Abstract
Support vector machines (SVMs) have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth the objective function of unconstrained SVMs. The three-order piecewise smooth support vector machine (TPWSSVMd) is proposed. The piecewise functions can get higher and higher approximation accuracy as required with the increase of parameter d. The global convergence proof of TPWSSVMd is given with the rough set theory. TPWSSVMd can efficiently handle large scale and high dimensional problems. Numerical results demonstrate TPWSSVMd has better classification performance and learning efficiency than other competitive baselines.
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