Model Selection for Support Vector Machines

New functionals for parameter (model) selection of Support Vector Machines are introduced based on the concepts of the span of support vectors and rescaling of the feature space. It is shown that using these functionals, one can both predict the best choice of parameters of the model and the relative quality of performance for any value of parameter.

[1]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[2]  L. A. G. Dresel,et al.  Elementary Numerical Analysis , 1966 .

[3]  E. Polak,et al.  Note sur la convergence de méthodes de directions conjuguées , 1969 .

[4]  Samuel D. Conte,et al.  Elementary Numerical Analysis: An Algorithmic Approach , 1975 .

[5]  Martin Fodslette Møller,et al.  A scaled conjugate gradient algorithm for fast supervised learning , 1993, Neural Networks.

[6]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[7]  U. M. Feyyad.  Data mining and knowledge discovery: making sense out of data , 1996 .

[8]  Michael Kearns,et al.  A Bound on the Error of Cross Validation Using the Approximation and Estimation Rates, with Consequences for the Training-Test Split , 1995, Neural Computation.

[9]  Bernhard Schölkopf,et al.  Kernel Principal Component Analysis , 1997, ICANN.

[10]  Bernhard Schölkopf,et al.  Support vector learning , 1997 .

[11]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[12]  J. Platt.  Sequential Minimal Optimization : A Fast Algorithm for Training Support Vector Machines , 1998 .

[13]  J. C. BurgesChristopher.  A Tutorial on Support Vector Machines for Pattern Recognition , 1998 .

[14]  Thorsten Joachims,et al.  Making large scale SVM learning practical , 1998 .

[15]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[16]  David Haussler,et al.  Exploiting Generative Models in Discriminative Classifiers , 1998, NIPS.

[17]  Eric Miller,et al.  Testing and evaluating computer intrusion detection systems , 1999, CACM.

[18]  Katharina Morik,et al.  Combining Statistical Learning with a Knowledge-Based Approach - A Case Study in Intensive Care Monitoring , 1999, ICML.

[19]  Tommi S. Jaakkola,et al.  Maximum Entropy Discrimination , 1999, NIPS.

[20]  R. C. Williamson,et al.  Kernel-dependent support vector error bounds , 1999 .

[21]  R. C. Williamson,et al.  Generalization Bounds via Eigenvalues of the Gram matrix , 1999 .

[22]  David Haussler,et al.  Probabilistic kernel regression models , 1999, AISTATS.

[23]  Bernhard Schölkopf,et al.  GACV for Support Vector Machines , 2000 .

[24]  Julian Ashbourn,et al.  Biometrics: Advanced Identity Verification , 2000, Springer London.

[25]  Sayan Mukherjee,et al.  Feature Selection for SVMs , 2000, NIPS.

[26]  Bernhard Schölkopf,et al.  Bounds on Error Expectation for SVM , 2000 .

[27]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[28]  Bernhard Schölkopf,et al.  New Support Vector Algorithms , 2000, Neural Computation.

[29]  Thorsten Joachims,et al.  Estimating the Generalization Performance of an SVM Efficiently , 2000, ICML.

[30]  Richard Lippmann,et al.  The 1999 DARPA off-line intrusion detection evaluation , 2000, Comput. Networks.

[31]  O. Chapelle,et al.  Bounds on error expectation for SVM , 2000 .

[32]  Hansong Zhang,et al.  Gacv for support vector machines , 2000 .

[33]  Tommi S. Jaakkola,et al.  Feature Selection and Dualities in Maximum Entropy Discrimination , 2000, UAI.

[34]  Peter L. Bartlett,et al.  Rademacher and Gaussian Complexities: Risk Bounds and Structural Results , 2003, J. Mach. Learn. Res..

[35]  N. Cristianini,et al.  On Kernel-Target Alignment , 2001, NIPS.

[36]  G. Cawley.  Model Selection for Support Vector Machines via Adaptive Step-Size Tabu Search , 2001 .

[37]  K. Johana,et al.  Benchmarking Least Squares Support Vector Machine Classifiers , 2022 .