Large-scale optimization-based classification models in medicine and biology

Annals of Biomedical Engineering

Volumn 35, Issue 6, 2007, Pages 1095-1109

  Lee, Eva K ^a,b,c  

^a Georgia Institute of Technology   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c EMORY UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Discrete support vector machine; Discriminant analysis; Integer programming; Machine learning; Medical diagnosis; Multi category classification models; Multi stage classification; Optimization; Prediction; Predictive health; Reserved judgment

Indexed keywords

DISCRIMINANT ANALYSIS; INTEGER PROGRAMMING; MATHEMATICAL MODELS; OPTIMIZATION; SUPPORT VECTOR MACHINES;

DISCRETE SUPPORT VECTOR MACHINE; MULTI CATEGORY CLASSIFICATION MODELS; MULTI STAGE CLASSIFICATION; PREDICTIVE HEALTH; RESERVED JUDGMENT;

DIAGNOSIS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; BIOLOGICAL MODEL; BIOLOGY; CLINICAL MEDICINE; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; METHODOLOGY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; BIOLOGY; CLINICAL MEDICINE; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; DIAGNOSIS, COMPUTER-ASSISTED; MODELS, BIOLOGICAL; PATTERN RECOGNITION, AUTOMATED;

EID: 34249741468     PISSN: 00906964     EISSN: 15739686     Source Type: Journal    
DOI: 10.1007/s10439-007-9317-7     Document Type: Conference Paper

References (89)

1. Anderson, J. A. Constrained discrimination between k populations. J. Roy. Stat. Soc. Ser. B 31:123-139, 1969.
2. Anderson, T. W. An Introduction to Multivariate Statistical Analysis. 2nd ed. New York: Wiley, 1984.
3. Bajgier, S. M., and A. V. Hill. An experimental comparison of statistical and linear programming approaches to the discriminant problems. Decision Sci. 13:604-618, 1982.
4. Banks, W. J., and P. L. Abad. An efficient optimal solution algorithm for the classification problem. Decision Sci. 22:1008-1023, 1991.
5. Bennett, K. P., and E. J. Bredensteiner. A parametric optimization method for machine learning. INFORMS J. Comput. 9:311-318, 1997.
6. Bennett, K. P., and O. L. Mangasarian. Multicategory discrimination via linear programming. Optimiz. Methods Software 3:27-39, 1993.
7. Bishop, C. M. Neural Networks for Pattern Recognition. Oxford: Oxford University Press, 1995.
8. Bixby, R. E., W. Cook, A. Cox, and E. K. Lee. Computational experience with parallel mixed integer programming in a distributed environment. Ann. Operat. Res. Spl. Issue Parallel Optimiz. 90:19-43, 1999.
9. Bradley, P. S., U. M. Fayyad, and O. L. Mangasarian. Mathematical programming for data mining: Formulations and challenges. INFORMS J. Comput. 11:217-238, 1999.
10. Breiman, L., J. H. Friedman, R. A. Olshen, and C. J. Stone. Classification and Regression Trees. Belmont, CA: Wadsworth, 1984.
11. Brock, G. J., T. H. Huang, C. M. Chen, and K. J. Johnson. A novel technique for the identification of CpG islands exhibiting altered methylation patterns (ICEAMP). Nucleic Acids. Res. 29:E123, 2001.
12. Broffit, J. D., R. H. Randles, and R.V. Hogg. Distribution-free partial discriminant analysis. J. Am. Stat. Assoc. 71:934-939, 1976.
13. Brooks, J. P., A. Wright, C. Zhu, and E. K. Lee. Discriminant analysis of motility and morphology data from human lung carcinoma cells placed on purified extracellular matrix proteins. Ann. Biomed. Eng., 2006 (in review).
14. Brooks, J. P., and E. K. Lee. Solving a mixed-integer, programming formulation of a multi-category constrained discrimination model. INFORMS Proc. Artif. Intell. Data Mining, 2006a (in press).
15. Brooks, J. P., and E. K. Lee. Mixed integer programming constrained discrimination model for credit screening. In: Proceedings of the Business Industry Symposium, Spring Simulation Multi-conference 2007, 2006b (in press).
16. Cavalier, T. M., J. P. Ignizio, and A. L. Soyster. Discriminant analysis via mathematical programming: certain problems and their causes. Comput. Operat. Res. 16:353-362, 1989.
17. Chevion, M., E. Berenshtein, and E. R. Stadtman. Human studies related to protein oxidation: protein carbonyl content as a marker of damage. Free Radic. Res. 33(Suppl):S99-S108, 2000.
18. Conway, K. E., B. B. McConnell, C. E. Bowring, C. D. Donald, S. T. Warren, and P. M. Vertino. TMS1, a novel proapoptotic caspase recruitment domain protein, is a target of methylation-induced gene silencing in human breast cancers. Cancer Res. 60:6236-6242, 2000.
19. Costello, J. F., M. C. Fruhwald, D. J. Smiraglia, L. J. Rush, G. P. Robertson, X. Gao, F. A. Wright, J. D. Feramisco, P. Peltomaki, J. C. Lang, D. E. Schuller, L. Yu, C. D. Bloomfield, M. A. Caligiuri, A. Yates, R. Nishikawa, H. H. Su, N. J. Petrelli, X. Zhang, M. S. O'Dorisio, W. A. Held, W. K. Cavenee, and C. Plass. Aberrant CpG-island methylation has non-random and tumour-type-specific patterns. Nat. Genet. 24:132-138, 2000.
20. Costello, J. F., C. Plass, and W. K. Cavenee. Aberrant methylation of genes in low-grade astrocytomas. Brain Tumor Pathol. 17:49-56, 2000.
21. Cristianini, N., and J. Shawe-Taylor. An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods. Cambridge University Press, 2000.
22. Duarte Silva, A. P., and A. Stam. Second order mathematical programming formulations for discriminant analysis. Eur. J. Operat. Res. 72:4-22, 1994.
23. Duda, R. O., P. E. Hart, and D. G. Stork. Pattern Classification, 2nd ed. Wiley, 2001.
24. Easton, T., K. Hooker, and E. K. Lee. Facets of the independent set polytope. Math. Program. B 98:177-199, 2003.
25. Feltus, F. A., E. K. Lee, J. F. Costello, C. Plass, and P. M. Vertino. Predicting aberrant CpG island methylation. Proc. Natl. Acad. Sci. 100(21):12253-12258, 2003.
26. Feltus, F. A., E. K. Lee, J. F. Costello, C. Plass, and P. M. Vertino. DNA signatures associated with CpG island methylation states. Genomics 87:572-579, 2006.
27. Fisher, R. A. The use of multiple measurements in taxonomic problems. Ann. Eugen. 7:179-188, 1936.
28. Freed, N., and F. Glover. A linear programming approach to the discriminant problem. Decision Sci. 12:68-74, 1981.
29. Freed, N., and F. Glover. Evaluating alternative linear programming models to solve the two-group discriminant problem. Decision Sci. 17:151-162, 1986.
30. Frommer, M., L. E. McDonald, D. S. Millar, C. M. Collis, F. Watt, G. W. Grigg, P. L. Molloy, and C. L. Paul. A genomic sequencing protocol that yields a positive display of 5-ethylcytosine residues in individual DNA strands. Proc. Natl. Acad. Sci. USA 89:1827-1831, 1992.
31. Fruhwald, M. C., M. S. O'Dorisio, L. J. Rush, J. L. Reiter, D. J. Smiraglia, G. Wenger, J. F. Costello, P. S. White, R. Krahe, G. M. Brodeur, and C Plass. Gene amplification in NETs/medulloblastomas: mapping of a novel amplified gene within the MYCN amplicon. J. Med. Genet. 37:501-509, 2000.
32. Gallagher, R. J., E. K. Lee, and D. Patterson. An optimization model for constrained discriminant analysis and numerical experiments with iris, thyroid, and heart disease datasets. In: Proceedings of the 1996 American Medical Informatics Association, edited by J. J. Cimino, 1996, pp. 209-213.
33. Gallagher, R. J., E. K. Lee, and D. A. Patterson. Constrained discriminant analysis via 0/1 mixed integer programming. Ann. Operat. Res., Spl. Issue on Non-Trad. Approach. Stat. Classif. Regress. 74:65-88, 1997.
34. Gardiner-Garden, M., and M. Frommer. CpG islands in vertebrate genomes. J. Mol. Biol. 196:261-282, 1987.
35. Garey, M. R., and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: Freeman, 1979.
36. Gehrlein, W. V. General mathematical programming formulations for the statistical classification problem. Operat. Res. Lett. 5:299-304, 1986.
37. Gessaman, M. P., and P. H. Gessaman. A comparison of some multivariate discrimination procedures. J. Am. Stat. Assoc. 67:468-472, 1972.
38. Glover, F. Improved linear programming models for discriminant analysis. Decision Sci. 21:771-785, 1990.
39. Glover, F., S. Keene, and B. Duea. A new class of models for the discriminant problem. Decision Sci. 19:269-280, 1988.
40. Gochet, W., A. Stam, V. Srinivasan, and S. Chen. Multigroup discriminant analysis using linear programming. Operat. Res. 45:213-225, 1997.
41. Habbema, J. D. F., J. Hermans, and A. T. Van Der Burgt. Cases of doubt in allocation problems. Biometrika 61:313-324, 1974.
42. Herman, J. G., J. R. Graff, S. Myohanen, B. D. Nelkin, and S. B. Baylin. Methylation-specific PCR: a novel PCR assay for methylation status of CpG islands. Proc. Natl. Acad. Sci. USA 93:9821-9826, 1996.
43. Horton, P., and K. Nakai. A probablistic classification system for predicting the cellular localization sites of proteins. Intell. Systems Mol. Biol. 4:109-115, 1996.
44. Koehler, G. J., and S. S. Erenguc. Minimizing misclassifications in linear discriminant analysis. Decision Sci. 21:63-85, 1990.
45. Lee, E. K. Computational Experience with a General Purpose Mixed 0/1 Integer Programming Solver (MIP-SOL), Software Report, School of Industrial and Systems Engineering, Georgia Institute of Technology, 1997.
46. Lee, E. K. A Linear-programming based parallel cutting plane algorithm for mixed integer programming problems. In: Proceeding for the Third Scandinavian Workshop on Linear Programming, 1999, pp. 22-31.
47. Lee, E. K. Branch-and-bound methods. In: Handbook of Applied Optimization, edited by M. G. C. Resende and P. M. Pardalos. Oxford University Press, 2001, ISBN 0-19-512594-0.
48. Lee, E. K. Generating cutting planes for mixed integer programming problems in a parallel distributed memory environment. INFORMS J. Comput. 16:1-28, 2004.
49. Lee, E. K. Discriminant analysis and predictive models in medicine. In: Interdisciplinary Research in Management Science, Finance, and HealthCare, edited by S. J. Deng. Peking University Press, 2006a (to appear).
50. Lee, E. K. Optimization-based predictive models in medicine and biology. Optimization in Medicine. Computer Science Series. Springer Netherlands, 2006b (to appear).
51. Lee, E. K., S. Ashfaq, D. P. Jones, S. D. Rhodes, W. S. Weintrau, C. H. Hopper, V. Vaccarino, D. G. Harrison, and A. A. Quyyumi. Prediction of early atherosclerosis in healthy adults via novel markers of oxidative stress and d-ROMs. Working paper, 2007.
52. Lee, E. K., T. Easton, and K. Gupta. Novel evolutionary models and applications to sequence alignment problems. Operat. Res. Med. - Comput. Optimiz. Med. Life Sci. 148:167-187, 2006.
53. Lee, E. K., A. Y. C. Fung, J. P. Brooks, and M. Zaider. Automated tumor volume contouring in soft-tissue sarcoma adjuvant brachytherapy treatment. Int. J. Radiat. Oncol. Biol. Phys. 47(11):1891-1910, 2002.
54. Lee, E. K., A. Y. C. Fung, and M. Zaider. Automated planning volume contouring in soft-tissue sarcoma adjuvant brachytherapy treatment. Int. J. Radiat. Oncol. Biol. Phys. 51:391, 2001: ASTRO 2001.
55. Lee, E. K., R. Gallagher, A. Campbell, and M. Prausnitz. Prediction of ultrasound-mediated disruption of cell membranes using machine learning techniques and statistical analysis of acoustic spectra. IEEE Trans. Biomed. Eng. 51(1):1-9, 2004.
56. Lee, E. K., R. J. Gallagher, and D. Patterson. A linear programming approach to discriminant analysis with a reserved judgment region. INFORMS J. Comput. 15(1):23-41, 2003.
57. Lee, E. K., S. Jagannathan, C. Johnson, and Z. S. Galis. Fingerprinting native and angiogenic microvascular networks through pattern recognition and discriminant analysis of functional perfusion data.PNAS (submitted).
58. Lee, E. L., and S. Maheshwary. Facets of conflict hypergraphs. Math. Operat. Res. (submitted).
59. Lee, E. K., and J. Mitchell. Computational experience of an interior-point SQP algorithm in a parallel branch-and-bound framework. High Performance Optimization Techniques, edited by H. Frenks, K. Roos, T. Terlaky, S. Zhang. Kluwer Academic Publishers, 1997, pp. 329-347.
60. Lee, E. K., and T. L. Wu. Classification and disease prediction via mathematical programming. In: Optimization in Medicine, edited by E. Romeijn and P. Pardalos. Kluwer Academic Publishers, 2006 (to appear).
61. Liittschwager, J. M., and C. Wang. Integer programming solution of a classification problem. Manage. Sci. 24:1515-1525, 1978.
62. Lim, T. S., W. Y. Loh, and Y. S. Shih. A comparison of prediction accuracy, complexity, and training time of thirty-three old and new classification algorithms. Machine Learn. 40:203-228, 2000.
63. Mangasarian, O. L. Mathematical programming in neural networks. ORSA J. Comput. 5:349-360, 1993.
64. Mangasarian, O. L., W. N. Street, and W. H. Wolberg. Breast cancer diagnosis and prognosis via linear programming. Operat. Res. 43570577.
65. Mangasarian, O. L. Mathematical programming in data mining. Data Mining Knowl. Discov. 1(2):183-201, 1997.
66. McCord, J. M. The evolution of free radicals and oxidative stress. Am. J. Med. 108:652-659, 2000.
67. McLachlan, G. J. Discriminant Analysis and Statistical Pattern Recognition. New York: Wiley, 1992.
68. Müller, K. R., S. Mika, G. Rätsch, K. Tsuda, and B. Schölkopf. An introduction to kernel-based learning algorithms. IEEE Trans. Neural Networks 12(2):181-201, 2001.
69. Murphy, P. M., and D. W. Aha. UCI Repository of machine learning databases. Department of Information and Computer Science, University of California, Irvine, California, 1994.
70. Nath, R., W. M. Jackson, and T. W. Jones. A comparison of the classical and the linear programming approaches to the classification problem in discriminant analysis. J. Stat. Comput. Simul. 41:73-93, 1992.
71. Nemhauser, G. L., and L. A. Wolsey. Integer and Combinatorial Optimization. New York: Wiley, 1988.
72. Ng, T-H., and R. H. Randles. Distribution-free partial discrimination procedures. Compur. Math. Appl. 12A:225-234, 1986.
73. Patterson, D. A. Three population constrained discrimination. Technical Report, Department of Mathematical Sciences, University of Montana, Missoula, MT, 1996.
74. Pavur, R., and C Loucopoulos. Examining optimal criterion weights in mixed integer programming approaches to the multiple-group classification problem. J. Operat. Res. Soc: 46:626-640, 1995.
75. Quesenberry, C. P., and M. P. Gessaman. Nonparametric discrimination using tolerance regions. Ann. Math. Stat. 39:664-673, 1968.
76. Raz, A., and A. Ben-Ze'ev. Cell-contact and -architecture of malignant cells and their relationship to metstasis. Cancer Metastasis Rev. 6:3-21, 1987.
77. Rush, L. J., Z. Dai, D. J. Smiraglia, X. Gao, F. A. Wright, M. Fruhwald, J. F. Costello, W. A. Held, L. Yu, R. Krahe, J. E. Kolitz, C. D. Bloomfield, M. A. Caligiuri, and C. Plass. Novel methylation targets in de novo acute myeloid leukemia with prevalence of chromosome 11 loci. Blood 97:3226-3233, 2001.
78. Sies, H. Oxidative Stress: Introductory Comments, edited by H. Sies. Oxidative Stress, pp. 1-8, 1985.
79. p-norm methods. Ann. Operat. Res. 74:1-36, 1997.
80. Stam, A., and E. A. Joachimsthaler. Solving the classification problem in discriminant analysis via linear and nonlinear programming. Decision Sci. 20:285-293, 1989.
81. Stam, A., and E. A. Joachimsthaler. A comparison of a robust mixed-integer approach to existing methods for establishing classification rules for the discriminant problem. Eur. J. Operat. Res. 46:113-122, 1990.
82. Stam, A., and C. T. Ragsdale. On the classification gap in mathematical-programming-based approaches to the discriminant problem. Naval Res. Log. 39:545-559, 1992.
83. Tahara, S., M. Matsuo, and T. Kaneko. Age-related changes in oxidative damage to lipids and DNA in rat skin. Mech. Ageing Dev. 122:415-426, 2001.
84. Vapnik, V. The Nature of Statistical Learning Theory. Springer-Verlag, 1999.
85. Wagner, G., P. Tautu, and U. Wolbler. Problems of medical diagnosis - a bibliography. Methods Inform. Med. 17:55-74, 1978.
86. Yan, P. S., C. M. Chen, H. Shi, F. Rahmatpanah, S. H. Wei, C. W. Caldwell, and T. H. Huang. Dissecting complex epigenetic alterations in breast cancer using CpG island microarrays. Cancer Res. 61:8375-8380, 2001.
87. Yan, P. S., M. R. Perry, D. E. Laux, A. L. Asare, C. W. Caldwell, and T. H. Huang. CpG island arrays: an application toward deciphering epigenetic signatures of breast cancer. Clin. Cancer Res. 6:1432-1438, 2000.
88. Zimmermann, A., and H. U. Keller. Locomotion of tumor cells as an element of invasion and metastasis. Biomed. Pharmacoth, 41:337-344, 1987.
89. Zopounidis, C., and M. Doumpos. Multicriteria classification and sorting methods: a literature review. Eur. J. Operat. Res. 138:229-246, 2002.