Converting SVDD scores into probability estimates: Application to outlier detection

To enable post-processing, the output of a support vector data description (SVDD) should be transformed into a calibrated probability, as it can be done for SVM. But standard SVDD only estimate a single level set and do not provide such probabilities. We present a method for estimating these probabilities from SVDD scores. The first step of our approach uses a generalization of the SVDD model that estimate simultaneously various coherent level sets. Then we introduce two calibration mechanisms for converting these level sets into probabilities. A synthetic dataset and datasets from the UCI repository are used to compare the performance of our method against a robust kernel density estimator in an outlier detection task, illustrating the interest of our approach.