Weighted support vector machine for classification with uneven training class sizes

In the standard support vector machines for classification, training sets with uneven class sizes results in classification biases towards the class with the large training size. That is to say, the larger the training sample size for one class is, the smaller its corresponding classification error rate is, while the smaller the sample size, the larger the classification error rate. The main causes lie in that the penalty of misclassification for each training sample is considered equally. Weighted support vector machines for classification are proposed in this paper where penalty of misclassification 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. Experimental simulations on breast cancer diagnosis show the effectiveness of the proposed methods.