Multi-kernel Support Vector Data Description with boundary information

Abstract The One-Class Classification (OCC) exists in many real-world applications, such as novelty detection, outlier detection, facial verification, and anomaly detection. SVDD is an efficient method to solve the OCC problem. How to describe a hypersphere with minimized volume that encloses almost all the target class samples is the key point of the SVDD. However, the existing SVDD-based methods generally neglect the boundary information of samples in the construction of the classifier. To fully utilize the boundary information to guide the training process, this paper introduces Multi-Kernel Learning (MKL) into the traditional Support Vector Data Description (SVDD) based on the boundary information, proposes a novel method called MKL-SVDD. The proposed MKL-SVDD first determines the boundary samples based on the geometrical and statistical information, and assigns the special weight for the boundary samples to improve the effect of the boundary samples in the optimization process. Meanwhile, to enhance the feature expression capabilities, the proposed MKL-SVDD utilizes the location information of samples as the supervised signal to design the kernel weights for multiple kernels to obtain the optimal kernel combination. Extensive experiments on 11 UCI datasets and 7 KEEL datasets demonstrate the superiority of the MKL-SVDD over the other state-of-the-art methods. The Bayesian analysis of the experiment results theoretically prove that the MKL-SVDD is superior to other methods on UCI and KEEL datasets with 100% and over 96% probability respectively.