Mixed integer programming approach of extended DEA-discriminant analysis

Abstract Several unique features of data envelopment analysis (DEA) are incorporated into discriminant analysis (DA). Such a combined use of the two approaches is referred to as “DEA–DA” (Eur. J. Operat. Res. 1999 (115) 564). Sueyoshi (Eur. J. Operat. Res. 2001 (131) 324) has recently extended DEA–DA in a manner that it can deal with a negative value in data. The new version is referred to as “Extended DEA–DA”. An important feature of extended DEA–DA is that it can estimate weights of a linear discriminant function by minimizing the total deviation of misclassified observations. As an extension of his research, this research proposes a new type of mixed integer programming formulations that provide these weight estimates by minimizing the total number of misclassified observations.

[1]  Bharat A. Jain,et al.  Artificial Neural Network Models for Pricing Initial Public Offerings , 1995 .

[2]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[3]  Nicola Yanev,et al.  A combinatorial approach to the classification problem , 1999, Eur. J. Oper. Res..

[4]  John M. Wilson,et al.  Integer programming formulations of statistical classification problems , 1996 .

[5]  James P. Ignizio,et al.  Discriminant analysis via mathematical programming: Certain problems and their causes , 1989, Comput. Oper. Res..

[6]  John Glen,et al.  Integer programming methods for normalisation and variable selection in mathematical programming discriminant analysis models , 1999, J. Oper. Res. Soc..

[7]  Toshiyuki Sueyoshi,et al.  Extended DEA-Discriminant Analysis , 2001, Eur. J. Oper. Res..

[8]  F. Glover,et al.  Simple but powerful goal programming models for discriminant problems , 1981 .

[9]  Constantin Zopounidis,et al.  Multicriteria Preference Disaggregation for Classification Problems with an Application to Global Investing Risk , 2001, Decis. Sci..

[10]  Cliff T. Ragsdale,et al.  Combining Neural Networks and Statistical Predictions to Solve the Classification Problem in Discriminant Analysis , 1995 .

[11]  James E. Falk,et al.  Robust separation of finite sets via quadratics , 2001, Comput. Oper. Res..

[12]  Prakash L. Abad,et al.  New LP based heuristics for the classification problem , 1993 .

[13]  Fred Glover,et al.  Applications and Implementation , 1981 .

[14]  John Glen,et al.  Classification accuracy in discriminant analysis: a mixed integer programming approach , 2001, J. Oper. Res. Soc..

[15]  Jiann-Ming Wu,et al.  Natural Discriminant Analysis Using Interactive Potts Models , 2002, Neural Computation.

[16]  Olvi L. Mangasarian,et al.  Arbitrary-norm separating plane , 1999, Oper. Res. Lett..

[17]  Antonie Stam,et al.  Second order mathematical programming formulations for discriminant analysis , 1994 .

[18]  Antonie Stam,et al.  Nontraditional approaches to statistical classification: Some perspectives on L_p-norm methods , 1997, Ann. Oper. Res..

[19]  A. Charnes,et al.  Goal programming and multiple objective optimizations: Part 1 , 1977 .

[20]  Toshiyuki Sueyoshi,et al.  DEA-discriminant analysis in the view of goal programming , 1999, Eur. J. Oper. Res..

[21]  Hirotaka Nakayama,et al.  Pattern Classification by Linear Goal Programming and its Extensions , 1998, J. Glob. Optim..

[22]  Paul A. Rubin,et al.  Heuristic solution procedures for a mixed‐integer programming discriminant model , 1990 .

[23]  Abraham Charnes,et al.  Optimal Estimation of Executive Compensation by Linear Programming , 1955 .

[24]  Constantin Zopounidis,et al.  Multicriteria classification and sorting methods: A literature review , 2002, Eur. J. Oper. Res..

[25]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[26]  Toshiyuki Sueyoshi,et al.  Efficiency measurement and strategic classification of Japanese banking institutions , 1998, Int. J. Syst. Sci..

[27]  C. A. Smith.  Some examples of discrimination. , 1947, Annals of eugenics.

[28]  Fred Glover,et al.  IMPROVED LINEAR PROGRAMMING MODELS FOR DISCRIMINANT ANALYSIS , 1990 .

[29]  Kim Fung Lam,et al.  An experimental comparison of some recently developed linear programming approaches to the discriminant problem , 1997, Comput. Oper. Res..

[30]  Laurel H. Carney,et al.  Evaluating Auditory Performance Limits: I. One-Parameter Discrimination Using a Computational Model for the Auditory Nerve , 2001, Neural Computation.

[31]  Edward P. Markowski,et al.  An experimental comparison of several approaches to the discriminant problem with both qualitative and quantitative variables , 1987 .

[32]  S. M. Bajgier,et al.  AN EXPERIMENTAL COMPARISON OF STATISTICAL AND LINEAR PROGRAMMING APPROACHES TO THE DISCRIMINANT PROBLEM , 1982 .

[33]  G. McLachlan.  Discriminant Analysis and Statistical Pattern Recognition , 1992 .

[34]  E. Joachimsthaler,et al.  Solving the Classification Problem in Discriminant Analysis Via Linear and Nonlinear Programming Methods , 1989 .