Showing papers on "Linear discriminant analysis published in 1982"

Analyzing and Interpreting Significant MANOVAs

Abstract: Multivariate statistical methods have been strongly recommended in educational and psychological research, which employs multiple dependent variables. While the techniques are readily available there is still controversy as to the proper use of the methods. This paper reviews the available methods for analyzing and interpreting data with multivariate analysis of variance and provides some guidelines for their use. In addition, causal models that underlie the various methods are presented to facilitate the use and understanding of the methods

Classification, pattern recognition, and reduction of dimensionality

Abstract: Discriminant Analysis for Time Series (R.H. Shumway). Optimum Rules for Classification into Two Multivariate Normal Populations with the Same Covariance Matrix (S. D. Gupta). Large Sample Approximations and Asymptotic Expansions of Classification Statistics (M. Siotani). Bayesian Discrimination (S. Geisser). Classification of Growth Curves (J.C. Lee). Nonparametric Classification (J.D. Broffitt). Logistic Discrimination (J.A. Anderson). Nearest Neighbor Methods in Discrimination (L. Devroye, T.J. Wagner). The Classification and Mixture Maximum Likelihood Approaches to Cluster Analysis (G.J. McLachlan). Graphical Techniques for Multivariate Data and for Clustering (J.M. Chambers, B. Kleiner). Cluster Analysis Software (R.K. Blashfield, M.S. Aldenderfer, L.C. Morey). Single-link Clustering Algorithms (F.J. Rohlf). Theory of Multidimensional Scaling (J. de Leeuw, W. Heiser). Multidimensional Scaling and its Applications (M. Wish, J.D. Carroll). Intrinsic Dimensionality Extraction (K. Fukunaga). Structural Methods in Image Analysis and Recognition (L.N. Kanal, B.A. Lambird, D. Lavine). Image Models (N. Ahuja, A. Rosenfeld). Image Texture Survey (R.M. Haralick). Applications of Stochastic Languages (K.S. Fu). A Unifying Viewpoint on Pattern Recognition (J.C. Simon, E. Backer, J. Sallentin). Logical Functions in the Problems of Empirical Prediction (G.S. Lbov). Inference and Data Tables with Missing Values (N.G. Zagoruiko, V.N. Yolkina). Recognition of Electrocardiographic Patterns (J.H. van Bemmel). Waveform Parsing Systems (C.G. Stockman). Continuous Speech Recognition: Statistical Methods (F. Jelinek, R.L. Mercer, L.R. Bahl). Applications of Pattern Recognition in Radar (A. Grometstein, W.H. Schoendorf). White Blood Cell Recognition (E.S. Gelsema, G.H. Landeweerd). Pattern Recognition Techniques for Remote Sensing Applications (P.H. Swain). Optical Character Recognition - Theory and Practice (G. Nagy). Computer and Statistical Considerations for Oil Spill Identification (Y.T. Chien, T.J. Killeen). Pattern Recognition in Chemistry (B.R. Kowalski, S. Wold). Covariance Matrix Representation and Object-Predicate Symmetry (T. Kaminuma, S. Tomita, S. Watanabe). Multivariate Morphometrics (P.A. Reyment). Multivariate Analysis with Latent Variables (P.M. Bentler, D.G. Weeks). Use of Distance Measures, Information Measures and Error Bounds in Feature Evaluation (M. Ben-Bassat). Topics in Measurement Selection (J.M. Van Campenhout). Selection of Variables under Univariate Regression Models (P.R. Krishnaiah). On the Selection of Variables under Regression Models using Krishnaiah's Finite Intersection Tests (J.L. Schmidhammer). Dimensionality and Sample Size Considerations in Pattern Recognition Practice (A.K. Jain, B. Chandrasekaran). Selecting Variables in Discriminant Analysis for Improving upon Classical Procedures (W. Schaafsma). Selection of Variables in Discriminant Analysis (P.R. Krishnaiah). Index.

A new procedure for analysis of medical classification.

Abstract: A number of classification techniques have been applied to the analysis of medical diagnostic systems and decision making. Commonly used approaches such as cluster analysis, linear discriminant analysis and Bayesian classification are subject to logical and statistical limitations. In this paper we present a methodology, called »grade of membership« analysis, which resolves many of those limitations. This methodology deals simultaneously with the dual problems of case clustering and estimation of discriminant coefficients. The methodology also permits the assessment of the reliability of externally defined medical diagnoses, multiple diagnoses for individuals, disease progression and severity, and permits the representation of patient heterogeneity within diagnostic category. Maximum likelihood principles are invoked both to obtain parameter estimates and as a basis for likelihood ratio testing of complex hypotheses about the model structure. The model is illustrated by an analysis of data on abdominal symptoms and disease.

1 Discriminant analysis for time series

Abstract: Publisher Summary The extension of classical pattern recognition techniques to experimental time series data is a problem of great practical interest. Time series classification problems are not restricted to geophysical applications but occur under many and varied circumstances in other fields. The potential applications of time series discriminant functions can be the identified recorded speech data where one may be interested in discriminating between the various speech patterns. This chapter reviews the standard approach to the problem of discriminating between two normal processes with unequal means or covariance functions. The two cases lead separately to linear or quadratic discriminant functions that can be approximated by spectral methods if the covariance function is stationary. The discriminant functions and their performance characteristics are approximated by frequency domain methods, leading to simple and easily computed expressions. The methods for determining whether the group patterns are better modelled as by differing in the mean values or covariance and the estimation of means and spectra from a learning population are discussed in the chapter. The chapter provides an example that shows the application of the techniques to the problem of discriminating between short period seismic recordings of earthquakes and explosions.

Variable selection techniques in discriminant analysis: II. Allocation

Abstract: The literature dealing with the selection of variables for allocation procedures is examined. Two types of technique are discussed, namely, those which use group separation as the criterion for variable selection and those which more appropriately employ error rates in allocation.

Variable selection techniques in discriminant analysis: I. Description

Abstract: The problem of assessing the relative importance of variable subsets in discriminant analysis is discussed. Attention is focused on techniques for determining those subsets which are ‘adequate’ for discrimination from the descriptive viewpoint. A number of procedures which have been proposed or used in the literature are described, illustrated and compared with reference to various aspects, including rationale, statistical significance testing and computational difficulties.

Discrimillant Analysis with Discrete and Continuous Variables

Abstract: A paradigmatic methodologic approach does not exist for the problem of discriminant analysis with both discrete and continuous explanatory variables. Procedures that have been employed in this situation include Fisher's linear discriminant function, the quadratic discriminant function, the linear discriminant furlction with higher-order terms, discriminant functions with logistic regression estimates of the coefficients, and the location model. Average optimal error rates for these procedures are reported for the case of one normal variable and two binary variables. These approaches are also compared for the prediction of two-year survival following recovery from myocardial infarction, employing resubstitution, jackknife and independent-sample estimates of the error rates. Recommendations for applications are presented.

Classification and misclassification in sexing the Black femur by discriminant function analysis.

Abstract: Stepwise discriminant function analysis for sex assessment was applied to 130 North American Black femora. The measurements included femoral length and three midshaft dimensions likely to be preserved in archaeologically derived and forensic remains. The method correctly assigned sex for 76.4% of the sample (range 70.8–81.5%). This compares favorably with results achieved with other skeletal parts; it also compares favorably with results using the femur in sexing other racial groups. Among our other conclusions are: (1) a “general size factor” is one of major significance in correct classification and in misclassification of sex, and most misclassified individuals are anomalous for this factor; (2) the inconsistency in the relation between circumference and femoral length, which characterizes the remaining misclassified individuals, suggests that anomalous functional demands of body weight/musculature are at fault, and affect circumference more than length; and (3) discriminant function analysis of the same variables in Whites produced similar results, suggesting that sex overrides race in sex assessment; this was confirmed by cross-validating the predictive accuracy of Black discriminant function coefficients on White data, and vice versa.

31 Pattern recognition in chemistry

Abstract: Publisher Summary Multivariate methods of pattern recognition, classification, discriminant analysis, factor and principal components analysis and the like have been found most useful in many types of chemical problems. With increasing experience of multivariate data analysis, chemists have reached a better understanding of the nature of chemical data and, thereby, have been able to specify more explicitly which kind of information one wants to extract from the data. This chapter describes this understanding of how to apply pattern recognition in chemistry. The multivariate nature of chemical measurements generated by modern chemical instrumentation together with the nature of chemical theory which involves unobservable “micro”-properties make a strong case for a rapidly increased use of multivariate data analysis including various methods of pattern recognition in chemistry. With the availability of fast, inexpensive and graphics-oriented computers, the large number of calculations is no longer a problem.

The Use of Shrinkage Estimators in Linear Discriminant Analysis

Abstract: Probably the most common single discriminant algorithm in use today is the linear algorithm. Unfortunately, this algorithm has been shown to frequently behave poorly in high dimensions relative to other algorithms, even on suitable Gaussian data. This is because the algorithm uses sample estimates of the means and covariance matrix which are of poor quality in high dimensions. It seems reasonable that if these unbiased estimates were replaced by estimates which are more stable in high dimensions, then the resultant modified linear algorithm should be an improvement. This paper studies using a shrinkage estimate for the covariance matrix in the linear algorithm. We chose the linear algorithm, not because we particularly advocate its use, but because its simple structure allows one to more easily ascertain the effects of the use of shrinkage estimates. A simulation study assuming two underlying Gaussian populations with common covariance matrix found the shrinkage algorithm to significantly outperform the standard linear algorithm in most cases. Several different means, covariance matrices, and shrinkage rules were studied. A nonparametric algorithm, which previously had been shown to usually outperform the linear algorithm in high dimensions, was included in the simulation study for comparison.

Discrimination with Mixed Binary and Continuous Data

Abstract: SUMMARY This paper consists of a case study in the use of different methods of Discriminant analysis. Methods used include Fisher's Linear discriminant function, various modifications of this technique, Logistic discrimination and Kernel methods using jack-knife maximum likelihood. These methods are applied on two sets of data. Their success is compared using the proportions misclassified, estimated by the "leaving-one-out" method where possible.

Estimation of Error Rates in Several-Population Discriminant Analysis:

Abstract: Researchers seeking to estimate the classification accuracy of linear discriminant functions in a more than two-population setting have had little guidance as to the most appropriate technique. The...

Nest-site characteristics of the avian community in the dune-ridge forest, Delta Marsh, Manitoba: a multivariate analysis

Abstract: Nest-site characteristics of nine bird species breeding in high densities in the dune-ridge forest at Delta Marsh, Manitoba, were analyzed using multivariate techniques. Varimax-rotated principal component analysis of the entire set of nest-site variables suggested partitioning of the data into nest-habitat and nest-tree subsets. Discriminant analysis of nest-habitat variables confirmed the ambiguous nature of species relationships in the factor analysis. Discriminant analysis of nest-tree variables identified three distinct groups of species, based primarily on vertical stratification. The existence of these groups and their memberships were supported by similar results derived from discriminant analysis of the entire nest-site data set. Within these groups, pairs of species showed sufficient similarity in nest sites to warrant detailed investigation.

Updating a Discriminant Function On the Basis of Unclassified Data

Abstract: The problem of updating a discriminant function on the basis of data of unknown origin is studied. There are observations of known origin from each of the underlying populations, and subsequently there is available a limited number of unclassified observations assumed to have been drawn from a mixture of the underlying populations. A sample discriminant function can be formed initially from the classified data. The question of whether the subsequent updating of this discriminant function on the basis of the unclassified data produces a reduction in the error rate of sufficient magnitude to warrant the computational effort is considered by carrying out a series of Monte Carlo experiments. The simulation results are contrasted with available asymptotic results.

Validity of Social Behavior Assessment in Discriminating Emotionally Disabled from Nonhandicapped Students

Abstract: Discriminant analyses and stepwise multiple regression techniques were applied to teacher ratings of 184 kindergarten through eighth-grade students using Stephen's Social Behavior Assessment (SBA) inventory and were used to predict group membership as emotionalyy disabled (ED) or non-ED. The results suggested that the SBA was highly effective in correctly discriminating ED from non-ED students. The linear discriminant function derived from the 30 SBA subcategories correctly classified 83% of the subjects, yielding a highly significant separation of groups of ED and non-ED children. While the results of the discriminant analyses have not yet been cross-validated, these findings support the discriminant validity of the SBA for ED versus non-ED classification and suggest that the SBA is potentially a useful instrument for school psychologists as one source of information in a multifactored assessment regarding the identification of children as ED.

Stock Identification of Sockeye Salmon (Oncorhynchus nerka) with Scale Pattern Recognition

Abstract: The non-Gaussian density functions underlying polynomial discrimant functions are employed in a classification scheme designed for sockeye salmon (Oncorhynchus nerka). A leaving-one-out approach is used to estimate the smoothing parameters in the density functions and to obtain nearly unbiased estimates of expected actual error rates in the classification scheme. The result is that all available observations of known origin may be used to determine the discriminant rule and estimate classification error rates. These are needed to obtain point estimates of the proportions of subpopulations present in areas of intermingling. Several additional improvements over the polynomial discriminant method are noted. The scheme is applied to scale measurement data of sockeye salmon from Bristol Bay, the Gulf of Alaska, and the Kamchatka Peninsula.Key words: stock identification, discriminant analysis, sockeye salmon

On using linear programming in discriminant problems

Abstract: This commentary evaluates the usefulness of the Freed and Glover [6] linear programming approach to the discriminant problem, relates linear programming to other parametric and nonparametric approaches, and evaluates the linear programming approach.

A test for additional information in canonical correlation analysis

Abstract: In canonical correlation analysis a hypothesis concerning the relevance of a subset of variables from each of the two given variable sets is formulated. The likelihood ratio statistic for the hypothesis and an asymptotic expansion for its null distribution are obtained. In discriminant analysis various alternative forms of a hypothesis concerning the relevance of a specified variable subset are also discussed.

Quadratic discriminant analysis as an aid to interpretive reporting of clinical laboratory tests.

Abstract: PHYSICIANS order more laboratory tests today than ever before. Because of the increasing likelihood of clinically spurious values with the increasing number of tests, the difficulty of detecting many medical conditions in early stages, and the difficulty in differentiating among certain medical conditions, interpretive reporting of laboratory results can be of diagnostic value. See also p 2261. A number of sophisticated mathematical approaches have been applied to the analysis of clinical laboratory data. 1-3 One of the more commonly used approaches is discriminant analysis (DA), 4,5 which is a complex mathematical form of pattern recognition, wherein it is determined whether two or more defined medical conditions can be differentiated on the basis of variables other than those used to define the medical conditions. Quadratic discriminant analysis (QDA) is a nonlinear form of DA that does not assume that the variability present in the discriminating variables (eg, clinical laboratory tests) is

The Study Of Effects In Manova.

Abstract: A particular strategy for investigating effects resulting from a MANOVA is proposed. The strategy involves multiple two-group multivariate analyses. The two groups result from considering multivariate pairwise group contrasts or multivariate complex group contrasts. Assuming a given two-group analysis yields real effects, the resultant single linear discriminant function (LDF) may be studied. A rationale based on a transformation of LDF weights, due to V. Y. Urbakh, is recommended for assessing variable relative contribution. The analysis strategy is described in detail and illustrated with real data sets.

Discriminant analysis based on binary and continuous variables

Abstract: An observation consisting of both binary and continuous variables may be classified into one of two populations by the double-discriminant function based on the point-biserial model. When the parameters are unknown or partially known, a sample double-discriminant function is obtained by replacing the unknown parameters by their sample estimates. A sampling scheme referred to as the double inverse sampling is proposed to ensure nonsingularity of the sample covariance matrices. An asymptotic expansion for the distribution of the sample double-discriminant function is given under the double inverse sampling scheme. Comparisons of three classification procedures—double-discriminant function, X-out procedure, and X-continuous procedure—are made.

6 Nonparametric classification

Abstract: Publisher Summary As the LDF and QDF rules have simple forms and are based on the normal distribution, they have become the most widely used rules for discriminant analysis. Recently, statisticians have shown greater awareness and concern for the presence of outliers in sample data — that is, the observations that are abnormally distant from the center or the main body of the data. The outliers are particularly hard to spot in multivariate data because one cannot plot points in more than two or three dimensions. It is because of the persistence of non-normal data that are interested in non-parametric classification. A method that uses ranks of the discriminant scores to classify z and reviews robust and non-parametric discriminant functions are presented in the chapter. A method of ranking discriminant scores is also presented in the chapter. The rules for partial and forced classification are defined in terms of these ranks. The rank method provides an opportunity to adaptively select discriminant functions.

A prior probability method for smoothing discriminant analysis classification maps

Abstract: A statistical method is presented for smoothing discriminant analysis classification maps by including pixel-specific prior probability estimates that have been determined from the frequency of tentative class assignments in a window moving across an initial per-point classification map. The class at the center of the window is reevaluated using the data for that location and the prior probability estimates obtained from the window area. An example using Landsat spectral data demonstrates the effectiveness of the method and shows an increase in classification accuracy after smoothing.

40 Selecting variables in discriminant analysis for improving upon classical procedures

Abstract: Publisher Summary This chapter discusses selecting variables in discriminant analysis for improving upon classical procedures. Standard procedures show often a degrading performance if the number of involved variables is increased beyond a certain bound p. This very interesting phenomenon has been observed by many scientists. Various intrinsically different illustrations can be made because the underlying aims can be different or be specified differently. Of course, the illustrations will also depend upon the underlying parameters and sample sizes. It is interesting to remark that for some completely specified aims holds that the performance of the standard procedure admits different specifications and that even the concept of standard procedure can be doubtful. These variations are of course of almost no importance when compared with the influences of the sample sizes, the underlying parameter and, in particular, the specification of the aim in mind. This phenomenon implies that the standard procedure based on all s variables can often be improved by deleting variables. It depends on the specific aim, performance, values of the underlying parameters and sample sizes that selection of variables should be made.

Approaches for the Interpretation of Multiple Discriminant Analysis in Organizational Research

Abstract: The use of plots of multiple discriminant analysis (MDA) results and the use of discriminant function rotations to improve interpretability of findings in organizational research applying MDA are examined and illustrated. A simple, innovative plotting procedure, which depicts overlaps of groups in MDA combined with the traditional depiction of differences among groups, is discussed and illustrated. An example taken from a health care administrative application is presented for illustrative purposes.