

![0_image_0.png](0_image_0.png) 

![0_image_1.png](0_image_1.png)

TABLE I
COMPARISONS OF CLASSIFICATION ACCURACIES AMONG C-SVM AND
GS-SVM

![0_image_2.png](0_image_2.png) 

Fig. 5. Accuracy versus C on "spect" data set.

## B. Benchmarks

We also evaluate GS-SVM on 8 standard data sets from UCI machine learning repository [13]. GS-SVM are compared with C-SVM on both the linear and Gaussian kernels.

The parameter C for both methods is tuned via 10-fold cross validation. So is the width parameter of Gaussian kernel. The performance of these two methods in 10-fold cross validation is summarized in Table I.

GS-SVM achieves a better performance on most data sets in both linear and Gaussian kernel. On remaining data sets, GS-SVM performs as well as C-SVM. The results on these benchmarks show that it is worth considering the global information of the data.

We notice an interesting role that ∆ performs: GS-SVM
can reach a higher accuracy with a smaller penalty value C
than C-SVM. It is not hard to understand from Eq. (6).

We select "spect" data set as an example and show the relationship between C and the accuracy in Fig. 5. Since the hyperplane translates toward the class of smaller projected scales on the normal of the hyperplane, it is more possible from the sum of slack variables Pli=1 ξito decrease. C is also used to minimize the classification error. The greater C is, the smaller the classification error will be. As the hyperplane translates, it is more possible for classification error to drop. Hence, GS-SVM will achieve a better performance with a lower C. Note that although C and ∆ have the same effect of adjusting the position of the hyperplane, they do not work in the same way. C adjusts the margin (the hyperplane lays in the middle of the margin) to minimize the training error, while ∆ scales the position of the hyperplane to minimize structural risk.

## V. Conclusion

In this paper, we propose a simple but efficient method to improve the generalization ability of C-SVM, called as GS-SVM. C-SVM only uses support vectors and ignores the information of other data points. Previous works have been done to consider global information in deciding the hyperplane. For binary classification problem, one approach is to translate the hyperplane toward the class with smaller projected scale on the direction that is perpendicular to the hyperplane. However, existing work of this approach is only for 1-D case. In this paper, this approach is extended from 1-D to multi-dimensional cases. Experimental results show that GS-SVM advances C-SVM on both toy data