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Comparison of Piecewise Polynomial Smooth Support Vector Machine to Classify Diagnosis of Cervical Cancer

Santi Wulan Purnami, Virasakdi Chosuvivatwong, Hutca Sriplung, Mukti Ratna Dewi, Epa Suryanto


One of a popular technique of binary data classification in machine learning is Support Vector Machine (SVM). SVM uses optimization with quadratic programming which inefficient when it applied in a large dataset. To overcome this disadvantage, reformulation SVM to unconstrained optimization problem using smoothing technique is constructed. It is called Smooth Support Vector Machine (SSVM) which used the integral sigmoid function to approximate the plus function. Variants of smoothing functions are proposed to increase performance, such as quadratic polynomial function, fourth polynomial function, spline function and piecewise polynomial functions. Comparison of four smooth function shows that the piecewise polynomial functions is better performance to approximate plus function. In this research, two formulation of piecewise polynomial smooth function is compared. The first piecewise polynomial function is proposed by Luo, et al (2006) and the second piecewise polynomial function is proposed by Wu and Wang (2013). The performance and the convergence of both functions are examined theoretically. And finally, the SSVM based on piecewise polynomial function is applied to classify cervical cancer diagnosis. The results show that the second piecewise polynomial functions has slightly better performance than the first piecewise polynomial function.


Piecewise Polynomial function, Smooth Support Vector Machine, Classification, Cervical Cancer

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