Is splitting the data set into train and validation applicable in unsupervised learning?
For an unsupervised technique, if you have some metric of "goodness of fit", it makes sense to have a train-test split. In your case, it seems as though you'd want to split the data so that you can see if your SVM classifies the test data as outliers.

However, your goal is unclear. It might help if you clarify what you mean.