Showing papers on "Linear discriminant analysis published in 1986"

Multivariate Data Analysis

Abstract: Foreword. 1. Data Coding and Initial Treatment. 2. Principal Components Analysis. 3. Cluster Analysis. 4. Discriminant Analysis. 5. Other Methods. 6. Case Study: IUE Low Dispersion Spectra. 7. Conclusion: Strategies for Analysing Data. Index.

Evaluating alternative linear programming models to solve the two-group discriminant problem

Abstract: The two-group discriminant problem has applications in many areas, for example, differentiating between good credit risks and poor ones, between promising new firms and those likely to fail, or between patients with strong prospects for recovery and those highly at risk. To expand our tools for dealing with such problems, we propose a class of nonpara-metric discriminant procedures based on linear programming (LP). Although these procedures have attracted considerable attention recently, only a limited number of computational studies have examined the relative merits of alternative formulations. In this paper we provide a detailed study of three contrasting formulations for the two-group problem. The experimental design provides a variety of test conditions involving both normal and nonnormal populations. Our results establish the LP model which seeks to minimize the sum of deviations beyond the two-group boundary as a promising alternative to more conventional linear discriminant techniques.

Correlation synthetic discriminant functions.

Abstract: Advanced filters are described for distortion-invariant space-invariant object identification and location in clutter using correlators. These correlation synthetic discriminant functions (SDFs) are extensions of earlier projection SDFs. They provide control of the sidelobe levels and the shape of the output correlation function as well as its peak intensity. The theory for synthesis of three such SDFs and a discussion of correlation plane detection criteria for use with these filters are presented.

Voiced/Unvoiced classification of speech with applications to the U.S. government LPC-10E algorithm

Abstract: This paper describes the development and application of a new voicing algorithm used in the 2400 bit per second U.S. Government's Enhanced Linear Predictive Coder (LPC-10E). Correct voicing is crucial to perceived quality and naturalness of LPC systems and therefore to user acceptance of LPC systems. This new voicing algorithm uses a smoothed adaptive linear discriminator to classify the signal as voiced or unvoiced speech. The classifier was determined using Fisher's method of linear discriminant analysis. The voicing decision smoother is a modified median smoother that uses both the linear discriminant and speech onsets to determine its smoothing. The voicing classifier adapts to various acoustic noise levels and features a powerful new set of signal measurements: biased zero crossing rate, energy measures, reflection coefficients, and prediction gains. The LPC-10E voicing algorithm improves upon other 2400 bps LPC voicing algorithms by providing higher quality synthesized speech. Higher quality is due to halving of the error rate and graceful degradation in the presence of acoustic noise.

Choice of the smoothing parameter and efficiency of k-nearest neighbor classification

Abstract: A simulation study was performed to investigate the sensitivity of the k -nearest neighbor (NN k ) rule of classification to the choice of k . The optimal choice of k was found to be a function of the dimension of the sample space, the size of the space, the covariance structure and the sample proportions. The nearest neighbor rules chosen using the k suggested by the simulations had correct classification rates at least as high as those rates for the linear discriminant function and the logistic regression method. In particular, the rule became more efficient as the difference in the covariance matrices increased, and also when the difference in sample proportion was large. An adaptive rule which selects k by iteratively maximizing the local Mahalanobis distance is shown to be efficient, thus abrogating the need to know the underlying population variance-covariance structure.

Notes and Communications RESOLVING CERTAIN DIFFICULTIES AND IMPROVING THE CLASSIFICATION POWER OF LP DISCRIMINANT ANALYSIS FORMULATIONS

Abstract: In certain settings, difficulties arise that limit the effectiveness of LP formulations for the discriminant problem. Explanations and possible remedies have been offered, but these have had only limited success. We provide a simple way to overcome these problems based on an appropriate use and interpretation of normalizations. In addition, we demonstrate a normalization that is invariant under all translations of the problem data, providing a stability property not shared by previous approaches. Finally, we discuss the possibility of using more general models to improve discrimination.

Regional flood frequency analysis II: Multivariate classification of drainage basins in Britain

Abstract: The homogeneity statistic developed in the previous paper (Wiltshire, 1986) is applied here to geographical regions and to clusters of basins formed in a flow-statistic dataspace. Clusters are seen to offer several advantages over geographical regions and they are interpreted in terms of basin characteristics through the use of a multivariate linear discriminant analysis. The discriminant scores of each basin based on basin characteristics can be used to assess the performance of the original independent classification based on flow statistics. An ungauged basin for which a design flood is required can have a fractional membership of more than one cluster, and the desired quantile can then be estimated as a weighted average of quantile estimates from each cluster. Experiments with hypothetical ungauged basins show that the allocation of basins to clusters is in accord with physical reasoning.

Multiple group logistic discrimination

Abstract: Among the many possible approaches suggested for statistical discrimination, the logistic method can be classified midway between fully distributional solutions, of which the assumption of multivariate normality is a classical example[16l, and the distribution-free techniques, using, for instance, kernel or nearest-neighbor methods[l,32]. Therefore it is often called a partially parametric or partially distributional method[l l]. This central position of the logistic model makes it one of the most attractive and widely used tools for solving regression and discrimination problems. Indeed, since there are fewer distributional assumptions than for fully parametric models, the logistic method is applicable to a larger family of multivariate distributions involving both discrete and continuous variables. Moreover, in spite of its wide applicability and generality, the method remains feasible and easy to use, in contrast with nonparametric methods. This paper is intended to review the basic ideas and principles of logistic discrimination[415,22-25] and also to bring additional results to some of the queries raised by Professor Anderson before his death. We restrict our attention to discrimination between qualitatively distinct groups and do not envisage the case where groups are quantitatively distinct or ordered[3,12,14]. We dedicate this paper to our friend and mentor, the late Professor J. A. Anderson, for his fundamental contribution to discriminant analysis and for his continuous support of our research efforts.

Categorizing Individuals: An Alternative to Linear Analysis

Abstract: A common problem concerns the relations between children's behaviour or characteristics at one age or in one situation, and those shown later or in another context. It is argued here that Pearson or rank order correlations may not be ubiquitously suitable for assessing such relations, primarily because independent variables (IV's) and dependent variables (DV's) may be related for only some of the children (e.g., those high on the IV may tend to be high on the DV, but for children with lower scores on the IV there may be no relation to the scores on the DV). Categorization procedures can help. It is shown that the use of Pearson correlations, multiple regression, continuous discriminant analysis and discrete discriminant analysis on the same data sets show up different types of relations between IV's and DV's. Categorization procedures can also facilitate examination of individual cases.

Minimum-variance synthetic discriminant functions

Abstract: The conventional synthetic discriminant functions (SDF’s) determine a filter matched to a linear combination of the available training images such that the resulting cross-correlation output is constant for all training images. We remove the constraint that the filter must be matched to a linear combination of training images and consider a general solution. This general solution is, however, still a linear combination of modified training images. We investigate the effects of noise in input training images and prove that the conventional SDF’s provide minimum output variance when the input noise is white. We provide the design equations for minimum-variance synthetic discriminant functions (MVSDF’s) when the input noise is colored. General expressions are also provided to characterize the loss of optimality when conventional SDF’s are used instead of optimal MVSDF’s.

Potential prediction bias in regression and discriminant analysis

Abstract: Prediction bias is the difference between a model's apparent and actual prediction errors. Prediction bias is likely to occur when a model contains many independent variables relative to sample siz...

Selection of variables in mixed-variable discriminant analysis

Abstract: A MANOVA-log-linear formulation of the location model for mixed-variable discriminant analysis is considered. A strategy for the selection of variables and terms in such a model is based on Akaike's criterion. To overcome problems caused by noncomparable submodels, some modifications to Akaike's criterion are proposed. An example of discrimination between bad and good melons illustrates the selection procedure.

Statistical methods in medical diagnosis.

Abstract: A review of statistical methods in medical diagnosis is presented Research has focused on three distinct tasks: classification of subjects into probable diagnostic categories on the basis of presenting clinical indicators (discriminant analysis), assessment of diagnostic test characteristics, and relation of diagnostic testing to subsequent patient management Although many sophisticated models have been developed for discriminant analysis, recent empirical comparisons indicate that standard methods such as linear discrimination and logistic regression work very well More research is needed to overcome practical difficulties that are not accommodated in the conventional assumptions Research on the assessment of diagnostic tests has been oriented more toward selection biases and practical problems There is a need to develop generalized models for the problem of differential diagnosis The relation of testing to subsequent management of the patient is a topic that has only recently been explored It represents an important task in the cost-effective management of health resources

An alternative choice of smoothing for kernel-based density estimates in discrete discriminant analysis

Abstract: SUMMARY The kernel method of estimating the cell probabilities of a multivariate categorical distribution, due to Aitchison & Aitken (1976), depends crucially on an unknown smoothing parameter A A method of estimating A is introduced which is explicitly connected to multivariate discrimination The method, based on maximization of the leaving-one-out estimator of the nonerror rate, is shown to be Bayes risk strongly consistent An example is given to illustrate the application

Using Categorical Variables in Discriminant Analysis

Abstract: Three methods of transforming unordered categorical response variables are described. One is a method using dummy variables. The second method, in which all categorical variables are analyzed simultaneously, is based on an eigenanalysis of frequency patterns scaled relative to within-groups variance, jointly developed by J. E. Overall and J. A. Woodward. With the third method, independently developed by R. A. Fisher and H. O. Lancaster, each categorical variable is analyzed separately with scale values generated so that the grouping variable and the categorical variable are maximally correlated. Results from analyzing two real data sets are used to illustrate the application of the three methods.

Variable Selection in Heteroscedastic Discriminant Analysis

Abstract: The likelihood ratio test statistic for the identity in means and covariance matrices of k normal populations has a well-known step-down decomposition measuring the contribution of each component of the vector observation. This decomposition in turn gives rise to three components testing the residual homo-scedasticity of each variable, the parallelism of its regression on its predecessors, and the identity of location. A variety of uses of this decomposition in selecting variables is proposed.

Multiple discriminant analysis in the presence of mixed continuous and categorical data

Abstract: It is shown that for the two-group case, classification by minimum distance is equivalent to classification from the maximum-likelihood discriminant rule based on the location model for mixed data. This enables straightforward extension to be made to classification in the g (>2)-group case with such data. An example is given in which the performance of the proposed rule is compared with the performance of the traditional normal-based rule.

Some Recent Results in Signal Detection.

Abstract: : Some recent results on the detection and estimation of signals in the presence of noise are discussed. An exact confidence lower bound is obtained for the discriminatory power of an estimated linear discriminant function for signal detection. Information theoretic criteria are suggested for the estimation of signals. A new method is proposed for determining the number of signals and estimating them in exponential signal models. Keywords: Discriminant function; Exponential signal models; Information criteria in model selection; Prony's method; Signal processing.

Site Surface Characteristics and Functional Inferences

Abstract: With the rise in importance of the archaeological survey as a major data-recovery tool has come greater concern over methods for making inferences about site subsurface characteristics from surface materials. One growing area of concern is the identification of site function using surface features and artifact assemblages. Here we examine the relations among architectural site types (defined using surface features), modeled functional site types, and surface artifact assemblage characteristics. Analysis proceeded in three stages, each one built on the previous stage. In the first stage we used site type models to predict surface assemblage differences between types and then tested these predictions with the surface assemblages from surveyed sites grouped by architecture type. The procedures involved analysis of variance, difference-of-means tests, and discriminant analysis. In the second stage, we used discriminant analysis to create a classification function for predicting site type on the basis of artifact assemblages. In the third stage of the analysis, we investigated possible reasons for the uneven classification results. We conclude our analyses by presenting an example of functional change that affects the ability of the discriminant analysis to distinguish between two of the site types.

Enological Parameters and Pattern Recognition Methods in the Geographic Differentiation of Spanish Red Wines

Abstract: Two hundred thirty wines, 1976 to 1983 vintages, from four different Spanish regions have been analyzed by pattern recognition methods in order to characterize the groups and classify unknown samples according to their geographic origin. The nine physico-chemical parameters determined are termed inexpensive variables since they can be evaluated at any enological station. The variables lactic, tartaric, and malic acids, titratable acidity, and potassium content are the most relevant in this study. The effect of factors such as varietal diversity, climatic conditions, or winemaking techniques, which account for the differences in the mean values of the variables for each region, are discussed. Coincident classification results have been found for all three supervised methods of analysis used: statistical linear discriminant analysis (SLDA), linear learning machine (LLM), and K-nearest neighbor (KNN). The correct classification percentage obtained has been ca 90% for all procedures employed.

On linear lon-odds and estimation of discriminant coefficients

Abstract: Fisher's Linear Discriminant Function Can be used to classify an individual who has sampled from one of two multivariate normal Populations. In the following, this function is viewed as the other given his data vector it is assumed that the Population means and common covariance matrix are unknown. The vector of discriminant coeffients β(p×1) is the gradient of posterior log-odds and certain of its lineqar functions are directional derivatives which have a practical meaning. Accordingly, we treat the problems of estimating several linear functions of β The usual estimatoes of these functions are scaled versions of the unbiased estmators. In this Paper, these estimators are domainated by explicit alterenatives under a quadratic loss function. we reduce the problem of estimating β to that of estimating the inverse convariance matrix.

A possible pitfall in the morphometric application of discriminant analysis: measurement bias

Abstract: Standard methods of evaluating the effectiveness of a discriminant analysis do not include an examination of the possible effect of measurement errors. An example (based on squid-beak morphometrics) is given, where a relatively small degree of bias could reduce the probability of correct classification of one species from 89% to less than 50%. This is used to illustrate a general procedure for evaluating the extent of bias in morphometric measurements and its potential effect on a discriminant function. It is recommended that such a procedure be part of the evaluation of any published discriminant based on morphometrics.

On a classification rule for multiple measurements

Abstract: In this paper an optimum procedure, based on the maximum-likehood criterion, for classification into one of two populations has been studied when multiple observations are available on the same variable for each individual. The distribution of the classification statistics, which turns out to be a nonlinear function of the mean and variance of the observations of the individual, are derived, and formulae (exact and approximate) for the computation of the conditional probability of misclassification are given when the parameters are known, as well as when the parameters are unknown. This procedure is further extended to more than two populations.

A note on rank transformation discriminant analysis

Abstract: Recent studies in the financial literature have developed models to predict the rating assigned to a firm's debt by the rating agencies. Multiple discriminant analysis (MDA) has served as the primary statistical tool; however, the results of MDA can be biased. This study presents a less biased procedure which more closely follows that suggested by the rating agencies. The improved results of the model support such a procedure.

Chance Factors in Nonparametric Linear Discriminant Studies

Abstract: Studies were performed to determine if the screening of large pools of prospective variables could lead to fortuitous improvements in the classification success rates provided by nonparametric linear discriminants. These studies parallel earlier work by Topliss and Edwards on regression analysis. It was found that fortuitous increases do occur, but could probably be kept low if the number of examined variables is kept below one-half the number of observations.

Speech recognition method

Abstract: 57 For improving the efficiency of a speech recognition system based on a vocabulary of statistical word models, initially coarse word preselections are made for utterances, and are marked in a training session to indicate whether the selections were correct or wrong. Furthermore, each utterance is matched against each word preselected for it to obtain a probability measure for that combination as in a usual recognition process. Based on this knowledge of the correct or erroneous result of the coarse selection plus the probability measure, a discriminant analysis is made to determine, for the whole population of word models, how each phone in each word model should be weighted so that an optimum discrimination between similar words is achieved. The weighting coefficients thus obtained are stored with the word models and are later used, during actual speech recognition, to weight the probabilistic contribution of each phone for the final word selection.