메뉴 건너뛰기




Volumn 74, Issue , 1997, Pages 89-112

Mathematical programming formulations for two-group classification with binary variables

Author keywords

Binary variables; Classification analysis; Discriminant analysis; Linear programming; Mixed integer programming

Indexed keywords


EID: 0031501860     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1023/a:1018995010063     Document Type: Article
Times cited : (8)

References (78)
  • 2
    • 0017109036 scopus 로고
    • Multivariate binary discrimination by the kernel method
    • J. Aitchison and C.G.G. Aitken, Multivariate binary discrimination by the kernel method, Biometrika 63(1976)413-420.
    • (1976) Biometrika , vol.63 , pp. 413-420
    • Aitchison, J.1    Aitken, C.G.G.2
  • 3
    • 77956889283 scopus 로고
    • Separate sample logistic discrimination
    • J.A. Anderson, Separate sample logistic discrimination, Biometrika 59(1972)19-35.
    • (1972) Biometrika , vol.59 , pp. 19-35
    • Anderson, J.A.1
  • 4
    • 85041935315 scopus 로고
    • Quadratic logistic discrimination
    • J.A. Anderson, Quadratic logistic discrimination, Biometrika 62(1975)149-154.
    • (1975) Biometrika , vol.62 , pp. 149-154
    • Anderson, J.A.1
  • 8
    • 0007936589 scopus 로고
    • Comparison of one-stage classifiers for assessment of the ability of children to construct grammatical structures consciously
    • I. Panchev, ed., Academic Publishing House 'Prof. Marin Drinov', Sofia, Bulgaria
    • O.K. Asparoukhov and T.B. Andreev, Comparison of one-stage classifiers for assessment of the ability of children to construct grammatical structures consciously, in: Multivariate Analysis in the Behavioral Sciences. Philosophical to Technical, I. Panchev, ed., Academic Publishing House 'Prof. Marin Drinov', Sofia, Bulgaria, 1995, pp. 1-13.
    • (1995) Multivariate Analysis in the Behavioral Sciences. Philosophical to Technical , pp. 1-13
    • Asparoukhov, O.K.1    Andreev, T.B.2
  • 9
    • 0002881703 scopus 로고
    • A representation of the joint distribution of response to n dichotomous items
    • H. Solomon, ed., Stanford University Press, Palo Alto, CA
    • R.R. Bahadur, A representation of the joint distribution of response to n dichotomous items, in: Studies in Item Analysis and Prediction, H. Solomon, ed., Stanford University Press, Palo Alto, CA, 1961, pp. 158-168.
    • (1961) Studies in Item Analysis and Prediction , pp. 158-168
    • Bahadur, R.R.1
  • 10
    • 0001521801 scopus 로고
    • An efficient optimal solution algorithm for the classification problem
    • W.J. Banks and P.L. Abad, An efficient optimal solution algorithm for the classification problem, Decision Sciences 22(1991)1008-1023.
    • (1991) Decision Sciences , vol.22 , pp. 1008-1023
    • Banks, W.J.1    Abad, P.L.2
  • 11
    • 0028766151 scopus 로고
    • On the performance of linear programming heuristics applied on a quadratic transformation in the classification problem
    • W.J. Banks and P.L. Abad, On the performance of linear programming heuristics applied on a quadratic transformation in the classification problem, European Journal of Operational Research 74(1994)23-28.
    • (1994) European Journal of Operational Research , vol.74 , pp. 23-28
    • Banks, W.J.1    Abad, P.L.2
  • 13
    • 0003035283 scopus 로고
    • Some procedures connected with the logistic qualitative response curve
    • F.N. David, ed., Wiley, New York
    • D.R. Cox, Some procedures connected with the logistic qualitative response curve, in: Research Papers in Statistics: Festschrift for J. Neyman, F.N. David, ed., Wiley, New York, 1966, pp. 55-71.
    • (1966) Research Papers in Statistics: Festschrift for J. Neyman , pp. 55-71
    • Cox, D.R.1
  • 14
    • 0043199985 scopus 로고
    • Theories and methods in classification: A review
    • T. Cacoullos, ed., Academic Press, New York
    • S. Das Gupta, Theories and methods in classification: A review, in: Discriminant Analysis and Applications, T. Cacoullos, ed., Academic Press, New York, 1973, pp. 77-137.
    • (1973) Discriminant Analysis and Applications , pp. 77-137
    • Das Gupta, S.1
  • 15
    • 0014097063 scopus 로고
    • A general maximum likelihood discriminant
    • N.B. Day and D.E. Kerridge, A general maximum likelihood discriminant, Biometrics 23(1967) 313-323.
    • (1967) Biometrics , vol.23 , pp. 313-323
    • Day, N.B.1    Kerridge, D.E.2
  • 18
    • 0028766145 scopus 로고
    • Second order mathematical programming formulations for discriminant analysis
    • A.P. Duarte Silva and A. Stam, Second order mathematical programming formulations for discriminant analysis, European Journal of Operational Research 72(1994)4-22.
    • (1994) European Journal of Operational Research , vol.72 , pp. 4-22
    • Duarte Silva, A.P.1    Stam, A.2
  • 19
    • 0000764772 scopus 로고
    • The use of multiple measurements in taxonomic problems
    • R.A. Fisher, The use of multiple measurements in taxonomic problems, Annals of Eugenics 7(1936) 179-188.
    • (1936) Annals of Eugenics , vol.7 , pp. 179-188
    • Fisher, R.A.1
  • 20
    • 84989432337 scopus 로고
    • A linear programming approach to the discriminant problem
    • N. Freed and F. Glover, A linear programming approach to the discriminant problem, Decision Sciences 12(1981)68-74.
    • (1981) Decision Sciences , vol.12 , pp. 68-74
    • Freed, N.1    Glover, F.2
  • 21
    • 0019565499 scopus 로고
    • Simple but powerful goal programming models for discriminant problems
    • N. Freed and F. Glover, Simple but powerful goal programming models for discriminant problems, European Journal of Operational Research 7(1981)44-60.
    • (1981) European Journal of Operational Research , vol.7 , pp. 44-60
    • Freed, N.1    Glover, F.2
  • 22
    • 0022882706 scopus 로고
    • General mathematical programming formulation for the statistical classification problem
    • W.V. Gehrlein, General mathematical programming formulation for the statistical classification problem, Operations Research Letters 5(1986)299-304.
    • (1986) Operations Research Letters , vol.5 , pp. 299-304
    • Gehrlein, W.V.1
  • 25
    • 84985822265 scopus 로고
    • A new class of models for the discriminant problem
    • F. Glover, S. Keene and B. Duea, A new class of models for the discriminant problem, Decision Sciences 19(1988)269-280.
    • (1988) Decision Sciences , vol.19 , pp. 269-280
    • Glover, F.1    Keene, S.2    Duea, B.3
  • 26
    • 0031096944 scopus 로고    scopus 로고
    • Multigroup discriminant analysis using linear programming
    • W. Gochet, A. Stam, V. Srinivasan and S. Chen, Multigroup discriminant analysis using linear programming, Operations Research 45(1997)213-225.
    • (1997) Operations Research , vol.45 , pp. 213-225
    • Gochet, W.1    Stam, A.2    Srinivasan, V.3    Chen, S.4
  • 28
    • 0000923625 scopus 로고
    • On nonparametric multivariate binary discrimination
    • P. Hall, On nonparametric multivariate binary discrimination, Biometrika 68(1981)287-294.
    • (1981) Biometrika , vol.68 , pp. 287-294
    • Hall, P.1
  • 29
    • 0007879740 scopus 로고
    • Optimal near neighbour estimator for use in discriminant analysis
    • P. Hall, Optimal near neighbour estimator for use in discriminant analysis, Biometrika 68(1981) 572-575.
    • (1981) Biometrika , vol.68 , pp. 572-575
    • Hall, P.1
  • 31
    • 0020375359 scopus 로고
    • Statistical pattern recognition on binary variables
    • J. Kittler, K.S. Fu and L.F. Pau, eds., Reidel, Boston, MA
    • D.J. Hand, Statistical pattern recognition on binary variables, in: Pattern Recognition Theory and Applications, J. Kittler, K.S. Fu and L.F. Pau, eds., Reidel, Boston, MA, 1982, pp. 19-33.
    • (1982) Pattern Recognition Theory and Applications , pp. 19-33
    • Hand, D.J.1
  • 32
    • 0020819614 scopus 로고
    • A comparison of two methods of discriminant analysis applied to binary data
    • D.J. Hand, A comparison of two methods of discriminant analysis applied to binary data, Biometrics 39(1983)683-694.
    • (1983) Biometrics , vol.39 , pp. 683-694
    • Hand, D.J.1
  • 35
    • 0007930963 scopus 로고
    • Discrimination and allocation with discrete data
    • M. Hills, Discrimination and allocation with discrete data, Applied Statistics 16(1967)237-250.
    • (1967) Applied Statistics , vol.16 , pp. 237-250
    • Hills, M.1
  • 38
    • 84985761637 scopus 로고
    • Four approaches to the classification problem in discriminant analysis: An experimental study
    • E.A. Joachimsthaler and A. Stam, Four approaches to the classification problem in discriminant analysis: An experimental study, Decision Sciences 19(1988)322-333.
    • (1988) Decision Sciences , vol.19 , pp. 322-333
    • Joachimsthaler, E.A.1    Stam, A.2
  • 39
    • 0002540982 scopus 로고
    • Mathematical programming approaches for the classification problem in two-group discriminant analysis
    • E.A. Joachimsthaler and A. Stam, Mathematical programming approaches for the classification problem in two-group discriminant analysis, Multivariate Behavioral Research 25(1990)427-454.
    • (1990) Multivariate Behavioral Research , vol.25 , pp. 427-454
    • Joachimsthaler, E.A.1    Stam, A.2
  • 40
    • 84985824432 scopus 로고
    • Minimizing misclassifications in linear discriminant analysis
    • G.J. Koehler and S.S. Erenguc, Minimizing misclassifications in linear discriminant analysis, Decision Sciences 21(1990)63-85.
    • (1990) Decision Sciences , vol.21 , pp. 63-85
    • Koehler, G.J.1    Erenguc, S.S.2
  • 41
    • 0001683328 scopus 로고
    • The performance of Fisher's linear discriminant function under non-optimal conditions
    • W.J. Krzanowski, The performance of Fisher's linear discriminant function under non-optimal conditions, Technometrics 19(1977)191-200.
    • (1977) Technometrics , vol.19 , pp. 191-200
    • Krzanowski, W.J.1
  • 42
    • 0000915896 scopus 로고
    • Distance between populations using mixed continuous and categorical variables
    • W.J. Krzanowski, Distance between populations using mixed continuous and categorical variables, Biometrika 70(1983)235-243.
    • (1983) Biometrika , vol.70 , pp. 235-243
    • Krzanowski, W.J.1
  • 44
    • 21144464643 scopus 로고
    • The location model for mixture of categorical and continuous variables
    • W.J. Krzanowski, The location model for mixture of categorical and continuous variables, Journal of Classification 10(1993)25-49.
    • (1993) Journal of Classification , vol.10 , pp. 25-49
    • Krzanowski, W.J.1
  • 45
    • 84879799188 scopus 로고
    • Estimation of error rates in discriminant analysis
    • P.A. Lachenbruch and M.R. Mickey, Estimation of error rates in discriminant analysis, Technometrics 10(1968)1-11.
    • (1968) Technometrics , vol.10 , pp. 1-11
    • Lachenbruch, P.A.1    Mickey, M.R.2
  • 47
    • 0007788288 scopus 로고
    • Integer programming solution of a classification problem
    • J.M. Liitschwager and C. Wang, Integer programming solution of a classification problem, Management Science 24(1978)1515-1525.
    • (1978) Management Science , vol.24 , pp. 1515-1525
    • Liitschwager, J.M.1    Wang, C.2
  • 48
    • 0024771475 scopus 로고
    • Pattern classification using neural networks
    • R.P. Lippmann, Pattern classification using neural networks, IEEE Communication Magazine (1989)47-64.
    • (1989) IEEE Communication Magazine , pp. 47-64
    • Lippmann, R.P.1
  • 49
    • 0000963583 scopus 로고
    • Linear and nonlinear separation of patterns by linear programming
    • O.L. Mangasarian, Linear and nonlinear separation of patterns by linear programming, Operations Research 13(1965)444-452.
    • (1965) Operations Research , vol.13 , pp. 444-452
    • Mangasarian, O.L.1
  • 50
    • 0023148215 scopus 로고
    • An experimental comparison of the discriminant problem with both qualitative and quantitative variables
    • C.A. Markowski and E.P. Markowski, An experimental comparison of the discriminant problem with both qualitative and quantitative variables, European Journal of Operational Research 28 (1987)74-78.
    • (1987) European Journal of Operational Research , vol.28 , pp. 74-78
    • Markowski, C.A.1    Markowski, E.P.2
  • 51
    • 0015302509 scopus 로고
    • Probability models, estimation, and classification for multivariate dichotomous populations
    • D.C. Martin and R.A. Bradly, Probability models, estimation, and classification for multivariate dichotomous populations, Biometrics 28(1972)203-221.
    • (1972) Biometrics , vol.28 , pp. 203-221
    • Martin, D.C.1    Bradly, R.A.2
  • 52
    • 0025700735 scopus 로고
    • Introduction to computation and learning in artificial neural networks
    • E. Másson and Y.-J. Wang, Introduction to computation and learning in artificial neural networks, European Journal of Operational Research 47(1990)1-28.
    • (1990) European Journal of Operational Research , vol.47 , pp. 1-28
    • Másson, E.1    Wang, Y.-J.2
  • 55
    • 84950632611 scopus 로고
    • Evaluation of five discriminant procedures for binary variables
    • D.H. Moore, Evaluation of five discriminant procedures for binary variables, Journal of the American Statistical Association 68(1973)399-404.
    • (1973) Journal of the American Statistical Association , vol.68 , pp. 399-404
    • Moore, D.H.1
  • 57
    • 0000016969 scopus 로고
    • Some classification procedures for multivariate binary data using orthogonal functions
    • J. Ott and R.A. Kronmal, Some classification procedures for multivariate binary data using orthogonal functions, Journal of the American Statistical Association 71(1976)391-399.
    • (1976) Journal of the American Statistical Association , vol.71 , pp. 391-399
    • Ott, J.1    Kronmal, R.A.2
  • 58
    • 0002040809 scopus 로고
    • Introducing discriminant analysis to the business statistics curriculum
    • C.T. Ragsdale and A. Stam, Introducing discriminant analysis to the business statistics curriculum, Decision Sciences 23(1992)724-745.
    • (1992) Decision Sciences , vol.23 , pp. 724-745
    • Ragsdale, C.T.1    Stam, A.2
  • 59
    • 0024701597 scopus 로고
    • Evaluating the maximize minimum distance formulation to the linear discriminant problem
    • P.A. Rubin, Evaluating the maximize minimum distance formulation to the linear discriminant problem, European Journal of Operational Research 41(1989)272-282.
    • (1989) European Journal of Operational Research , vol.41 , pp. 272-282
    • Rubin, P.A.1
  • 60
    • 0028766182 scopus 로고
    • A comment regarding polynomial discriminant analysis
    • P.A. Rubin, A comment regarding polynomial discriminant analysis, European Journal of Operational Research 72(1994)29-31.
    • (1994) European Journal of Operational Research , vol.72 , pp. 29-31
    • Rubin, P.A.1
  • 62
    • 84988828223 scopus 로고
    • Neural networks: A new tool for predicting thrift failures
    • L.M. Salchenberger, E.M. Cinar and N.A. Lash, Neural networks: A new tool for predicting thrift failures, Decision Sciences 23(1992)899-916.
    • (1992) Decision Sciences , vol.23 , pp. 899-916
    • Salchenberger, L.M.1    Cinar, E.M.2    Lash, N.A.3
  • 64
    • 0001352933 scopus 로고
    • Some examples of discrimination
    • C.A.B. Smith, Some examples of discrimination, Annals of Eugenics 13(1947)272-282.
    • (1947) Annals of Eugenics , vol.13 , pp. 272-282
    • Smith, C.A.B.1
  • 65
    • 0343019657 scopus 로고
    • Pattern classifier design by linear programming
    • F.W. Smith, Pattern classifier design by linear programming, IEEE Transactions on Computing C-17(1968)367-372.
    • (1968) IEEE Transactions on Computing , vol.C-17 , pp. 367-372
    • Smith, F.W.1
  • 66
    • 0011468067 scopus 로고
    • ODA 1.0: Optimal Discriminant Analysis for DOS
    • Chicago, IL
    • R.C. Soltysik and P.R. Yarnold, ODA 1.0: Optimal Discriminant Analysis for DOS, Optimal Data Analysis, Chicago, IL, 1993.
    • (1993) Optimal Data Analysis
    • Soltysik, R.C.1    Yarnold, P.R.2
  • 67
    • 0028485738 scopus 로고
    • The Warmack-Gonzalez algorithm for linear two-category multivariate optimal discriminant analysis
    • R.C. Soltysik and P.R. Yarnold, The Warmack-Gonzalez algorithm for linear two-category multivariate optimal discriminant analysis, Computers and Operations Research 21(1994)735-745.
    • (1994) Computers and Operations Research , vol.21 , pp. 735-745
    • Soltysik, R.C.1    Yarnold, P.R.2
  • 68
    • 84985810486 scopus 로고
    • Solving the classification problem in discriminant analysis via linear and nonlinear programming methods
    • A. Stam and E.A. Joachimsthaler, Solving the classification problem in discriminant analysis via linear and nonlinear programming methods, Decision Sciences 20(1989)285-293.
    • (1989) Decision Sciences , vol.20 , pp. 285-293
    • Stam, A.1    Joachimsthaler, E.A.2
  • 69
    • 0025699785 scopus 로고
    • A comparison of a robust mixed-integer approach to existing methods for establishing classification rules for the discriminant problem
    • A. Stam and E.A. Joachimsthaler, A comparison of a robust mixed-integer approach to existing methods for establishing classification rules for the discriminant problem, European Journal of Operational Research 46(1990)113-122.
    • (1990) European Journal of Operational Research , vol.46 , pp. 113-122
    • Stam, A.1    Joachimsthaler, E.A.2
  • 70
    • 84986739471 scopus 로고
    • Classification performance of mathematical programming techniques in discriminant analysis: Results for small and medium sample sizes
    • A. Stam and D.G. Jones, Classification performance of mathematical programming techniques in discriminant analysis: Results for small and medium sample sizes, Managerial and Decision Economics 11(1990)243-253.
    • (1990) Managerial and Decision Economics , vol.11 , pp. 243-253
    • Stam, A.1    Jones, D.G.2
  • 71
    • 84873015232 scopus 로고
    • Algorithm AS 165. An algorithm to construct a discriminant function in FORTRAN for categorical data
    • E. Sturt, Algorithm AS 165. An algorithm to construct a discriminant function in FORTRAN for categorical data, Applied Statistics 30(1980)313-325.
    • (1980) Applied Statistics , vol.30 , pp. 313-325
    • Sturt, E.1
  • 72
    • 84997479670 scopus 로고
    • Managerial applications of neural networks: The case of bank failure predictions
    • K.Y. Tam and M.Y. Kiang, Managerial applications of neural networks: The case of bank failure predictions, Management Science 38(1992)926-947.
    • (1992) Management Science , vol.38 , pp. 926-947
    • Tam, K.Y.1    Kiang, M.Y.2
  • 74
    • 0007979632 scopus 로고
    • Classical discriminant analysis and Lancaster models for qualitative data
    • Physica-Verlag, Vienna
    • H.J. Trampisch, Classical discriminant analysis and Lancaster models for qualitative data, in: Compstat 1978, Proceedings in Computational Statistics, Physica-Verlag, Vienna, 1978, pp. 205-211.
    • (1978) Compstat 1978, Proceedings in Computational Statistics , pp. 205-211
    • Trampisch, H.J.1
  • 75
    • 84872999338 scopus 로고    scopus 로고
    • Examining the effect of second-order terms in mathematical programming approaches to the classification problem
    • to appear
    • P. Wanarat and R. Pavur, Examining the effect of second-order terms in mathematical programming approaches to the classification problem, European Journal of Operational Research, to appear.
    • European Journal of Operational Research
    • Wanarat, P.1    Pavur, R.2
  • 76
    • 0026860706 scopus 로고
    • Methods of combining multiple classifiers and their application to handwriting recognition
    • L. Xu, A. Krzyzak and C.Y. Suen, Methods of combining multiple classifiers and their application to handwriting recognition, IEEE Transactions on Systems, Man and Cybernetics SMC-22(1992) 418-435.
    • (1992) IEEE Transactions on Systems, Man and Cybernetics , vol.SMC-22 , pp. 418-435
    • Xu, L.1    Krzyzak, A.2    Suen, C.Y.3
  • 77
    • 0028343226 scopus 로고
    • Heart rate variability and susceptibility for sudden cardiac death: An example of multivariable optimal discriminant analysis
    • P.R. Yarnold, R.C. Soltysik and G.J. Martin, Heart rate variability and susceptibility for sudden cardiac death: An example of multivariable optimal discriminant analysis, Statistics in Medicine 13(1994)1015-1021.
    • (1994) Statistics in Medicine , vol.13 , pp. 1015-1021
    • Yarnold, P.R.1    Soltysik, R.C.2    Martin, G.J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.