ot the two schemes involving dimensional analysis, that which uses correlations of scores on variables with high maximue likalihood factor loadings again-A discriminant scores appeared more attractive. (Author) ON THE VARIABLE SELECTION PROBLEM IN WILTIPLE GROUP DISCRIMINANT ANALYSIS U S DEPARTMENT OF MEALiN. EDUCATION & WELFARE OFFICE OI EDL.CATION THIS DOCUMENT hAS BEEN ArP1GOLICED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ONIGINATING IT POINTS OF V,EW OR OPN'ONS 57,010 00 507 NECE.5 SA RILS REPRESENT OFFICIAL OFF ICE OF IOU CA 1105 POSITION C t POLICY
TL;DR: In this article, the Wherry-Doolittle procedure has been used for over 30 years to reduce the number of variables in a multiple correlation, and techniques for obtaining the same kind of reduction in the cases of canonical correlation discriminant analysis and multivariate analysis of variance have been described.
Abstract: The Wherry-Doolittle proceedure has been used for over 30 years to reduce the number of variables in a multiple correlation. This paper describes techniques for obtaining the same kind of reduction of number of variables in the cases of canonical correlation discriminant analysis and multivariate analysis of variance. Statistical tests comparable to those used in the Wherry-Doolittle procedure are cited.
TL;DR: It is shown, that simply adding blood sugar values, taken at different intervals after glucose load, meets up with certain sources of error and a better method to combine different blood Sugar values is the discriminant analysis.
Abstract: It is shown, that simply adding blood sugar values, taken at different intervals after glucose load, meets up with certain sources of error. A better method to combine different blood sugar values is the discriminant analysis. Two discriminant functions are communicated for a material of 1262 non-diabetics and 267 diabetics; these functions can be replaced by nomograms.
01 Jan 1971
TL;DR: In this paper, a preliminary study of the feasibility of using categorical variables in discriminant function analysis was performed and the results showed that the use of categorical data has much potential as a statistical tool in classification procedures.
Abstract: The Effectiveness of Categorical Variables in Discriminant Function Analysis by Preston Jay Waite, Master of Science Utah State University, 1971 Major Professor: Dr. Rex L. Hurst Department: Applied Statistics A preliminary study of the feasibility of using categorical variables in discriminant function analysis was preformed. Data including both continuous and categorical variables were used and predictive results examined. The discriminant function techniques were found to be robust enough to include the use of categorical variables. Some problems were encountered with using the trace criterion for selecting the most discriminating variables when these variables are categorical. No monotonic relationship was found to exist between the trace and the number of correct predictions. This study did show that the use of categorical variables does have much potential as a statistical tool in classification procedures.
01 Jan 1971
TL;DR: A calibration run conducted in the northern area of the East Canton oilfield verified that valid forecasts can be obtained by the discriminant analysis procedure, and indicated to be adequate and potentially helpful in arriving at decisions concerning well completion.
Abstract: Discriminant analysis, a statistical technique, was used to classify oil wells into productivity groups based upon data obtained from geophysical well logs. A calibration run conducted in the northern area of the East Canton oilfield verified that valid forecasts can be obtained by the procedure. Of 20 wells studied, four appeared to have a greater potential than that indicated by actual production figures. A similar study of the southern area of the East Canton reservoir also proved discriminant analysis to be effective for predicting productivity, although different variables were significant than those for the north reservoir. Discriminant analysis was indicated to be adequate and potentially helpful in arriving at decisions concerning well completion.
TL;DR: A criterion is proposed for the admissible order of this rounding off of the discriminant function coefficients and it is shown that the order in which the coefficients are rounded off affects the classification power of the function.
Abstract: The loss of the classification power of a linear discriminant function caused by rounding off the discriminant function coefficients is evaluated. A criterion is proposed for the admissible order of this rounding off.