Robust one-class classification with support vector data description and mixed exponential loss function

Support vector data description (SVDD) has received a lot of attention due to its outstanding performance to perform one-class classification or novelty detection tasks. However, the same weight is directly imposed on all slack variables in the process of modeling, which may result in degraded learning performance when training data are contaminated by some outliers or mislabeled observations. In this paper, an extended SVDD model is therefore proposed by reformulating the original optimization problem of SVDD with a mixed exponential loss function. Since this loss function can emphasize the importance of the samples that tend to be the target class, and weaken the influence of those tending to be outliers, it can be viewed as a weighted SVDD. However, the weights in the new model are automatically calculated rather than being calculated in advance using some specific manners. To solve the optimization problem of the proposed model effectively, the half-quadratic optimization technique has been adopted to perform the optimization, generating a dynamic optimization algorithm. Meanwhile, the convergence and computational complexity of this dynamic optimization algorithm are analyzed from a theoretical respective. Experimental results on a synthetic data set and some publicly available real world data sets are reported to demonstrate the performance superiority of the new method in comparison with SVDD and other competitive SVDD variants.