Support vector data description (SVDD) is a well-known kernel method that constructs a minimal hypersphere regarded as a data description for a given data set. However SVDD does not take into account any statistical distribution of the data set in constructing that optimal hypersphere, and SVDD is applied to solving one-class classification problems only. This paper proposes a new approach to SVDD to address those limitations. We formulate an optimisation problem for binary classification in which we construct two hyperspheres, one enclosing positive samples and the other enclosing negative samples, and during the optimisation process we move the two hyperspheres apart to maximise the margin between them while the data samples of each class are still inside their own hyperspheres. Experimental results show good performance for the proposed method.
Nguyen, P., & Tran, D. (2015). Repulsive-SVDD classification. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9077, pp. 277–288). Springer Verlag. https://doi.org/10.1007/978-3-319-18038-0_22