A weighted Lq adaptive least squares support vector machine classifiers – Robust and sparse approximation

The standard Support Vector Machine (SVM) minimizes the ε-insensitive loss function subject to L2 penalty, which equals solving a quadratic programming. While the least squares support vector machine (LS-SVM) considers equality constraints instead of inequality constrains, which corresponds to solving a set of linear equations to reduce computational complexity, loses sparseness and robustness. These two learning methods are non-adaptive since their penalty functions are pre-defined in a top-down manner, which do not work well in all situations. In this paper, we try to solve these two drawbacks and propose a weighted Lq adaptive LS-SVM model (WLq-LS-SVM) classifiers that combines the prior knowledge and adaptive learning process, which adaptively chooses q according to the data set structure. An evolutionary strategy-based algorithm is suggested to solve the WLq-LS-SVM. Simulation and real data tests have shown the effectiveness of our method.