Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Multiple kernel learning, conic duality, and the SMO algorithm
ICML '04 Proceedings of the twenty-first international conference on Machine learning
The Entire Regularization Path for the Support Vector Machine
The Journal of Machine Learning Research
Learning the Kernel with Hyperkernels
The Journal of Machine Learning Research
Model-based transductive learning of the kernel matrix
Machine Learning
Two-dimensional solution path for support vector regression
ICML '06 Proceedings of the 23rd international conference on Machine learning
Large Scale Multiple Kernel Learning
The Journal of Machine Learning Research
An introduction to kernel-based learning algorithms
IEEE Transactions on Neural Networks
Path Algorithms for One-Class SVM
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
Analysis of the distance between two classes for tuning SVM hyperparameters
IEEE Transactions on Neural Networks
Optimising multiple kernels for SVM by genetic programming
EvoCOP'08 Proceedings of the 8th European conference on Evolutionary computation in combinatorial optimization
An effective regularization path for ν-support vector classification
IITA'09 Proceedings of the 3rd international conference on Intelligent information technology application
An improved algorithm for the solution of the regularization path of support vector machine
IEEE Transactions on Neural Networks
Framelet kernels with applications to support vector regression and regularization networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on gait analysis
Accurate on-line ν-support vector learning
Neural Networks
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The choice of the kernel function which determines the mapping between the input space and the feature space is of crucial importance to kernel methods. The past few years have seen many efforts in learning either the kernel function or the kernel matrix. In this paper, we address this model selection issue by learning the hyperparameter of the kernel function for a support vector machine (SVM). We trace the solution path with respect to the kernel hyperparameter without having to train the model multiple times. Given a kernel hyperparameter value and the optimal solution obtained for that value, we find that the solutions of the neighborhood hyperparameters can be calculated exactly. However, the solution path does not exhibit piecewise linearity and extends nonlinearly. As a result, the breakpoints cannot be computed in advance. We propose a method to approximate the breakpoints. Our method is both efficient and general in the sense that it can be applied to many kernel functions in common use.