Different Testing Results on SVM with Double Penalty Parameters

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.