摘要
Support vector machines （SVMs） have shown remarkable success in many applications. However, the non-smooth feature of objective function is a limitation in practical application of SVMs. To overcome this disadvantage, a twice continuously differentiable piecewise-smooth function is constructed to smooth the objective function of unconstrained support vector machine （SVM）, and it issues a piecewise-smooth support vector machine （PWESSVM）. Comparing to the other smooth approximation functions, the smooth precision has an obvious improvement. The theoretical analysis shows PWESSVM is globally convergent. Numerical results and comparisons demonstrate the classification performance of our algorithm is better than other competitive baselines.
Support vector machines （SVMs） have shown remarkable success in many applications. However, the non-smooth feature of objective function is a limitation in practical application of SVMs. To overcome this disadvantage, a twice continuously differentiable piecewise-smooth function is constructed to smooth the objective function of unconstrained support vector machine （SVM）, and it issues a piecewise-smooth support vector machine （PWESSVM）. Comparing to the other smooth approximation functions, the smooth precision has an obvious improvement. The theoretical analysis shows PWESSVM is globally convergent. Numerical results and comparisons demonstrate the classification performance of our algorithm is better than other competitive baselines.
基金
supported by the National Natural Science Foundation of China (61100165, 61100231, 61105064, 51205309)
the Natural Science Foundation of Shaanxi Province (2012JQ8044, 2011JM8003, 2010JQ8004)
the Foundation of Education Department of Shanxi Province (2013JK1096)
