Before revision:  We are the first, to the best of our knowledge, to prove that even the simplest hard-margin one-class SVM with outliers problem is NP-complete, and has no fully PTAS unless P=NP  . For the data sanitization defense, we link it to the intrinsic dimensionality of data;
After revision:  We are the first, to the best of our knowledge, to prove that even the simplest hard-margin one-class SVM with outliers problem is NP-complete, and has no fully PTAS unless P=NP (that means it is hard to achieve an even approximate algorithm) . For the data sanitization defense, we link it to the intrinsic dimensionality of data;