Abstract
Mathematical theory of optimization has found many applications in the area of medicine over the last few decades. Several data analysis and decision making problems in medicine can be formulated using optimization and data mining techniques. The significance of the mathematical models is greatly realized in the recent years owing to the growing technological capabilities and the large amounts of data available. In this paper, we attempt to give a brief overview of some of the most interesting applications of mathematical programming and data mining in medicine. In the overview, we include applications like radiation therapy treatment, microarray data analysis, and computational neuroscience.
Similar content being viewed by others
References
Abeyratne R, Kinouchi Y, Oki H, Okada J, Shichijo F, Matsumoto K (1991) Artificial neural networks for source localization in the human brain. Brain Topogr 4(1):3–21
Aleman DM, Glaser D, Romeijn HE, Dempsey JF (2007) A primal-dual interior point algorithm for fluence map optimization in intensity modulated radiation therapy treatment planning. Technical report, Gainesville, Florida: Department of Industrial and Systems Engineering, University of Florida
Aleman DM, Romeijin HE, Dempsey JF (2008) Beam orientation optimization methods in intensity modulated radiation therapy treatment planning. In: Optimization in medicine and biology. Auerbach Publications, pp 223–251
Alves CJS, Pardalos PM, Vicente LN (eds) (2008) Optimization in medicine. Springer optimization and its applications, vol 12. Springer, Berlin
Bensmail H, Semmes OJ, Haoudi A (2007) Clustering proteomics data using Bayesian principal component analysis clustering proteomics data using Bayesian principal component analysis. In: Data mining in biomedicine. Springer optimization and its applications, vol 7. Springer, Berlin, pp 339–362
Busygin S, Pardalos PM (2007) Exploring microarray data with correspondence analysis. In: Data mining in biomedicine. Springer optimization and its applications, vol 7. Springer, Berlin, pp 25–37
Busygin S, Prokopyev OA, Pardalos PM (2005) Feature selection for consistent biclustering via fractional 0–1 programming. J Comb Optim 10:7–21
Busygin S, Prokopyev O, Pardalos PM (2007) Biclustering in data mining. Comput Oper Res 35(9):2964–2987
Chaovalitwongse W (2003) Optimization and dynamical approaches in nonlinear time series analysis with application in bioengineering. PhD thesis, University of Florida
Cheng Y, Church GM (2000) Biclustering of expression data. In: Proceedings of the eighth international conference on intelligent system for molecular biology, pp 93–103
Dhillon IS (2001) Co-clustering documents and words using bipartite spectral graph partitioning. In: Proceedings of the seventh ACM SIGKDD international conference on knowledge discovery and data mining, pp 269–274
Fan N, Boyko N, Pardalos PM (2010) Recent advances of data biclustering with application in computational neuroscience. Springer, Berlin (in press)
Floudas C, Pardalos PM (eds) (2000) Optimization in computational chemistry and molecular biology. Kluwer Academic, Dordrecht
Gorodnitsky IF, George JS, Rao BD (1995) Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm. Electroencephalogr Clin Neurophysiol, pp 231–251
Intensity Modulated Radiation Therapy Collaborative Working Group (2001) Intensity modulated radiotherapy: current status and issues of interest. Int J Radiat Oncol Biol Phys 51:880–914
Hallez H, Vanrumste B, Grech R, Muscat J, De Clercq W, Vergult A, D’Asseler Y, Camilleri KP, Fabri SG, Van Huffel S, Lemahieu I (2007) Review on solving the forward problem in EEG source analysis. J NeuroEng Rehabil 4(46)
Iasemidis LD (1990) On the dynamics of the human brain in temporal lobe epilepsy. PhD thesis, University of Michigan, Ann Arbor
Jiang T, Li X, Kruggel F (2000) Global optimization approaches to MEG source localization. pp 223–230
Kalinowski T (2008) Multileaf collimator shape matrix decomposition. In: Optimization in medicine and biology. Auerbach Publications, pp 253–286
Kamath S, Sahni S, Palta J, Ranka S, Lim J (2009) Algorithms for sequencing multileaf collimator. In: Handbook of optimization in medicine. Springer optimization and its applications, vol 26. Springer, Berlin, pp 223–242
Kluger Y, Basri R, Chang JT, Gerstein M (2003) Spectral biclustering of microarray data: coclustering genes and conditions. Genome Res 13:703–716
Küfer KH, Monz M, Scherrer A, Süss P, Alonso F, Azizi Sultan AS, Bortfeld T, Thieke C (2009) Multicriteria optimization in intensity modulated radiotherapy planning. In: Handbook of optimization in medicine. Springer optimization and its applications, vol 26. Springer, Berlin, pp 123–167
Kundakcioglu OE, Pardalos PM (2009) The complexity of feature selection for consistent biclustering. In: Chaovalitwongse, WA, Butenko, S, Pardalos, PM (eds) Clustering challenges in biological networks, pp 257–266
Legras J, Legras B, Lambert J (1982) Software for linear and non-linear optimization in external radiotherapy. Comput Programs Biomed 15:223–242
Lim GJ (2008) Introduction to radiation therapy planning optimization. In: Optimization in medicine and biology. Auerbach Publications, pp 197–221
Lim GJ (2009) Optimization models and computational approaches for three-dimensional conformal radiation treatment planning. In: Handbook of optimization in medicine. Springer optimization and its applications, vol 26. Springer, Berlin, pp 53–81
Lim GJ, Lee EK (eds) (2008) Optimization in medicine and biology. Auerbach Publications
Lim GJ, Ferris MC, Wright SJ, Shepard DM, Earl MA (2007) An optimization framework for conformal radiation treatment planning. INFORMS J Comput 19(3):366–380
Madeira SC, Oliveira AL (2004) Biclustering algorithms for biological data analysis: a survey. IEEE/ACM Trans Comput Biol Bioinform 1:24–45
McNay D, Michielssen E, Rogers RL, Taylor SA, Akhtari M, Sutherling WW (1996) Multiple source localization using genetic algorithms. J Neurosci Methods 64(2):163–172
Miga MI, Kerner TE, Darcey TM (2002) Source localization using a current-density minimization approach. Biomed Eng, IEEE Trans Biomed Eng 49(7):743–745
Milton J, Jung P (eds) (2003) Epilepsy as a dynamic disease. Springer, Berlin
Mondaini RP, Pardalos PM (eds) (2008) Mathematical modelling of biosystems, vol 102. Springer, Berlin
Mormann F, Andrzejak RG, Elger CE, Lehnertz K (2007) Seizure prediction: the long and winding road. Brain 130(2):314–333
Pardalos PM, Hansen P (eds) (2008) Data mining and mathematical programming. American Mathematical Society, Providence
Pardalos PM, Principe JC (eds) (2002) Biocomputing. Biocomputing, vol 1. Springer, Berlin
Pardalos PM, Romeijn HE (eds) (2009) Handbook of optimization in medicine. Springer optimization and its applications, vol 26. Springer, Berlin
Pardalos PM, Yatsenko VA (2006) Optimization approach to the estimation and control of Lyapunov exponents. J Optim Theory Appl 128:29–48
Pardalos PM, Iasemidis L, Shiau DS, Sackellares JC, Chaovalitwongse W (2003a) Prediction of human epileptic seizures based on optimization and phase changes of brain electrical activity. Optim Methods Softw 18(1):81–104
Pardalos PM, Iasemidis L, Shiau DS, Sackellares V, Yatsenko J, Chaovalitwongse W (2003b) Analysis of EGG data using optimization, statistics, and dynamical systems techniques. Comput Stat Data Anal 44:391–408
Pardalos PM, Chaovalitwongse W, Iasemidis LD, Sackellares JC, Shiau DS, Carney PR, Prokopyev OA, Yatsenko VA (2004a) Seizure warning algorithm based on optimization and nonlinear dynamics. Math Program 101(2):365–385
Pardalos PM, Sackellares C, Carney P, Iasemidis L (eds) (2004b) Quantitative neuroscience. Kluwer Academic, Dordrecht
Pardalos PM, Sackellares JC, Carney PR, Iasemidis LD (eds) (2004c) Quantitative neuroscience models, algorithms, diagnostics, and therapeutic applications. Kluwer Academic, Dordrecht
Pardalos PM, Boginski V, Vazakopoulos A (eds) (2007) Data mining in biomedicine. Springer optimization and its applications, vol 7. Springer, Berlin
Pascual-Marqui RD (1999) Review of methods for solving the EEG inverse problem. Int J Bioelectromagn 1:75–86
Pugachev A, Xing L (2001) Pseudo beam’s-eye-view as applied to beam orientation selection in intensity-modulated radiation therapy. Int J Radiat Oncol, Biol, Phys 51:1361–1370
Reemtsen R, Albert M (2009) Continuous optimization of beamlet intensities for intensity modulated photon and proton radiotherapy. In: Handbook of optimization in medicine. Springer optimization and its applications, vol 26. Springer, Berlin, pp 83–122
Rege M, Dong M, Fotouhi F (2008) Bipartite isoperimetric graph partitioning for data co-clustering. Data Min Knowl Discov 16(3):276–312
Robert C, Gaudy JF, Limoge A (2002) Electroencephalogram processing using neural networks. Clin Neurophysiol 113(5):694–701
Romeijn HE, Dempsey JF (2008) Intensity modulated radiation therapy treatment plan optimization. TOP Off J Span Soc Stat Oper Res 16(2):215–243
Sackellares JC (2008) Seizure prediction. Epilepsy Curr 8(3):55–59
Sano M, Sawada Y (1985) Measurement of the Lyapunov spectrum from a chaotic time series. Phys Rev Lett 55:1082–1085
Santosa B, Conway T, Trafalis T (2007) A hybrid knowledge based-clustering multi-class SVM approach for genes expression analysis. In: Data mining in biomedicine. Springer optimization and its applications, vol 7. Springer, Berlin, pp 262–274
Sclabassi RJ, Sonmez M, Sun M (2001) EEG source localization: a neural network approach. Neurol Res 23(5):457–464
Seref O, Kundakcioglu OE, Pardalos PM (eds) (2008) Data mining, systems analysis, and optimization in biomedicine, vol 953. Springer, Berlin
Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905
Shiau DS, Luo Q, Gilmore SL, Roper SN, Pardalos PM, Sackellares JC, Iasemidis LD (2000) Epileptic seizures resetting revisited. Epilepsia 41(S7):208–209
Sun M, Sclabassi RJ (2000) The forward EEG solutions can be computed using artificial neural networks. IEEE Trans Biomed Eng 47(8):1044–1050
Tanay A, Sharan R, Shamir R (2002) Discovering statistically significant biclusters in gene expression data. Bioinformatics 18(Suppl 1):S136–S144
Tanay A, Sharan R, Shamir R (2005) Biclustering algorithms: a survey. In: Handbook of computational molecular biology. Chapman and Hall/CRC Press, London/Boca Raton, pp 26–1, 26–17
Tun AK, Lye NT, Guanglan Z, Abeyratne UR, Saratchandran P (2000) RBF networks for source localization in quantitative electrophysiology. Crit Rev Biomed Eng 28:463–472
Van Hoey G, De Clercq J, Vanrumste B, Walle R, Lemahieu I, D’Have’ M, Boon P (2000) EEG dipole source localization using artificial neural networks. Phys Med Biol 45:997–1011
Weinstein DM, Zhukov L, Potts G (2000) Localization of multiple deep epileptic sources in a realistic head model via independent component analysis. School of computing technical report UUCS-2000-004, University of Utah
Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time series. Physica D 16:285–317
Wu TH (1997) A note on a global approach for general 0–1 fractional programming. Eur J Oper Res 101:220–223
Xanthopoulos P, Boyko N, Fan N, Pardalos PM (2010) Biclustering: algorithms and application in data mining. In: Wiley of operations research and management science (in press)
Yang J, Wang H, Wang W, Yu P (2003) Enhanced biclustering on expression data. In: Proceeding of the third IEEE conference on bioinformatics and bioengineering, pp 321–327
Zha H, He X, Ding C, Simon H, MGu (2001) Bipartite graph partitioning and data clustering. In Proceedings of the tenth international conference on Information and knowledge management, pp 25–32
Zhukov L, Weinstein D, Johnson CR (2000) Independent component analysis for EEG source localization in realistic head models. Proc IEEE Eng Med Biol Soc, 22nd Ann Int Conf 3(19):87–96
Author information
Authors and Affiliations
Corresponding author
Additional information
This invited paper is discussed in the comments available at: doi:10.1007/s11750-009-0125-0, doi:10.1007/s11750-009-0127-y, doi:10.1007/s11750-009-0128-x, doi:10.1007/s11750-009-0129-9, doi:10.1007/s11750-009-0130-3.
Rights and permissions
About this article
Cite this article
Pardalos, P.M., Tomaino, V. & Xanthopoulos, P. Optimization and data mining in medicine. TOP 17, 215–236 (2009). https://doi.org/10.1007/s11750-009-0124-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-009-0124-1