Showing papers on "Linear discriminant analysis published in 1992"

Discriminant Analysis and Statistical Pattern Recognition

Abstract: Provides a systematic account of the subject area, concentrating on the most recent advances in the field. While the focus is on practical considerations, both theoretical and practical issues are explored. Among the advances covered are: regularized discriminant analysis and bootstrap-based assessment of the performance of a sample-based discriminant rule and extensions of discriminant analysis motivated by problems in statistical image analysis. Includes over 1,200 references in the bibliography.

Managerial Applications of Neural Networks: The Case of Bank Failure Predictions

Abstract: This paper introduces a neural-net approach to perform discriminant analysis in business research. A neural net represents a nonlinear discriminant function as a pattern of connections between its processing units. Using bank default data, the neural-net approach is compared with linear classifier, logistic regression, kNN, and ID3. Empirical results show that neural nets is a promising method of evaluating bank conditions in terms of predictive accuracy, adaptability, and robustness. Limitations of using neural nets as a general modeling tool are also discussed.

The detection of fault-prone programs

Abstract: The use of the statistical technique of discriminant analysis as a tool for the detection of fault-prone programs is explored. A principal-components procedure was employed to reduce simple multicollinear complexity metrics to uncorrelated measures on orthogonal complexity domains. These uncorrelated measures were then used to classify programs into alternate groups, depending on the metric values of the program. The criterion variable for group determination was a quality measure of faults or changes made to the programs. The discriminant analysis was conducted on two distinct data sets from large commercial systems. The basic discriminant model was constructed from deliberately biased data to magnify differences in metric values between the discriminant groups. The technique was successful in classifying programs with a relatively low error rate. While the use of linear regression models has produced models of limited value, this procedure shows great promise for use in the detection of program modules with potential for faults. >

Linear discriminant analysis for improved large vocabulary continuous speech recognition

Abstract: The interaction of linear discriminant analysis (LDA) and a modeling approach using continuous Laplacian mixture density HMM is studied experimentally. The largest improvements in speech recognition could be obtained when the classes for the LDA transform were defined to be sub-phone units. On a 12000 word German recognition task with small overlap between training and test vocabulary a reduction in error rate by one-fifth was achieved compared to the case without LDA. On the development set of the DARPA RM1 task the error rate was reduced by one-third. For the DARPA speaker-dependent no-grammar case, the error rate averaged over 12 speakers was 9.9%. This was achieved with a recognizer using LDA and a set of only 47 Viterbi-trained context-independent phonemes. >

Characterizing the effect of matching using linear propensity score methods with normal distributions

Abstract: SUMMARY Matched sampling is a standard technique for controlling bias in observational studies due to specific covariates. Since Rosenbaum & Rubin (1983), multivariate matching methods based on estimated propensity scores have been used with increasing frequency in medical, educational, and sociological applications. We obtain analytic expressions for the effect of matching using linear propensity score methods with normal distributions. These expressions cover cases where the propensity score is either known, or estimated using either discriminant analysis or logistic regression, as is typically done in current practice. The results show that matching using estimated propensity scores not only reduces bias along the population propensity score, but also controls variation of components orthogonal to it. Matching on estimated rather than population propensity scores can therefore lead to relatively large variance reduction, as much as a factor of two in common matching settings where close matches are possible. Approximations are given for the magnitude of this variance reduction, which can be computed using estimates obtained from the matching pools. Related expressions for bias reduction are also presented which suggest that, in difficult matching situations, the use of population scores leads to greater bias reduction than the use of estimated scores.

Affinely Invariant Matching Methods with Ellipsoidal Distributions

Abstract: Matched sampling is a common technique used for controlling bias in observational studies. We present a general theoretical framework for studying the performance of such matching methods. Specifically, results are obtained concerning the performance of affinely invariant matching methods with ellipsoidal distributions, which extend previous results on equal percent bias reducing methods. Additional extensions cover conditionally affinely invariant matching methods for covariates with conditionally ellipsoidal distributions. These results decompose the effects of matching into one subspace containing the best linear discriminant, and the subspace of variables uncorrelated with the discriminant. This characterization of the effects of matching provides a theoretical foundation for understanding the performance of specific methods such as matched sampling using estimated propensity scores. Calculations for such methods are given in subsequent articles.

A Comment on the Coefficient of Determination for Binary Responses

Abstract: Linear logistic or probit regression can be closely approximated by an unweighted least squares analysis of the regression linear in the conditional probabilities provided that these probabilities for success and failure are not too extreme. It is shown how this restriction on the probabilities translates into a restriction on the range of the coefficient of determination R 2 so that, as a consequence, R 2 is not suitable to judge the effectiveness of linear regressions with binary responses even if an important relation is present.

An efficient algorithm for foley–sammon optimal set of discriminant vectors by algebraic method

Abstract: This paper presents a new method for computing the discriminant vectors of the Foley–Sammon optimal set. First, an equivalent criterion is presented to replace the Fisher criterion; then, the probl...

Feature-based detection of the K-complex wave in the human electroencephalogram using neural networks

Abstract: The main difficulties in reliable automated detection of the K-complex wave in EEG are its close similarity to other waves and the lack of specific characterization criteria. The authors present a feature-based detection approach using neural networks that provides good agreement with visual K-complex recognition: a sensitivity of 90% is obtained with about 8% false positives. The respective contribution of the features and that of the neural network is demonstrated by comparing the results to those obtained with (i) raw EEG data presented to neural networks, and (ii) features presented to Fisher's linear discriminant. >

The Use of Artificial Neural Networks in QSAR

Abstract: Artificial neural networks (ANN) have their origins in efforts to produce computer models of the information processing that takes place in the brain. They have found application in a wide variety of fields such as image analysis of facial features, traffic management of underground station platforms, hand-writing verification of cheques, stock market predictions, etc. They have also been applied to computer-aided molecular design, notably protein structure prediction, and more recently ANN have been used to perform statistical tasks such as discriminant analysis and multiple linear regression in the investigation of Quantitative Structure-Activity Relationships (QSAR). We have begun a study of the properties of ANN when used to perform such multivariate statistical analyses. The most popular network used in QSAR-type applications is the multi-layer feed-forward network, also known as the back propagation multi-layer perceptron (MLP). The approaches of MLP and multiple linear regression to modelling are discussed. In order to give some insight into the operation of MLP networks we have carried out experiments with artificial data. Finally, we report two examples of MLP in computer-aided design, a QSAR analysis and the prediction of secondary protein structure.

Discriminant versus rough sets approach to vague data analysis

Abstract: This paper presents a comparative study of the use of two different methods of data analysis on a common set of data. The first is a method based on rough sets theory and the second is the location model method from the field of discriminant analysis. To investigate the comparative performance of these methods, a set of real medical data has been used. The data considered are of both discrete and continuous character. During the comparison, particular attention is paid to data reduction and to the derivation of decision rules and classification functions from the reduced set.

Managerial Applications of Neural Networks

Abstract: This paper introduces a neural-net approach to perform discriminant analysis in business research. A neural net represents a nonlinear discriminant function as a pattern of connections between its ...

Towards an Objective Classification Scheme for Organizational Task Environments

Abstract: SUMMARY This study replicates, refines, cross-validates and simplifies a scheme of operationalization and measurement of environmental dimensions proposed by Dess and Beard (1984). Employing a sample of 60 industries and data over a 16-year period, this study found considerable support for the viability of the three dimensions of munificence, dynamism and complexity. The data intensive and computationally complex operationalization scheme was simplified using a discriminant analysis approach and the discriminant functions were cross-validated using an alternate data set.

On the classification gap in mathematical programming-based approaches to the discriminant problem

Abstract: This article proposes a mathematical-programming-based approach to solve the classification problem in discriminant analysis which explicitly considers the classification gap. The procedure consists of two distinct phases and initially treats the classification gap as a fuzzy set in which the classification rule is not yet established. The nature of the classification gap is examined and a variety of methods are discussed which can be applied to identify the most appropriate classification rule over the fuzzy set. The proposed methodology has several potential advantages. First, it offers a more refined approach to the classification problem, facilitating careful analysis of the fuzzy region where the classification decision may not be obvious. Secondly, the two-phase approach enables the analysis of larger data sets when using computer-intensive procedures such as mixed-integer programming. Finally, because of the restricted choice of separating hyperplanes in phase 2, the approach appears to be more robust than other classification techniques with respect to outlier-contaminated data conditions. The robustness issue and computational advantage of our proposed methodology are illustrated using a limited simulation experiment.

A coupling procedure for the discrimination of mixed data.

Abstract: A procedure is described for coupling different discriminators to a new (common) decision rule using the corresponding allocation vectors only. This enables one to cope jointly with data of different structure and/or scales of measurement but without strong restrictions on the number of (especially categorical) features. The method is combined with a consequent cross-validation process securing the results reached. Examples from medical diagnostics demonstrate the usefulness of the proposed procedure, especially in comparison with the known linear discriminant analysis as judged from the error rates obtained.

Unrestricted principal components analysis of brain electrical activity: Issues of data dimensionality, artifact, and utility

Abstract: Principal components analysis (PCA) was performed on the 1536 spectral and 2944 evoked potential (EP) variables generated by neurophysiologic paradigms including flash VER, click AER, and eyes open and closed spectral EEG from 202 healthy subjects aged 30 to 80. In each case data dimensionality of 1500 to 3000 was substantially reduced using PCA by magnitudes of 20 to over 200. Just 20 PCA factors accounted for 70% to 85% of the variance. Visual inspection of the topographic distribution of factor loading scores revealed complex loadings across multiple data dimensions (time-space and frequency-space). Forty-two non-artifactual factors were successful in classifying age, gender, and a separate group of 60 demented patients by linear discriminant analysis. Discrimination of age and gender primarily involved EP derived factors, whereas dementia primarily involved EEG derived factors. Thirty-eight artifactual factors were identified which, alone, could not discriminate age but were relatively successful in discriminating gender and dementia. The need to parsimoniously develop real neurophysiologic measures and to objectively exclude artifact are discussed. Unrestricted PCA is suggested as a step in this direction.

Statistical methods in diagnosis

Abstract: Motivations are presented for exploring formal statistical methods for use in medical diagnosis and the advantages and disadvantages are discussed. A brief review is presented of classical linear discriminant analysis, quadratic discriminant analysis, logistic regression, nearest neighbour and kernel methods, recursive partitioning methods, the independence model, regularized discriminant analysis, structured conditional probability distributions, methods for categorical data, and other methods. Criteria on which a choice might be made are presented and methods for assessing diagnostic performance are outlined. Particular applications of screening and chromosome analysis are used as illustrations and available software is described.

An assessment of critical anthropometric dimensions for predicting the fit of a half-mask respirator.

Abstract: The purpose of this study was to determine if facial dimensions for a group of subjects were predictive of the fit factors measured while one brand of half-mask respirator was worn. Fit factors and 12 facial dimensions measured on 30 female and 38 male subjects were analyzed by correlation coefficients; weighted, multiple linear regression; and discriminant analysis. Data were analyzed for all subjects, gender subgroups, a race subgroup (whites only), and race/gender subgroups. Significant correlation coefficients with the log-transformed fit factors were found for four dimensions; four dimensions had significant coefficients in four or more multiple linear regression models. Only two dimensions had significant coefficients in four or more discriminant analysis models. Menton-subnasale (lowerface) length was the only dimension included in all three of these groups. Gender-specific regression models had very high coefficient of determination values (R2>0.85). Discriminant analysis of the data for all subje...

USe of morphometric parameters for the determination of sex of Adelie penguins.

Abstract: The sex of Addie penguins, Pygoscelis adeliae, may be determined by cloacal examination during the early part of the breeding season. Later in the season it becomes increasingly difficult to determine the sex of penguins by this method as the structures used for identification regress. Discriminant analysis of morphometric characters has been suggested as an alternative. This technique was examined for breeding birds of known sex near Mawson Station, Antarctica. The sex of 89% of breeding birds could be correctly determined by comparing the discriminant score D = 0.582 Bl + 1.118 Bd + 0.219Fw, where Bl is bill length, Bd is bill depth and Fw is flipper width, with a mean discriminant score (MDS) of 55.39. In all, the sexes of 87% were correctly determined by means of length and depth only (D=0.601Bl+ 1.154Bd, MDS=44.96). The sex of juvenile birds could not be determined. Determination of sex by discriminant analysis is shown to give acceptable estimates of morphometric characters divided by sex where only the mean and variance of these variables but not the sexual identity of individual birds is required. Where absolute accuracy in sex determination is required, 80% of the birds in our samples would have to be discarded to be 90% confident of the sex of the remainder.

Segmentation-recognition algorithm for zip code field recognition

Abstract: This paper describes a recognition algorithm for zip code field recognition. The algorithm consists of an initial character segmentation algorithm and a connected-numeral splitting algorithm. The initial character segmentation algorithm employs connected component analysis with component merge technique based on proximity. The numeral splitting algorithm consists of a slant splitting algorithm based on discriminant analysis and two postprocessing algorithms based on local shape analysis. The splitting algorithm is integrated with a statistical classifier to form a segmentation-recognition algorithm to resolve the ambiguity of connected numeral splitting. The performance is tested by recognition experiments on zip code fields collected from real USPS mail envelopes.

Projection pursuit discriminant analysis for two groups

Abstract: In this paper we determine the two groups linear discriminant function which minimizes the total probability of missclassification when a priori probabilities of the two groups are specified. On one hand, this problem is shown to be a special case of the projection pursuit technique in discriminant analysis which provides efficient algorithms for solving optimization of this kind. On the other hand, this linear function is shown to be a generalization of the best linear discriminant function (the version concerned with the total probability of missclassification) introduced by Anderson & Bahadur (1962).Kernel estimation of the discrimination rule and a computer implementation are discussed, and it is shown that the estimate is consistent.

Comparing the performance of neural networks to well-established methods of multivariate data analysis: the classification of mass spectral data

Abstract: The performance of neural networks in classifying mass spectral data is evaluated and compared to methods of multivariate data analysis and pattern recognition. Back propagation networks are matched with linear discriminant analysis, Kohonen feature maps are compared to the knearest neighbour clustering algorithm. Eight classifiers were trained, in order to discriminate mass spectra of steroids from eight distinct classes of chemical compounds. The results obtained show slightly better performance of Kohonen networks compared to k-nearest neighbour clustering and equal performance of multi-layer perceptrons and discriminant analysis.

Adaptive Ho-Kashyap rules for perceptron training

Abstract: Three adaptive versions of the Ho-Kashyap perceptron training algorithm are derived based on gradient descent strategies. These adaptive Ho-Kashyap (AHK) training rules are comparable in their complexity to the LMS and perceptron training rules and are capable of adaptively forming linear discriminant surfaces that guarantee linear separability and of positioning such surfaces for maximal classification robustness. In particular, a derived version called AHK II is capable of adaptively identifying critical input vectors lying close to class boundaries in linearly separable problems. The authors extend this algorithm as AHK III, which adds the capability of fast convergence to linear discriminant surfaces which are good approximations for nonlinearly separable problems. This is achieved by a simple built-in unsupervised strategy which allows for the adaptive grading and discarding of input vectors causing nonseparability. Performance comparisons with LMS and perceptron training are presented. >