Least Squares Support Vector Machine Classifiers
Neural Processing Letters
Support Vector Machines for Pattern Classification (Advances in Pattern Recognition)
Support Vector Machines for Pattern Classification (Advances in Pattern Recognition)
A Direct Method for Building Sparse Kernel Learning Algorithms
The Journal of Machine Learning Research
Building Support Vector Machines with Reduced Classifier Complexity
The Journal of Machine Learning Research
Sparse least squares support vector training in the reduced empirical feature space
Pattern Analysis & Applications
Optimizing the kernel in the empirical feature space
IEEE Transactions on Neural Networks
Sparse support vector regressors based on forward basis selection
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Kernelizing the proportional odds model through the empirical kernel mapping
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advances in computational intelligence - Volume Part I
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In this paper we discuss sparse least squares support vector regressors (sparse LS SVRs) defined in the reduced empirical feature space, which is a subspace of mapped training data. Namely, we define an LS SVR in the primal form in the empirical feature space, which results in solving a set of linear equations. The independent components in the empirical feature space are obtained by deleting dependent components during the Cholesky factorization of the kernel matrix. The independent components are associated with support vectors and controlling the threshold of the Cholesky factorization we obtain a sparse LS SVM. For linear kernels the number of support vectors is the number of input variables at most and if we use the input axes as support vectors, the primal and dual forms are equivalent. By computer experiments we show that we can reduce the number of support vectors without deteriorating the generalization ability.