Abstract
By applying recent results in optimization transfer, a new algorithm for kernel Fisher Discriminant Analysis is provided that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The algorithm is simple, easily programmed and is shown to perform as well as or better than a number of leading machine learning algorithms on a substantial benchmark. It is then applied to a set of extreme small-sample-size problems in virtual screening where it is found to be less accurate than a currently leading approach but is still comparable in a number of cases.
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References
Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. John Wiley & Sons, Chichester (1973)
Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002)
Mika, S., Rätsch, G., Weston, J., Schölkopf, B., Smola, A., Müller, K.-R.: Constructing descriptive and discriminative nonlinear features: Rayleigh Coefficients in kernel feature spaces. IEEE T. Pattern Anal. 25 (2003)
Billings, S.A., Lee, K.L.: Nonlinear fisher discriminant analysis using a minimum squared error cost function and the orthogonal least squares algorithm. Neural Networks 15, 263–270 (2002)
Leach, A., Gillet, V.: An Introduction to Chemoinformatics. Kluwer Academic Publishers, Dordrecht (2003)
Harper, G., Bradshaw, J., Gittins, J.C., Green, D., Leach, A.R.: Prediction of biological activity for high-throughput screening using binary kernel discrimination. J. Chem. Inf. Comp. Sci. 41, 1295–1300 (2001)
Chen, B., Harrison, R.F., Pasupa, K., Willett, P., Wilton, D.J., Wood, D.J., Lewell, X.Q.: Virtual screening using binary kernel discrimination: Effect of noisy training data and the optimization of performance. J. Chem. Inf. Mod. 46, 478–486 (2006)
Kiwiel, K.C.: An exact penalty function algorithm for non-smooth convex constrained minimization problems. IMA J. Numer. Anal. 5, 111–119 (1985)
Hunter, D.R., Li, R.: Variable selection using MM algorithms. Ann. Stat. 33, 1617–1642 (2005)
Lange, K., Hunter, D.R., Yang, I.: Optimization transfer using surrogate objective functions. J. Comput. Graph. Stat. 9, 1–59 (2000)
Dutter, R., Huber, P.J.: Numerical methods for the nonlinear robust regression problem. J. Stat. Comput. Sim. 13, 79–113 (1981)
Krishnapuram, B., Carin, L., Figueiredo, M.A., Hartemink, A.J.: Sparse multinomial logistic regression: fast algorithms and generalization bounds. IEEE T. Pattern Anal. 27, 957–968 (2005)
Rätsch, G., Onoda, T., Müller, K.-R.: Soft margins for AdaBoost. Mach. Learn. 42, 287–320 (2001)
MDL Information Systems Inc. The MDL Drug Data Report Database, http://www.mdli.com
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© 2007 Springer Berlin Heidelberg
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Pasupa, K., Harrison, R.F., Willett, P. (2007). Parsimonious Kernel Fisher Discrimination. In: Martí, J., Benedí, J.M., Mendonça, A.M., Serrat, J. (eds) Pattern Recognition and Image Analysis. IbPRIA 2007. Lecture Notes in Computer Science, vol 4477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72847-4_68
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DOI: https://doi.org/10.1007/978-3-540-72847-4_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72846-7
Online ISBN: 978-3-540-72847-4
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