ISSN:0143-6570    

DOI:10.1002/mde.4090110402

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractThe 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.

ISSN:0143-6570    

DOI:10.1002/mde.4090110403

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractThis 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.

ISSN:0143-6570    

DOI:10.1002/mde.4090110404

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractThis paper reports the results of an experimental comparison between a linear programming (LP) approach and Fisher's linear discriminant function (FLDF) for solving discriminant analysis problems. In particular, we examine the two‐group, two‐variable problem and the associated error rates for the two groups when each of the models is applied to various sets of simulated data. In contrast to previous research, we concentrate on individual error rates for the two groups, i.e. we count the number of group 1 values classified into group 2 and the number of group 2 values classified into group 1. The results indicate that not only is FLDF better at overall classification but it also provides a much better balance between error rates for the two gro

ISSN:0143-6570    

DOI:10.1002/mde.4090110405

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractThe 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

ISSN:0143-6570    

DOI:10.1002/mde.4090110406

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractMixed‐integer programming models for the two‐group discriminant problem appear to be more promising, in terms of accuracy, than are linear programming models, but at a substantial computational cost. This paper poses a particular mixed‐integer model and suggests heuristics, based on linear programming, for obtaining suboptimal but “good” solutions to it. The heuristics are compared to the mixed‐integer model using Monte Carlo simulation with Ga

ISSN:0143-6570    

DOI:10.1002/mde.4090110407

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

摘要:

AbstractMany important real‐world discriminant problems require application of linear discriminant analysis to data that are contaminated with outliers and do not approximate the assumptions required for the near‐optimal performance of the standard statistical model. A robust diagnostic methodology is developed based on least‐absolute‐value estimation which addresses both descriptive and classification objectives of discriminant analysis. When used in conjunction with standard discriminant analysis this methodology allows the assessment of the impact of contamination on standard discriminant analysis and identification of possible assumption violations and contaminating data points through an informal graphical display. An application to the mortgage loan‐granting problem is used as a basis for demonstrating the me

ISSN:0143-6570    

DOI:10.1002/mde.4090110408

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY

ISSN:0143-6570    

DOI:10.1002/mde.4090110401

出版商:John Wiley&Sons, Ltd.    

年代:1990

数据来源: WILEY