Solving a Multigroup Mixed-Integer Programming-Based Constrained Discrimination Model

References

• Anderson JA (1969) Constrained discrimination between k populations. J. Roy. Statist. Soc. Ser. B (Methodological) 31:123–139.Google Scholar
• Atamtürk A, Nemhauser GL, Savelsbergh MWP (2000) Conflict graphs in solving integer programming problems. Eur. J. Oper. Res. 121:40–55.Crossref, Google Scholar
• Bennett KP (1999) Semi-supervised support vector machines. Kearns MS, Solla SA, Cohn DA, eds. Advances in Neural Information Processing Systems Proc. 1998 Conf. (MIT Press, Cambridge, MA), 368–374.Google Scholar
• Bixby RE, Lee EK (1998) Solving a truck dispatching scheduling problem using branch-and-cut. Oper. Res. 46:355–367.Link, Google Scholar
• Borndörfer R (1997) Aspects of set packing, partitioning and covering. Ph.D. thesis, Technische Universität Berlin, Berlin, Germany.Google Scholar
• Brooks JP (2011) Support vector machines with the ramp loss and the hard margin loss. Oper. Res. 59:467–479.Link, Google Scholar
• Brooks JP, Lee EK (2010) Analysis of the consistency of a mixed integer programming-based multi-category constrained discriminant model. Ann. Oper. Res. 174:147–168.Crossref, Google Scholar
• Chapelle O, Sindhwani V, Keerthi SS (2008) Optimization techniques for semi-supervised support vector machines. J. Machine Learn. Res. 9:203–233.Google Scholar
• Chen C, Mangasarian OL (1996) Hybrid misclassification minimization. Adv. Comput. Math. 5:127–136.Crossref, Google Scholar
• Crammer K, Singer Y (2001) On the algorithmic implementation of multiclass kernel-based vector machines. J. Machine Learn. Res. 2:265–292.Google Scholar
• Detrano R, Janosi A, Steinbrunn W, Pfisterer M, Schmid J, Sandhu S, Guppy K, Lee S, Froelicher V (1989) International application of a new probability algorithm for the diagnosis of coronary artery disease. Amer. J. Cardiology 64:304–310.Crossref, Google Scholar
• Devroye L, Györfi L, Lugosi G (1996) A Probabilistic Theory of Pattern Recognition (Springer, New York).Crossref, Google Scholar
• Duda RO, Hart PE, Stork DG (2001) Pattern Classification (Wiley, New York).Google Scholar
• Easton T, Hooker K, Lee E (2003) Facets of the independent set polytope. Math. Programming, Ser. B 98:177–199.Crossref, Google Scholar
• Euler R, Jünger M, Reinelt G (1987) Generalizations of cliques, odd cycles and anticycles and their relation to independence system polyhedra. Math. Oper. Res. 12:451–462.Link, Google Scholar
• Feltus FA, Lee EK, Costello JF, Plass C, Vertino PM (2003) Predicting aberrant CpG island methylation. Proc. National Acad. Sci. 100:12253–12258.Crossref, Google Scholar
• Feltus FA, Lee EK, Costello JF, Plass C, Vertino PM (2006) DNA motifs associated with aberrant CpG island methylation. Genomics 87:572–579.Crossref, Google Scholar
• Gallagher RJ, Lee EK, Patterson DA (1997) Constrained discriminant analysis via 0/1 mixed integer programming. Ann. Oper. Res. 74:65–88.Crossref, Google Scholar
• Gallagher RJ, Patterson DA, Lee EK (1996) An optimization model for constrained discriminant analysis and numerical experiments with iris, thyroid, and heart disease data sets. Cimino JJ, ed. Proc. 1996 Amer. Medical Informatics Assoc. (Hanley & Belfus, Philadelphia), 209–213.Google Scholar
• Golumbic MC, Rotem D, Urritia J (1983) Comparability graphs and intersection graphs. Discrete Math. 43:37–46.Crossref, Google Scholar
• Joachims T (1999) Making large-scale SVM learning practical. Schölkopf B, Burges C, Smola A, eds. Advances in Kernel Methods (MIT Press, Cambridge, MA), 169–184.Google Scholar
• Johnson EL, Padberg MW (1982) Degree-two inequalities, clique facets, and biperfect graphs. Ann. Discrete Math. 16:169–187.Google Scholar
• Koehler GJ, Erenguc SS (1990) Minimizing misclassifications in linear discriminant analysis. Decision Sci. 21:63–85.Crossref, Google Scholar
• Laurent M (1989) A generalization of antiwebs to independence systems and their canonical facets. Math. Programming 45:97–108.Crossref, Google Scholar
• Lee EK (1993) Solving a truck dispatching scheduling problem using branch-and-cut. Ph.D. thesis, Computational and Applied Mathematics, Rice University, Houston.Google Scholar
• Lee EK (2007a) Large-scale optimization-based classification models in medicine and biology. Ann. Biomedical Engrg., Systems Biol. Bioinformatics 35:1095–1109.Crossref, Google Scholar
• Lee EK (2007b) Optimization-based predictive models in medicine and biology. Alves CJS, Pardalos P, Vincente LN, eds. Springer Series in Optimization and Its Application, Optimization in Medicine, Vol. 12 (Springer, New York), 127–151.Google Scholar
• Lee EK, Maheshwary S (2004) Conflict hypergraphs in integer programming. Technical report, Georgia Institute of Technology, Atlanta.Google Scholar
• Lee EK, Maheshwary S (2009) Facets of Conflict Hypergraphs. Technical report, Georgia Institute of Technology, Atlanta.Google Scholar
• Lee EK, Wu TL (2007) Classification and disease prediction via mathematical programming. Seref O, Kundakcioglu OE, Pardalos P, eds. Data Mining, Systems Analysis, and Optimization in Biomedicine (American Institute of Physics, Melville, NY), 1–42.Crossref, Google Scholar
• Lee EK, Gallagher RJ, Patterson DA (2003) A linear programming approach to discriminant analysis with a reserved-judgment region. INFORMS J. Comput. 15:23–41.Link, Google Scholar
• Lee EK, Fung AYC, Brooks JP, Zaider M (2002) Automated planning volume definition in soft-tissue sarcoma adjuvant brachytherapy. Biol. Phys. Medicine 47:1891–1910.Crossref, Google Scholar
• Lee EK, Gallagher RJ, Campbell AM, Prausnitz MR (2004) Prediction of ultrasound-mediated disruption of cell membranes using machine learning techniques and statistical analysis of acoustic spectra. IEEE Trans. Biomedical Engrg. 51:1–9.Crossref, Google Scholar
• Lee EK, Jagannathan S, Johnson C, Galis GS (2006) Fingerprinting native and angiogenic microvascular networks through pattern recognition and discriminant analysis of functional perfusion data. Technical report, Georgia Institute of Technology, Atlanta.Google Scholar
• Liaw A, Wiener M (2002) Classification and regression by random-Forest. R News 2(3):18–22.Google Scholar
• Maheshwary S (2008) Facets of Conflict Hypergraphs. Ph.D. thesis, Georgia Institute of Technology, Atlanta.Google Scholar
• Müller R, Schulz AS (2002) Transitive packing: A unifying concept in combinatorial optimization. SIAM J. Optim. 13:335–367.Crossref, Google Scholar
• Nemhauser G, Trotter L (1974) Properties of vertex packing and independence system polyhedra. Math. Programming 6:48–61.Crossref, Google Scholar
• Newman DJ, Hettich S, Blake CL, Merz CJ (1998) UCI repository of machine learning databases. Accessed March 17, 2014, http://www.ics.uci.edu/∼mlearn/MLRepository.html.Google Scholar
• Niskanen S, Östergård PRJ (2003) Cliquer user's guide, version 1.0. Technical Report T48, Communications Laboratory, Helsinki University of Technology, Espoo, Finland.Google Scholar
• Orsenigo C, Vercellis C (2003) Multivariate classification trees based on minimum features discrete support vector machines. IMA J. Management Math. 14:221–234.Crossref, Google Scholar
• Padberg M (1973) On the facial structure of set packing polyhedra. Math. Programming 5:199–215.Crossref, Google Scholar
• Querec TD, Akondy R, Lee EK, Cao W, Nakaya HI, Teuwen K, Pirani Aet al. (2009) Systems biology approaches predict immunogenicity of the yellow fever vaccine in humans. Nature Immunology 10:116–125.Crossref, Google Scholar
• R Development Core Team (2010) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org.Google Scholar
• Sekiguchi Y (1983) A note on node packing polytopes on hypergraphs. Oper. Res. Lett. 2:243–247.Crossref, Google Scholar
• Venables WN, Ripley BD (2002) Modern Applied Statistics with S, 4th ed. (Springer, New York).Crossref, Google Scholar
• Wright AH (1999) The role of integrins in the differential upregulation of tumor cell motility by endothelial extracellular matrix proteins. Ph.D. thesis, Georgia Institute of Technology,Atlanta.Google Scholar