Showing papers on "Linear discriminant analysis published in 1990"

A neural network model for bankruptcy prediction

Abstract: A neural network model is developed for prediction of bankruptcy, and it is tested using financial data from various companies. The same set of data is analyzed using a more traditional method of bankruptcy prediction, multivariate discriminant analysis. A comparison of the predictive abilities of both the neural network and the discriminant analysis method is presented. The results show that neural networks might be applicable to this problem

Improved linear programming models for discriminant analysis

Abstract: Discriminant analysis is an important tool for practical problem solving. Classical statistical applications have been joined recently by applications in the fields of management science and artificial intelligence. In a departure from the methodology of statistics, a series of proposals have appeared for capturing the goals of discriminant analysis in a collection of linear programming formulations. The evolution of these formulations has brought advances that have removed a number of initial shortcomings and deepened our understanding of how these models differ in essential ways from other familiar classes of LP formulations. We will demonstrate, however, that the full power of the LP discriminant analysis models has not been achieved, due to a previously undetected distortion that inhibits the quality of solutions generated. The purpose of this paper is to show how to eliminate this distortion and thereby increase the scope and flexibility of these models. We additionally show how these outcomes open the door to special model manipulations and simplifications, including the use of a successive goal method for establishing a series of conditional objectives to achieve improved discrimination.

Minimizing Misclassifications in Linear Discriminant Analysis

Abstract: A procedure is developed for determining two-group linear discriminant classifiers that misclassify the fewest number of observations in the training sample. An experimental study confirms the value of this approach.

Survey of mathematical programming models and experimental results for linear discriminant analysis

Abstract: The mathematical programming approach to linear disciminant analysis was first introduced in the early 1980's. Since then, numerous mathematical programming models have appeared in the literature. Some of these models were merely formulated while others were subjected to experimentation, in some cases rather extensively. The purpose of this paper is to present a unified survey of these models and their experimental results where applicable. Some mathematical programming (MP) models, unfortunately, have certain pathologies inherent in their structure which puts the degree of usefulness of these models in doubt. When known, such pathologies are also identified for the specific model in question.

Mathematical Programming Approaches for the Classification Problem in Two-Group Discriminant Analysis.

Abstract: The authors introduce mathematical programming formulations as new approaches to solve the classification problem in discriminant analysis. These formulations have recently emerged as powerful alternatives to the existing methods of maximizing correct classification of entities into groups. The research literature on mathematical programming formulations is reviewed and summarized. An illustration using a real-world classification problem is provided. issues relevant to potential users of these formulations as well as fruitful future research avenues are discussed.

Heuristic least-cost computation of discrete classification functions with uncertain argument values

Abstract: We consider the problem of minimizing the expected cost of computing the correct value of a discrete-valued function when it is costly to determine (“inspect”) the values of its arguments. This type of problem arises in distributed computing, in the design of interactive expert systems, in reliability analysis of coherent systems, in classification of pattern vectors, and in many other applications. In this paper, we first show that the general problem is NP-hard and then introduce several efficient heuristic sequential inspection procedures for solving it approximately. We obtain theoretical results showing that the heuristics are optimal in important special cases; moreover, their computational structures make them well suited for parallel implementation. Next, for the special case of linear threshold (or “discrete linear discriminant”) functions, which are widely used in statistical classification procedures, we use Monte Carlo simulation to analyze the performances of the heuristics and to compare the heuristic solutions with the exact (true minimum expected cost) solutions over a wide range of randomly generated test problems. All of the heuristics give average relative errors, compared to the exact optimal solutions, of less than 2%. The best heuristic for this class of functions gives an average relative error of less than 0.05% and runs two to four orders of magnitude faster than the exact solution procedure, for functions with ten arguments.

Classification of cheese varieties by multivariate analysis of HPLC profiles.

Abstract: Water extracts of Cheddar, Edam, Gouda, Swiss, and Parmesan cheeses were analyzed by HPLC with a reversed phase C8 column. Principal component and discriminant analyses were applied to 55 peak areas from each cheese chromatogram. Discriminant analysis on data from a single HPLC column was able to correctly classify cheeses by variety at a greater than 90% success rate. This classification rate dropped to 64% when data from four HPLC columns were combined, implicating the between-column variations are large. Average rate of correct classification calculated from the rates of four columns was 96.5% for the total of 106 cheese samples. Sensory tests carried out by a semi-trained panel correctly classified cheeses by variety at a 63% success rate for the same cheese samples.

EMG spectral shift as an indicator of fatigability in an heterogeneous muscle group.

Abstract: Changes in electromyogram (EMG) power spectra were investigated in the triceps surae musclesof two classes of individuals (untrained subjects and athletes) maintaining a plantarflexion torque of 80% of maximal voluntary contraction until exhaustion. A set of 23 parameters describing changes in the frequency content and power of EMG was defined. For most experiments, classical changes were found, indicating a shift of the EMG spectra towards lower frequencies and an increase in the total power of the signals. In 12% of the experiments, alternations in activity between synergistic muscles were found, leading to a large variability in the spectral parameters. After the expression of each experiment in terms of a reduced data matrix and matrix to vector transformations, three methods of discrimination were used to classify subjects with respect to changes in the EMG signal during sustained contraction: (1) evaluation of the most discriminating parameter, (2) principal components analysis, (3) transformation maximizing differences between classes. Method (3) was found to be preferable since it led to good separation of the two classes in a reference group of subjects and a satisfactory projection of each individual from a group of unknowns into the appropriate class. These results suggest using a method such as this for ergonomic or athletic training purposes rather than the usual method of monitoring the frequency shift of the EMG.

What Is in a Municipal Bond Rating

Abstract: Studies on the determinants of municipal bond ratings contain two conspicuous patterns: the use of financial accounting variables and the application of discriminant analysis to them. Over 70 different financial accounting variables have been specified, leading to different findings across the studies. In addition, discriminant analysis has been applied in these studies without correcting for violations of its underlying assumptions. Akaike's information criterion and Lachenbruch's U method are used to show how a probit model specified with economic base diversification, economic expansion, and fiscal management variables may be an improvement over the application of discriminant analysis to financial accounting variables in the determination of a triple A bond rating.

A Comparison of Linear Programming and Parametric Approaches to the Two‐Group Discriminant Problem*

Abstract: Recent simulation-based studies of linear programming models for discriminant analysis have used the Fisher linear discriminant function as the benchmark for parametric methods. This article reports experimental evidence which suggests that, while some linear programming models may match or even exceed the Fisher approach in classification accuracy, none of the fifteen models tested is as accurate on normally distributed data as the Smith quadratic discriminant function. At the minimum, further testing is warranted with an emphasis on data sets that arise from significantly non-Gaussian populations.

Stepwise canonical discriminant analysis of continuous digitalized signals: Application to chromatograms of wheat proteins

Abstract: Continuous digitalized signals such as spectra, electrophoregrams or chromatograms generally have a large number of data points and contain redundant information. It is therefore troublesome performing discriminant analysis without any preliminary selection of variables. A procedure for the application of canonical discriminant analysis (CDA) on this kind of data is studied. CDA can be presented as a succession of two principal component analyses (PCAs). The first is performed directly on the raw data and gives PC scores. The second is applied on the gravity centres of each qualitative group assessed on the normalized PC scores. A stepwise procedure for selection of the relevant PC scores is presented. The method has been tested on an illustrative collection of 165 size-exclusion high-performance (SE-HPLC) chromatograms of proteins of wheat belonging to 55 genotypes and grown in three locations. The discrimination of the growing locations was performed using seven to nine PC scores and gave more than 86% accurate classifications of the samples both in the training sets and the verification sets. The genotypes were also rather well identified, with more than 85% of the samples correctly classified. The studied method gives a way of assessing relevant mathematical distances between digitalized signals according to qualitative knowledge of the samples.

Discrimination of whole from broken corn kernels with image analysis

Abstract: Image Analysis In Conjunction With Statistical Pattern Recognition Was Used To Discriminate Whole Corn From Broken Com Kemels. Multivariate Discriminant Analysis Was Used To Develop Classification Rules To Aid In The Identification Of Whole Kernels And/Or Broken Kernels. Twelve Parameters Describing The Shape And Size Of Com Kernels Were Considered As Discriminators. A Stepwise Discriminant Analysis Was Performed To Identify Different Subsets Of The 12 Parameters To Consider As Discriminators. Subsets Of 7 And 4 Parameters, Along With The Full Set Of 12 Parameters, Were Evaluated For Discrimination Performance. Experiments Were Conducted With Different Optical Settings To Evaluate The Effect Of Image Resolution On The Results Of Discriminant Analysis. All Of The Broken And 98% Of The Whole Com Kemels In An Independent Set Of Unknown Kemels Were Correctly Identified When Using The Procedures Developed.

Discriminant analysis and supervised vector quantization for continuous speech recognition

Abstract: Several attempts to improve recognition accuracy with the use of supervised clustering techniques are described. These techniques modify the distance metric and/or the clustering procedure in a discrete hidden Markov model recognition system in an attempt to improve phonetic modeling. Three techniques considered are linear discriminant analysis, a hierarchical supervised vector quantization technique, and Kohonen's LVQ2 technique. All experiments were performed on the DARPA resource management speech corpus using the BBN BYBLOS system. Even though the techniques improved the phonetic recognition capability of the vector quantization, the overall word and sentence recognition accuracy did not improve. >

Adaptive-clustering optical neural net.

Abstract: Pattern recognition techniques (for clustering and linear discriminant function selection) are combined with neural net methods (that provide an automated method to combine linear discriminant functions into piecewise linear discriminant surfaces). The resulting adaptive-clustering neural net is suitable for optical implementation and has certain desirable properties in comparison with other neural nets. Simulation results are provided.

Interesting Projections of Multidimensional Data by Means of Generalized Principal Component Analyses

Abstract: Principal Component Analysis can produce several interesting projections of a point cloud if suitable inner products are chosen for measuring the distances between the units. We discuss two examples of such choices. The first one allows us to display outliers, while the second is expected to display clusters. Doing so we introduce a robust estimate of a covariance matrix and we investigate some of its properties.

Classification performance of mathematical programming techniques in discriminant analysis: Results for small and medium sample sizes

Abstract: The performance on small and medium-size samples of several techniques to solve the classification problem in discriminant analysis is investigated. The techniques considered are two widely used parametric statistical techniques (Fisher's linear discriminant function and Smith's quadratic function), and a class of recently proposed nonparametric estimation techniques based on mathematical programming (linear and mixed-integer programming). A simulation study is performed, analyzing the relative performance of the above techniques in the two-group case, for various small sample sizes, moderate group overlap and across six different data conditions. Training samples as well as validation samples are used to assess the classificatory performance of the techniques. The degree of group overlap and sample sizes selected for analysis in this paper are of interest in practice because they closely reflect conditions of many real data sets. The results of the experiment show that Smith's nonlinear quadratic function tends to be superior on the training samples and validation samples when the variances–covariances across groups are heterogeneous, while the mixed-integer technique performs best on the training samples when the variances–covariances are equal, and on validation samples with equal variances and discrete uniform independent variables. The mixed-integer technique and the quadratic discriminant function are also found to be more sensitive than the other techniques to the sample size, giving disproportionally inaccurate results on small samples.

Considerations for mathematical programming models in discriminant analysis

Abstract: This paper surveys problems that may appear in mathematical programming formulations for linear discriminant analysis. For some, there are known solutions. Other problems have not been adequately addressed. Specific problems and considerations include the choice of objective, unacceptable or improper solutions, side constraints, data translation and transformations, unbounded solutions, inconsistencies, gaps, and the balancing of misclassifications. Subject areas: Linear discriminant analysis, statistical methods, linear programming.

Discriminant Analysis Using Least Absolute Deviations

Abstract: Several linear programming methods have been suggested as discrimination procedures. A least absolute deviations regression procedure is developed here which is simpler to use and does not suffer from any lack of invariance. A simulation study shows it to be at least as effective as any of the methods previously discussed for normal and heavy-tailed distributions.

Neural networks for ECG classification

Abstract: The performance of the neural network approach in the diagnostic classification of 12-lead electrocardiograms (ECG) is investigated. For this study a validated ECG database established at the University of Leuven is used. Previous results obtained from the same database to derive two classifiers based on statistical models (linear discriminant analysis and logistic discriminant analysis) are taken as reference points in the evaluation. A simple neural network architecture is chosen: the feed-forward structure with the use of the back-propagation algorithm. Sensitivity, specificity, total and partial accuracy are the indices used for the assessment of the performance. The results show a comparable behavior with the two statistical methods. >

Stability and bias of classification rates in biological applications of discriminant analysis

Abstract: We assessed the sampling stability of classification rates in discriminant analysis by using a factorial design with factors for multivariate dimensionality, dispersion structure, configuration of group means, and sample size. A total of 32,400 discriminant analyses were conducted, based on data from simulated populations with appropriate underlying statistical distributions. Simulation results indicated strong bias in correct classification rates when group sample sizes were small and when overlap among groups was high. We also found that stability of the correct classification rates was influenced by these factors, indicating that the number of samples required for a given level of precision increases with the amount of overlap among groups. In a review of 60 published studies, we found that 57% of the articles presented results on classification rates, though few of them mentioned potential biases in their results. Wildlife researchers should choose the total number of samples per group to be at least 2 times the number of variables to be measured when overlap among groups is low. Substantially more samples are required as the overlap among groups increases. J. WILDL. MANAGE. 54(2):331-341 Researchers often analyze biological data with discriminant analysis, a statistical method useful for classifying individuals into groups and for highlighting group differences. Necessary features for applications are the separability of samples into distinct groups and the measurement of 1 or more attributes on each sample unit. Typical applications by wildlife biologists involve the identification of groups of distinct animal or plant species and the examination of group differences based on habitat attributes (Edge et al. 1987). Other applications include morphometric analysis of species differences (Troy 1985) and analysis of plant or animal assemblages based on species abundances (Matthews 1979). Williams (1981, 1983) characterized ecological applications of the methodology by their grouping indices and attributes, and Williams and Titus (1988) described more recent applications in terms of sample sizes, system dimensions, and other statistical attributes. In many biological applications of discriminant analysis, the classification functions are characterized by substantial variability associated with small sample sizes and high multivariate dimensionality. There have been several theoretical assessments of the statistical properties of classification rates, especially asymptotic properties under various distributional assumptions (Anderson 1973, Gordon and Olshen 1978). However, the few studies that focused on small sample properties were limited in scope (Van Ness 1979, Page 1985) and generally focused on biases in apparent classification rates (Moran 1975, McLachlan 1976). Because wildlife studies often are hindered by an inability to collect a large number of independent samp es, the sources of variability in classification rates based on small sample sizes need to be examined. We report classification success as part of a simulation study of discriminant analysis (see Williams and Titus [1988] for canonical variates analysis). Our objective was to identify sources of variability in classification rates and to determine minimum sample sizes necessary for es imating these rates. Our study focused on assessment of discriminant analysis in representing system structure known to underlie the data under investigation. Our results compliment the work of Rexstad et al. (1988), who used data with no apparent underlying system structure to document a tendency, under certain conditions, for discriminant analysis to generate spurious relationships. We thank G. W. Pendleton, E. F. Burton, and K. Boone for technical support. D. E. Capen, D. W. Sparling, and J. S. Hatfield provided preliminary reviews and helpful comments. 1 Present address: Office of Migratory Bird Management, U.S. Fish and Wildlife Service, 18th and C Street NW, Washington, DC 20240. 2 Present address: Alaska Department of Fish and Game, Division of Wildlife Conservation, P.O. Box 20, Douglas, AK 99824.

A multiple discriminant approach to identifying frequent fliers in airline travel: some implications for market segmentation, target marketing, and product differentiation

Abstract: This study uses multiple discriminant analysis and other statistical techniques to identify the behavioral, attitudinal, and demographic correlates of frequent-flier members and non-members as well as light, medium, and heavy users of air travel in the United States. These membership categories are viable bases for segmentation and the appropriate marketing mixes are then designed to conform to the discriminating characteristics of the target markets of different airlines.

Error-rate estimation in two-group discriminant analysis using the linear discriminant function

Abstract: Fisher's linear discriminant function, adapted by Anderson for allocating new observations into one of two existing groups, is considered in this paper. Methods of estimating the misclassification error rates are reviewed and evaluated by Monte Carlo simulations. The investigation is carried out under both ideal (Multivariate Normal data) and non-ideal (Multivariate Binary data) conditions. The assessment is based on the usual mean square error (MSE) criterion and also on a new criterion of optimism. The results show that although there is a common cluster of good estimators for both ideal and non-ideal conditions, the single best estimators vary with respect to the different criteria