Support Vector Machine Classification for High Dimensional Microarray Data Analysis, With Applications in Cancer Research

  • Hao Helen Zhang
Part of the Applied Bioinformatics and Biostatistics in Cancer Research book series (ABB)


Support Vector Machine Variable Selection Reproduce Kernel Hilbert Space Linear Support Vector Machine Machine Learn Research 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Agresti, A. (2002). Categorical Data Analysis. Wiley-Interscience, New York.CrossRefGoogle Scholar
  2. Bach, F., Lanckriet, G. R., and Jordan, M. I. (2004). Multiple kernel learning, conic duality, and the smo algorithm. In Proceeding of the Twenty-First International Conference on Machine Learning, Vol. 69, ACM, New York.Google Scholar
  3. Bi, J., Bennett, K. P., Embrechts, M., Breneman, C. M., and Song, M. (2003). Dimensionality reduction via sparse support vector machines. Journal of Machine Learning Research, 3:1229–1243.CrossRefGoogle Scholar
  4. Boser, B. E., Guyon, I. M., and Vapnik, V. (1992). A training algorithm for optimal margin classifiers. In Haussler, D., editor, Proceedings of the Fifth Annual Workshop on Computational Learning Theory, pp. 144–152. ACM Press, Pittsburgh, PA.CrossRefGoogle Scholar
  5. Bradley, P. S. and Mangasarian, O. L. (1998). Feature selection via concave minimization and support vector machines. In Shavlik, J., editor, Machine Learning Proceedings of the Fifteenth International Conference (ICML ’98), pages 82–90. Morgan Kaufmann, San Francisco, CA.Google Scholar
  6. Bredensteiner, E. J. and Bennett, K. P. (1999). Multicategory classification by support vector machines. Computational Optimization and Applications, 12:35–46.CrossRefGoogle Scholar
  7. Burges, C. J. C. (1998). A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2:121–167.CrossRefGoogle Scholar
  8. Chaplle, O., Vapnik, V., Bousquet, O., and Mukherjee, S. (2002). Choosing kernel parameters for support vector machines. Machine Learning, 46:131–159.CrossRefGoogle Scholar
  9. Cortes, C. and Vapnik, V. (1995). Support vector networks. Machine Learning, 20:1–25.Google Scholar
  10. Cox, D. and O’Sullivan, F. (1990). Asymptotic analysis of penalized likelihood and related estimator. Annals of Statistics, 18:1676–1695.CrossRefGoogle Scholar
  11. Cristianini, N. and Shawe-Taylor, J. (2000). An Introduction to Support Vector Machines. Cambridge University Press, Cambridge, UK.Google Scholar
  12. Duan, K., Keerthi, S., and Poo, A. (2001). Evaluation of simple performance measures for tuning svm hyperparameters. Technical Report CD-01-11, Department of Mechanical Engineering, National University of Singapore.Google Scholar
  13. Dudoit, S., Fridlyand, J., and Speed, T. (2002). Comparison of discrimination methods for the classification of tumors using gene expression data. Journal of American Statistical Association, 97:77–87.CrossRefGoogle Scholar
  14. Evgeniou, T., Pontil, M., and Poggio, T. (1999). A unified framework for regularization networks and support vector machines. Technical report, M.I.T. Artificial Intelligence Laboratory and Center for Biological and Computational Learning Department of Brain and Cognitive Sciences.Google Scholar
  15. Fan, J. and Li, R. Z. (2001). Variable selection via penalized likelihood. Journal of the American Statistical Association, 96:1348–1360.CrossRefGoogle Scholar
  16. Fletcher, R. (1987). Practical Methods of Optimization. Wiley-Interscience, New York, NY.Google Scholar
  17. Fung, G. and Mangasarian, O. L. (2001). Multicategory proximal support vector machine classifiers. Technical Report 01–06, University of Wisconsin-Madison, Data Mining Institute.Google Scholar
  18. Fung, G. and Mangasarian, O. L. (2004). A feature selection newton method for support vector machine classification. Computational Optimization and Applications Journal, 28(2):185–202.CrossRefGoogle Scholar
  19. Furey, T., Cristianini, N., Duffy, N., Bednarski, D., Schurmmer, M., and Haussler, D. (2000). Support vector machine classification and validation of cancer tissue samples using microarray expression data. Bioinformatics, 16:906–914.PubMedCrossRefGoogle Scholar
  20. Grandvalet, Y. and Canu, S. (2002). Adaptive scaling for feature selection in SVMs. Neural Information Processing Systems, 553–560.Google Scholar
  21. Guermeur, Y. (2002). Combining discriminant models with new multi-class SVMs. Pattern Analysis and Applications, 5:168–179.CrossRefGoogle Scholar
  22. Gunn, S. R. and Kandola, J. S. (2002). Structural modeling with sparse kernels. Machine Learning, 48:115–136.CrossRefGoogle Scholar
  23. Guyon, I., Weston, J., and Barnhill, S. (2002). Gene selection for cancer classification using support vector machines. Machine Learning, 46:389–422.CrossRefGoogle Scholar
  24. Hall, P., Marrson, S., and Neeman, A. (2005). Geometric representation for high dimension low sample size data. Journal of Royal Statistical Society, B, 67:427–444.CrossRefGoogle Scholar
  25. Hand, D. J. (1997). Construction and Assessment of Classification Rules. John Wiley and Sons, Chichester, England.Google Scholar
  26. Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Element of Statistical Learning. Springer, New York.Google Scholar
  27. Hastie, T., Rosset, S., Tibshirani, R., and Zhu, J. (2004). The entire regularization path for the support vector machines. Journal of Machine Learning Research, 5:1391–1415.Google Scholar
  28. Hu, Z., Fan, C., Marron, J. S., He, X., Qaqish, B. F., Karaca, G., Livasy, C., Carey, L., Reynolds, E., Dressler, L., Nobel, A., Parker, J., Ewend, M. G., Sawyer, L. R., Xiang, D., Wu, J., Liu, Y., Karaca, M., Nanda, R., Tretiakova, M., Orrico, A. R., Dreher, D., Palazzo, J. P., Perreard, L., Nelson, E., Mone, M., Hansen, H., Mullins, M., Quackenbush, J. F., Olapade, O. I., Bernard, B. S., and Perou, C. M. (2005). The molecular portraits of breast tumors are conserved across microarray platforms. submitted.Google Scholar
  29. Joachims, T. (2000). Estimating the generalization performance of an SVM efficiently. In Proceedings of ICML-00, 17th International Conference on Machine Learning, Morgan Kaufman, San Francisco, 431–438.Google Scholar
  30. Khan, J., Wei, J., Ringer, M., Saal, L., Ladanyi, M., Westerman, F., Berthold, F., Schwab, M., Antonescu, C., Peterson, C., and Meltzer, P. (2001). Classification and diagnostic prediction of cancers using gene expression profiling and artificial neural network. Nature Medicine, Jun.; 7(6):673–679.PubMedCrossRefGoogle Scholar
  31. Kimeldorf, G. and Wahba, G. (1971). Some results on Tchebycheffian spline functions. Journal of Mathematical Analysis and Applications, 33:82–85.CrossRefGoogle Scholar
  32. Kittler, J. (1986). Feature selection and extraction. In T.Y.Young and K.-S. Fu, editors, Handbook of Pattern Recognition and Image Processing. Academic Press, New York.Google Scholar
  33. Lee, Y. and Cui, Z. (2006). Characterizing the solution path of multicategory support vector machines. Statistica Sinica, 16:391–409.Google Scholar
  34. Lee, Y. and Lee, C. (2003). Classification of multiple cancer types by multicategory support vector machines using gene expression data. Bioinformatics, 19:1132–1139.PubMedCrossRefGoogle Scholar
  35. Lee, Y., Lin, Y., and Wahba, G. (2004). Multicategory support vector machines, theory, and application to the classification of microarray data and satellite ra diance data. Journal of American Statistical Association, 99:67–81.CrossRefGoogle Scholar
  36. Lin, Y. (2002). SVM and the Bayes rule in classification. Data Mining and Knowledge Discovery, 6:259–275.CrossRefGoogle Scholar
  37. Lin, Y. and Zhang, H. H. (2006). Component selection and smoothing in smoothing spline analysis of variance models. Annals of Statistics, 34:2272–2297.CrossRefGoogle Scholar
  38. Lin, Y., Lee, Y., and Wahba, G. (2002). Support vector machines for classification in nonstandard situations. Machine Learning, 46:191–202.CrossRefGoogle Scholar
  39. Liu, Y. and Shen, X. (2006). Multicategory psi-learning and support vector machine: computational tools. Journal of American Statistical Association, 99:219–236.Google Scholar
  40. Liu, Y., Shen, X., and Doss, H. (2004). Multicategory psi-learning and support vector machine: computational tools. Journal of Computational and Graphical Statistics, 14:219–236.CrossRefGoogle Scholar
  41. Pan, W. (2002). A comparative review of statistical methods for discovering differently expressed genes in replicated microarray experiments. Bioinformatics, 18:546–554.PubMedCrossRefGoogle Scholar
  42. Perou, C., Srlie, T., Eisen, M., van de Rijn, M., Jeffrey, S., Rees, C., Pollack, J., Ross, D., Johnsen, H., Akslen, L., Fluge, O., Pergamenschikov, A., Williams, C., Zhu, S., Lning, P., Brresen-Dale, A., Brown, P., and Botstein, D. (2000). Molecular portraits of human breast tumors. Nature, 406:747–752.PubMedCrossRefGoogle Scholar
  43. Rakotomamonjy, A. (2003). Variable selection using svm-based criteria. Journal of Machine Learning Research, 3:1357–1370.CrossRefGoogle Scholar
  44. Schölkopf, B. and Smola, A. J. (2002). Learning with Kernels. MIT Press, Cambridge, MA.Google Scholar
  45. Shawe-Taylor, J. and Cristianini, N. (2004). Kernel Methods for Pattern Recognition. Cambridge University Press, Cambridge, UK.Google Scholar
  46. Sotiriou, C., Neo, S., McShane, L., Korn, E., Long, P., Jazaeri, A., Martiat, P., Fox, S., Harris, A., and Liu, E. (2003). Breast cancer classification and prognosis based on gene expression profiles from a population-based study. Proceedings of the National Academy of Sciences, 100(18):10393–10398.CrossRefGoogle Scholar
  47. Tang, Y. and Zhang, H. H. (2005). Multiclass proximal support vector machines. Journal of Computational and Graphical Statistics, 15:339–355.CrossRefGoogle Scholar
  48. Tibshirani, R. J. (1996). Regression shrinkage and selection via the lasso. Journal of Royal Statistical Society, B, 58:267–288.Google Scholar
  49. Tibshirani, R., Hastie, T., Narasimhan, B., and Chu, G. (2002). Diagnosis of multiple cancer types by shrunken centroids of gene expression. Proceedings of the National Academy of Sciences USA, 99:6567–6572.CrossRefGoogle Scholar
  50. Vapnik, V. N. (1998). Statistical Learning Theory. Wiley, New York.Google Scholar
  51. Veer, L. V., Dai, H., van de Vijver, M., He, Y., Hart, A., Mao, M., Peterse, H., van der Kooy, K., Marton, M., Witteveen, A., Schreiber, G., Kerkhoven, R., Roberts, C., Linsley, P., Bernards, R., and Friend, S. (2002). Gene expression profiling predicts clinical outcome of breast cancer. Nature, 415:530–536.CrossRefGoogle Scholar
  52. Wahba, G. (1990). Spline Models for Observational Data, volume 59. SIAM. CBMS-NSF Regional Conference Series in Applied Mathematics.Google Scholar
  53. Wahba, G. (1999). Support vector machines, reproducing kernel Hilbert spaces and the randomized GACV. In Scholkopt, B., Burges, C., and Smola, A., editors, Advances in Kernel Methods–Support Vector Learning. MIT Press, Cambridge, MA.Google Scholar
  54. Wahba, G., Lin, Y., and Zhang, H. H. (2000). Generalized approximate cross validation for support vector machines, or, another way to look at margin-like quantities. In Smola, Bartlett, Scholkopf, and Schurmans, editors, Advances in Large Margin Classifiers. MIT Press.Google Scholar
  55. Wang, L. and Shen, X. (2007). On 11-norm multiclass support vector machines: methodology and theory. Journal of American Statistical Association, 102:583–594.CrossRefGoogle Scholar
  56. Weston, J. and Watkins, C. Multi-class support vector machines, In Verleysen, M., editor, Proceedings of ESANN99, Brussels, D. Facto Press (1999).Google Scholar
  57. Weston J, Mukherjee S, Chapelle O, Pontil M, Poggio T, Vapnik V. Feature selection for SVMs. In Advances in Neural Information Processing Systems (NIPS) 13, (2000). (Edited by: TK Leen, TG Dietterich, V Tresp). MIT Press 2001, 668–674.Google Scholar
  58. Zhang, T. (2004). Statistical behavior and consistency of classification methods based on convex risk minimization. Annals of Statistics, 32:56–85.CrossRefGoogle Scholar
  59. Zhang, H. (2006). Variable selection for support vector machines via smoothing spline anova. Statistica Sinica, 16:659–674.Google Scholar
  60. Zhang, H., Ahn, J., Lin, X., and Park, C. (2006). Gene selection using support vector machines with nonconvex penalty. Bioinformatics, 22:88–95.PubMedCrossRefGoogle Scholar
  61. Zhang, H., Liu, Y., Wu, Y., and Zhu, J. (2008). Variable selection for multicategory SVM via supnorm regularization. The Electronic Journal of of Statistics. to appear.Google Scholar
  62. Zhu, J., Rosset, S., Hastie, T., and Tibshirani, R. (2003). 1-norm support vector machines. NIPS 16. MIT Press.Google Scholar
  63. Zou, H. and Yuan, M. (2008). The F support vector machines. Statistica Sinica, 18:379–398.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of StatisticsDepartment of StatisticsRaleighUSA

Personalised recommendations