The nature of statistical learning theory
The nature of statistical learning theory
On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems
Theoretical Computer Science
A D. C. Optimization Algorithm for Solving the Trust-Region Subproblem
SIAM Journal on Optimization
Feature Selection via Concave Minimization and Support Vector Machines
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Neural Computation
An introduction to variable and feature selection
The Journal of Machine Learning Research
A Feature Selection Newton Method for Support Vector Machine Classification
Computational Optimization and Applications
Combined SVM-Based Feature Selection and Classification
Machine Learning
Exact 1-Norm Support Vector Machines Via Unconstrained Convex Differentiable Minimization
The Journal of Machine Learning Research
Support vector machines with adaptive Lq penalty
Computational Statistics & Data Analysis
A continuous approach for the concave cost supply problem via DC programming and DCA
Discrete Applied Mathematics
Surrogate maximization/minimization algorithms and extensions
Machine Learning
Stable feature selection via dense feature groups
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Stochastic methods for l1 regularized loss minimization
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Consensus group stable feature selection
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Sparse Online Learning via Truncated Gradient
The Journal of Machine Learning Research
Recovering sparse signals with a certain family of nonconvex penalties and DC programming
IEEE Transactions on Signal Processing
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This paper considers a class of feature selecting support vector machines (SVMs) based on L"q-norm regularization, where q@?(0,1). The standard SVM [Vapnik, V., 1995. The Nature of Statistical Learning Theory. Springer, NY.] minimizes the hinge loss function subject to the L"2-norm penalty. Recently, L"1-norm SVM (L"1-SVM) [Bradley, P., Mangasarian, O., 1998. Feature selection via concave minimization and support vector machines. In: Machine Learning Proceedings of the Fifteenth International Conference (ICML98). Citeseer, pp. 82-90.] was suggested for feature selection and has gained great popularity since its introduction. L"0-norm penalization would result in more powerful sparsification, but exact solution is NP-hard. This raises the question of whether fractional-norm (L"q for q between 0 and 1) penalization can yield benefits over the existing L"1, and approximated L"0 approaches for SVMs. The major obstacle to answering this is that the resulting objective functions are non-convex. This paper addresses the difficult optimization problems of fractional-norm SVM by introducing a new algorithm based on the Difference of Convex functions (DC) programming techniques [Pham Dinh, T., Le Thi, H., 1998. A DC optimization algorithm for solving the trust-region subproblem. SIAM J. Optim. 8 (2), 476-505. Le Thi, H., Pham Dinh, T., 2008. A continuous approach for the concave cost supply problem via DC programming and DCA. Discrete Appl. Math. 156 (3), 325-338.], which efficiently solves a reweighted L"1-SVM problem at each iteration. Numerical results on seven real world biomedical datasets support the effectiveness of the proposed approach compared to other commonly-used sparse SVM methods, including L"1-SVM, and recent approximated L"0-SVM approaches.