二次损失函数支持向量机性能的研究

通过比较二次损失函数支持向量机和标准支持向量机在模式识别问题上的表现，分析了二次损失函数支持向量机的性能．实验表明这两种支持向量机对平衡数据有相似的分类能力，但二次损失函数支持向量机的优化参数更小，支持向量更多；对不平衡数据，二次损失函数支持向量机的分类准确率随不平衡度的增加而急剧下降．研究同时表明基于RM界的梯度方法对某些数据无效．文中定性分析了导致上述各种现象的原因．最后提出了一种利用黄金分割原理缩减二次损失函数支持向量机支持向量的方法，该方法冗余的支持向量数不超过一个．

Experimental Study on the Performance of Support Vector Machine with Squared Cost Function

The parameter optimization is one of the main study directions of SVM. Recently, a gradient descent algorithm based on RM bound has been developed, which can tune multiple parameters of SVM with squared cost function automatically and efficiently. But till now, few issues related to practical use of this type SVM have been discussed. In this paper, the performance of SVM with squared cost function on pattern recognition is studied and compared with the standard SVM. The results indicate that for balanced data, both SVMs have almost the same classifying accuracy, but the SVM with square cost function possess more support vectors and smaller optimized parameters than standard SVM. For unbalanced data, when the unbalanced degree between two classes of training samples increases, the classifying accuracy of the SVM with squared cost function decreases rapidly. The experiments also show that the gradient descent algorithm based on RM bound is not suitable for some data. Some analysis on properties of the SVM with square cost function are also included in the paper. Finally, a pruning algorithm based on golden section rule is proposed and applied to increase the sparseness of SVM with squared cost function. Using this algorithm, the number of the redundant support vectors can be reduced to one or zero.