When performing the linear SVM classification, it is often helpful to normalize the training data, for example by subtracting the mean and dividing by the standard deviation, and afterwards scale the test data with the mean and standard deviation of training data. Why this process changes dramatically the classification performance?
As i understand, the main advantage of scaling is to avoid attributes in greater numeric ranges dominating those in smaller numeric ranges. Another advantage is to avoid numerical difficulties during the kernel calculation.However, i am not quite clear why the test set needs to be scaled with the mean and std of the training set instead of its own? In some case, the later seems perform euqlly well or even better when the two classes of samples are well balanced in the test set.
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