Tangent Circular Arc Smooth SVM (TCA-SSVM) Research

Spatial hypersurface plays a very important role in the classification problem. In SVM, classification hypersurface is emphasized because of the direct induction of the support vectors, so the hypersurface reflecting the relation between categorical attribute and condition attributes acquired by SVM promotes the classification effect. In traditional SVM solution algorithms, objective function is a strictly convex unconstrained optimization problem, but is not differentiable due to x+, which precludes the most used optimization algorithms. This paper presents a new TCA-Smooth technology which used a segment of circular arc tangent to the given plus function x+  to approximate the original un-differentiable model, thus the traditional SVM model is converted into a differentiable model. The proposed approach is experimentally evaluated in three datasets that are benchmarks for data mining applications and in a real-world dataset, leading to interesting results.