Matrix analysis
The nature of statistical learning theory
The nature of statistical learning theory
Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
Proximal support vector machine classifiers
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
SSVM: A Smooth Support Vector Machine for Classification
Computational Optimization and Applications
Choosing Multiple Parameters for Support Vector Machines
Machine Learning
Asymptotic behaviors of support vector machines with Gaussian kernel
Neural Computation
Lagrangian support vector machines
The Journal of Machine Learning Research
On the influence of the kernel on the consistency of support vector machines
The Journal of Machine Learning Research
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Learning a kernel matrix for nonlinear dimensionality reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Improvements to Platt's SMO Algorithm for SVM Classifier Design
Neural Computation
Neural Computation
On the optimal parameter choice for ν-support vector machines
IEEE Transactions on Pattern Analysis and Machine Intelligence
An overview of statistical learning theory
IEEE Transactions on Neural Networks
Successive overrelaxation for support vector machines
IEEE Transactions on Neural Networks
Asymptotic convergence of an SMO algorithm without any assumptions
IEEE Transactions on Neural Networks
Granular support vector machine based on mixed measure
Neurocomputing
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The classification problem by the nonlinear support vector machine (SVM) with kernel function is discussed in this paper. Firstly, the stretching ratio is defined to analyze the performance of the kernel function, and a new type of kernel function is introduced by modifying the Gaussian kernel. The new kernel function has many properties as good as or better than Gaussian kernel: such as its stretching ratio is always lager than 1, and its implicit kernel map magnifies the distance between the vectors in local but without enlarging the radius of the circumscribed hypersphere that includes the whole mapping vectors in feature space, which maybe gets a bigger margin. Secondly, two aspects are considered to choose a good spread parameter for a given kernel function approximately and easily. One is the distance criterion which minimizes the sum-square distance between the labeled training sample and its own center and maximizes the sum-square distance between the training sample and the other labeled-center, which is equivalent to the famous Fisher ratio. The other is the angle criterion which minimizes the angle between the kernel matrix and the target matrix. Then a better criterion is given by combined those aspects. Finally, some experiments show that our methods are efficient.