According to my readings (Support Vector Method for Novelty Detection, for instance), One-Class SVM can be used for novelty detection only. The purpose of the $\nu$ parameter is to defined the maximum proportion of outliers in the training data and this value is set by the user itself. I guess we can't talk about outlier detection in that case.
However, I was reading an issue on scikit-learn and one contributor explained OCSVM can be used for outlier detection and novelty detection.
So I want to know: how can we use OCSVM for outlier detection? Is it an unsupervised method as LOF or should I have a training and testing set?