Learning adaptive kernels for model diagnosis

ABSTRACT

This paper looks into the tradeoff between model complexity and prediction accuracy using data examples from the benchmark problem of breast cancer. In particular, we take into account several crucial aspects in model construction using learning kernel classifiers. Given its importance, a more generalized form of the basis kernel function definition is then applied. Moreover, model selection is performed in terms of kernel machine hyperparameters, and results are evaluated in terms of the model development cost time.

References

1. {1} C. J. Merz and P. M. Murphy, "UCI repository of machine learning databases," 1998. Available at http://www.ics.uci.edu/~mlearn/MLRepository.html, Department of Information and Computer Science, University of California, Irvine, CA, USA.
2. {2} M. Wrensch, T. Chew, G. Farren, J. B. and Flavia Belli, C. Clarke, C. A. Erdmann, M. Lee, M. Moghadassi, R. Peskin-Mentzer, C. P. Quesenberry, V. Souders-Mason, L. Spence, M. Suzuki, and M. Gould, "Risk factors for breast cancer in a population with high incidence rates," Breast Cancer Res, vol. 5, pp. R88-R102, 2003.
3. {3} O. L. Mangasarian, W. N. Street, and W. H. Wolberg, "Breast cancer diagnosis and prognosis via linear programming" Operations Research, vol. 43, no. 4, pp. 570-577, 1995.
4. {4} D.B. Fogel, E. C. Wasson, E. M. Boughon, V. W. Porto, and P. J. Angeline, "Linear and neural models for classifying breast masses," IEEE Transactions on Medical Imaging, vol. 17, no. 3, pp. 485-488, 1998.
5. {5} O. L. Mangasarian, "Mathematical programming in data mining," Data Mining and Knowledge Discovery, vol. 42, no. 1, pp. 183-201, 1997.
6. {6} E. B. Baum and D. Haussler, "What size net gives valid generalization?," Neural Computation, vol. 1, pp. 151-160, 1989.
7. {7} D. B. Fogel, E. C. Wasson, E. M. Boughon, and V. W. Porto, "A step toward computer assisted mammography using evolutionary programming and neural networks," Cancer Letters, pp. 93-97, 1998.
8. {8} P. S. Bradley, O. L. Mangansarian, and W. N. Street, "Clustering via concave minimization," in Advances in Neural Information Processing Systems (M. C. Mozer, M. I. Jordan, and T. Pesche, eds.), vol. 9, pp. 368-374, Cambridge, MA: MIT Press, 1997.
9. {9} M. K. Markeya, J. Y. Lo, G. D. Tourassi, and C. E. F. Jr., "Self-organizing map for cluster analysis of a breast cancer database" Artificial Intelligence in Medicine, vol. 27, pp. 113-127, 2003.
10. {10} C. Cortes and V. Vapnik, "Support vector networks;' Machine Learning, vol. 20, pp. 273-297, 1995.
11. {11} G. Wahba, "Support vector machines, reproducing kernel Hilbert spaces and the randomized GACV," in Advances in Kernel Methods -- Support Vector Learning (B. Schölkopf, C. J. C. Burges, and A. J. Smola, eds.), (Cambridge, MA), pp. 69-88, MIT Press, 1999.
12. {12} T. Mercer, "Functions of positive and negative and their connections to the theory of integral equations," Trans. London Phil. Soc. (A), vol. 209, pp. 415-446, 1909.
13. {13} V.N. Vapnik, statistical learning theory. New York: Wiley, 1998.
14. {14} V. Vapnik, E. Levin, and Y. L. Cun, "Measuring the VC-dimension of a learning machine," Neural Computation , vol. 6, no. 5, pp. 851-876, 1994.
15. {15} V. Cherkassy, "Model complexity control and statistical learning," Natural Computing, vol. 1, pp. 109-133, 2002.
16. {16} V. Vapnik, "Inductive principles of statistics and learning theory;' in Mathematical Perspectives on Neural Networks (P. Smolensky, M. C. Mozer, and D. E. Rumelhart, eds.), Mahwah, NJ: Lawrence Erlbaum, 1995.
17. {17} V. Vapnik and A. Chervonenkis, "Necessary and sufficient conditions for the uniform convergence of means to their expectatians," Theory of Probability and its Applications, vol. 26, no. 3, pp. 532-553, 1981.
18. {18} M. Poutil and A. Verri, Properties of support vector machines" Neural Computation, vol. 10, pp. 955-974, 1997.
19. {19} T. Evgeniou, M. Pontil, and T. Poggio, "Regularization networks and support vector machines," Advances in Computational Mathematics, vol. 13, no. 1, pp. 1-50, 2000.
20. {20} R. Courant and D. Hilbert, Methods of Mathematical Physics I, Springer-Verlag, 1924.
21. {21} V. Vapnik, The Nature of Statistical Learning Theory. New York: Springer Verlag, 1995.
22. {22} N. Cristianini and J. Shawe-Taylor, Support Vector Machines and Other Kernel based Learning Methods. Cambridge University Press, 2000.
23. {23} B. Ribeiro, "Kernalized based functions with minkovsky's norm for svm regression," in Proceedings of the 2002 International Joint Conference on Neural Networks, vol. 3, pp. 2198-2203, IEEE, 2002.
24. {24} C.-C. Chang and C.-J. Lin, "LIBSVM: a library for support vector machines," tech. rep., Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, 2000.

Index Terms

• Applied computing

  • Life and medical sciences

• Computing methodologies

  • Machine learning

    • Learning paradigms

      • Supervised learning

        • Supervised learning by classification

    • Machine learning approaches

      • Classification and regression trees