Different Testing Results on SVM with Double Penalty Parameters

Chengkuan Yao,Liyong Cao,Jianhua Xu,Mingya Yang,Javier Martinez Torres

doi:10.1155/2021/4031626

Abstract

The Support Vector Machine proposed by Vapnik is a generalized linear classifier which makes binary classification of data based on the supervised learning. SVM has been rapidly developed and has derived a series of improved and extended algorithms, which have been applied in pattern recognition, image recognition, etc. Among the many improved algorithms, the technique of regulating the ratio of two penalty parameters according to the ratio of the sample quantities of the two classes has been widely accepted. However, the technique has not been verified in the way of rigorous mathematical proof. The experiments based on USPS sets in the study were designed to test the accuracy of the theory. The optimal parameters of the USPS sets were found through the grid-scanning method, which showed that the theory is not accurate in any case because there is absolutely no linear relationship between ratios of penalty parameters and sample sizes.

Highlights

In the mid-1990s, the research team led by Vapnik proposed the advanced Support Vector Machine (SVM) [1,2,3]
Based on statistical learning theory and empirical risk minimization, SVM solving the optimization problem with the dual theory has become a valuable algorithm in the field of artificial intelligence
D is the order of polynomial; N+ and N− are the sizes of samples of the two classes, respectively; and C+ and C− are the penalty parameters of the two categories

Summary

Research Article Different Testing Results on SVM with Double Penalty Parameters

Received 28 July 2021; Revised 27 September 2021; Accepted November 2021; Published December 2021. E Support Vector Machine proposed by Vapnik is a generalized linear classifier which makes binary classification of data based on the supervised learning. SVM has been rapidly developed and has derived a series of improved and extended algorithms, which have been applied in pattern recognition, image recognition, etc. Among the many improved algorithms, the technique of regulating the ratio of two penalty parameters according to the ratio of the sample quantities of the two classes has been widely accepted. E experiments based on USPS sets in the study were designed to test the accuracy of the theory. E optimal parameters of the USPS sets were found through the grid-scanning method, which showed that the theory is not accurate in any case because there is absolutely no linear relationship between ratios of penalty parameters and sample sizes The technique has not been verified in the way of rigorous mathematical proof. e experiments based on USPS sets in the study were designed to test the accuracy of the theory. e optimal parameters of the USPS sets were found through the grid-scanning method, which showed that the theory is not accurate in any case because there is absolutely no linear relationship between ratios of penalty parameters and sample sizes

Introduction

In order to find whether the optimal parameters in