Robust solutions to fuzzy one-class support vector machine

• Reformulate the one-class SVM model by introducing both fuzziness and robustness.
• Derive the relationship between fuzziness and robustness.
• Prove that the fuzzy membership has lower bound μmin given the bounded perturbation η.
• The input data from different sources with different quality could be in full use.
• The proposed model improves the classification performance.

One-class SVM is used for classification which distinguishes one class of data from the rest in the feature space. For the training samples coming from different sources with different quality, in this letter, a reformulation of one-class SVM is proposed by simultaneously incorporating robustness and fuzziness to improve the classification performance. Based on the proposed model, we derive the relationship between the lower bound of fuzziness μmin and the upper bound of perturbation η in the input data. Specifically, for a given η, only when the assigned fuzziness to the input data is larger than μmin, could the input data be in full use and differentiated effectively. The experiments verify the mathematical analysis and illustrate that the proposed model can achieve better classification performance.