Generalized support vector data description for anomaly detection. (April 2020) - Turkoz, Mehmet; Kim, Sangahn; Son, Youngdoo; Jeong, Myong K.; Elsayed, Elsayed A.
Highlights: In this paper, a generalized SVDD procedure called GSVDD for multi-class data is introduced. The proposed procedure finds n hyperspheres. GSVDD uses each class information. Thus, each hypersphere keeps as many as corresponding observations as possible inside the boundary and attempts to keep other classes' observations outside the hypersphere. In addition, Bayesian generalized SVDD procedure is proposed by considering a probabilistic behavior of the parameters by taking 'prior knowledge' into account. This procedure enables each observation to have a probabilistic information. Thus, these probabilities are used for classification. Although there are some existing multi-class SVDD procedures, they do not consider the information from each class. Moreover, none of these procedures do not provide probabilistic interpretation. Abstract: Traditional anomaly detection procedures assume that normal observations are obtained from a single distribution. However, due to the complexities of modern industrial processes, the observations may belong to multiple operating modes with different distributions. In such cases, traditional anomaly detection procedures may trigger false alarms while the process is indeed in another normally operating mode. We propose a generalized support vector-based anomaly detection procedure called generalized support vector data description which can be used to determine the anomalies in multimodal processes. The proposed procedure constructs hyperspheres for each class in order to include as many observations as possible and keep other class observations as far apart as possible. In addition, we introduce a generalized Bayesian framework which does not only consider the prior information from each mode, but also highlights the relationships among the modes. The effectiveness of the proposed procedure is demonstrated through various simulation studies and real-life applications.