The entire regularization path for the support vector domain description

The support vector domain description is a one-class classi- fication method that estimates the shape and extent of the distribution of a data set. This separates the data into outliers, outside the decision boundary, and inliers on the inside. The method bears close resemblance to the two-class support vector machine classifier. Recently, it was shown that the regularization path of the support vector machine is piecewise linear, and that the entire path can be computed efficiently. This pa- per shows that this property carries over to the support vector domain description. Using our results the solution to the one-class classification can be solved for any amount of regularization with roughly the same computational complexity required to solve for a particularly value of the regularization parameter. The possibility of evaluating the results for any amount of regularization not only offers more accurate and re- liable models, but also makes way for new applications. We illustrate the potential of the method by determining the order of inclusion in the model for a set of corpora callosa outlines.