Deep embedding kernel mixture networks for conditional anomaly detection in high-dimensional data

In various industrial problems, sensor data are often used to detect the abnormal state of manufacturing systems. Sensor data are sometimes influenced by contextual variables that are not related to the system health status and may exhibit different behaviours depending on their values, even if the system is in a normal condition. In this case, a conditional anomaly detection method should be used to consider the effects of contextual variables. In this study, we propose a conditional anomaly detection method, particularly for high-dimensional and complex data, using a deep embedding kernel mixture network. The proposed method comprises embedding and kernel mixture networks. The embedding network learns low-dimensional embeddings from high-dimensional data, and the kernel mixture network models the distribution of the learned embeddings conditional on contextual variables. The two networks enable a flexible estimation of conditional density using the high expressive power of deep neural networks. The two networks are trained simultaneously such that the high-dimensional data are embedded into a low-dimensional space, to assist conditional density estimation. The effectiveness of the proposed model is demonstrated using real data examples from the UCI repository and a case study from a tire company.