The proposed Elastic SCAD SVM algorithm provides the advantages of the SCAD penalty and at the same time avoids sparsity limitations for non-sparse data. Elastic SCAD SVM was the only method providing robust classifiers in sparse and non-sparse situations. Moreover, Elastic SCAD SVM provided sparser classifiers in terms of median number of features selected than Elastic Net SVM and often better predicted than Elastic Net in terms of misclassification error.Finally, we applied the penalization methods described above on four publicly available breast cancer data sets. Our simulation study showed that Elastic SCAD SVM outperformed LASSO (L1) and SCAD SVMs. Feature selection methods with combined penalties (Elastic Net and Elastic SCAD SVMs) are more robust to a change of the model complexity than methods using single penalties. Regularisation approaches extend SVM to a feature selection method in a flexible way using penalty functions like LASSO, SCAD and Elastic Net.We propose a novel penalty function for SVM classification tasks, Elastic SCAD, a combination of SCAD and ridge penalties which overcomes the limitations of each penalty alone.Since SVM models are extremely sensitive to the choice of tuning parameters, we adopted an interval search algorithm, which in comparison to a fixed grid search finds rapidly and more precisely a global optimal solution. Although Support Vector Machine ( SVM) algorithms are among the most powerful classification and prediction methods with a wide range of scientific applications, the SVM does not include automatic feature selection and therefore a number of feature selection procedures have been developed. Becker, Natalia Toedt, Grischa Lichter, Peter Benner, Axel Classification and variable selection play an important role in knowledge discovery in high-dimensional data. Finally, we develop a robust linear rank SVM tool for public use. We discuss different implementation issues and extensions with detailed experiments. In this letter, we systematically study existing works, discuss their advantages and disadvantages, and propose an efficient algorithm.
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