## A DC programming approach for feature selection in support vector machines learning.(English)Zbl 1284.90057

Summary: Feature selection consists of choosing a subset of available features that capture the relevant properties of the data. In supervised pattern classification, a good choice of features is fundamental for building compact and accurate classifiers. In this paper, we develop an efficient feature selection method using the zero-norm $$l_0$$ in the context of support vector machines (SVMs). Discontinuity at the origin for $$l_0$$ makes the solution of the corresponding optimization problem difficult to solve. To overcome this drawback, we use a robust DC (difference of convex functions) programming approach which is a general framework for non-convex continuous optimisation. We consider an appropriate continuous approximation to $$l_0$$ such that the resulting problem can be formulated as a DC program. Our DC algorithm (DCA) has a finite convergence and requires solving one linear program at each iteration. Computational experiments on standard datasets including challenging feature-selection problems of the NIPS 2003 feature selection challenge and gene selection for cancer classification show that the proposed method is promising: while it suppresses up to more than 99% of the features, it can provide a good classification. Moreover, the comparative results illustrate the superiority of the proposed approach over standard methods such as classical SVMs and feature selection concave.

### MSC:

 90C26 Nonconvex programming, global optimization 62-07 Data analysis (statistics) (MSC2010) 68T05 Learning and adaptive systems in artificial intelligence

### Keywords:

feature selection; SVM; nonconvex optimisation; DC programming; DCA
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### References:

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