Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
A decision-theoretic generalization of on-line learning and an application to boosting
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Least Squares Support Vector Machine Classifiers
Neural Processing Letters
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Trust-region methods
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
SSVM: A Smooth Support Vector Machine for Classification
Computational Optimization and Applications
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Combinations of basis functions are applied here to generate and solve a convex reformulation of several well-known machine learning algorithms like certain variants of boosting methods and Support Vector Machines. We call such a reformulation a Convex Networks (CN) approach. The nonlinear Gauss-Seidel iteration process for solving the CN problem converges globally and fast as we prove. A major property of CN solution is the sparsity, the number of basis functions with nonzero coefficients. The sparsity of the method can effectively be controlled by heuristics where our techniques are inspired by the methods from linear algebra. Numerical results and comparisons demonstrate the effectiveness of the proposed methods on publicly available datasets. As a consequence, the CN approach can perform learning tasks using far fewer basis functions and generate sparse solutions.