A new nu-support vector machine for training sets with duplicate samples

Analyzed theoretically, ν-SVM was found to be over-dependent on each training sample, even if the samples have same value. This dependence would result in more time for training, more support vectors and more decision time. In order to overcome this problem, we propose a new ν-SVM. This new ν-SVM multiplies each slack variable in the objective function by a weight factor, and automatically computes each weight factor by the number of corresponding samples with same value before training. Theoretical analysis and the results of experiments show that the new ν-SVM has the same classification precision rate as the standard ν-SVM and the new ν-SVM is faster than the ν-SVM in training and decision if the training sets have same value samples.