On the regularization path of the support vector domain description

The internet and a growing number of increasingly sophisticated measuring devices make vast amounts of data available in many applications. However, the dimensionality is often high, and the time available for manual labelling scarce. Methods for unsupervised novelty detection are a great step towards meeting these challenges, and the support vector domain description has already shown its worth in this field. The method has recently received more attention, since it has been shown that the regularization path is piece-wise linear, and can be calculated efficiently. The presented work restates the new findings in a manner which permits the calculation with O(n.n"B) complexity in each iteration step instead of On^2+n"B^3, where n is the number of data points and n"B is the number of boundary points. This is achieved by updating and downdating the system matrix to avoid redundant calculations. We believe this will further promote the use of this method.