Abstract: In order to focus on the non-smooth and non-convex problems of the semi-supervised support vector machine,a piecewise function based on piecewise ideas was proposed to approach the non-convex and non-smooth objective function.The approach degree of the piecewise function to objective function can be chosen according to the accuracy demand.A new piecewise smooth semi-supervised support vector machine (PWSS³VM) model based on piecewise function was constructed.LDS algorithm was applied to solve the model and its approximation performance to the symmetric hinge loss function was analyzed.Theoretical analysis and numerical experiments confirm that PWSS³VM model has better classification performance and higher classification efficiency than previous smooth models.

Key words: Algorithms,Classifiers,Optimization,Semi-supervised support vector machine,Segment function,Smooth technologies