Weighted support vector machine for classification

In the standard support vector machines for classification, the use of training sets with uneven class sizes results in classification biases towards the class with the large training size. The main causes lie in that the penalty of misclassfication for each training sample is considered equally. Weighted support vector machines for classification are proposed in this paper where penalty of misclassfication for each training sample is different. By setting the equal penalty for the training samples belonging to same class, and setting the ratio of penalties for different classes to the inverse ratio of the training class sizes, the obtained weighted support vector machines compensate for the undesirable effects caused by the uneven training class size, and the classification accuracy for the class with small training size is improved. But this improvement is obtained at the cost of the possible decrease of classification accuracy for the class with large training size and the possible decrease of the total classfication accuracy. Two weighted support vector machines, namely weighted C-SVM and v-SVM, corresponding to C-SVM and V-SVM are given respectively. Experimental simulations on breast cancer diagnosis show the effectiveness of the proposed methods.