Electrical conduction among cardiac tissue is commonly modeled with partial differential equations, i.e., reaction-diffusion equation, where the reaction term describes cellular stimulation and diffusion term describes electrical propagation. Detecting and identifying of cardiac cells that produce abnormal electrical impulses in such nonlinear dynamic systems are important for efficient treatment and planning. To model the nonlinear dynamics, simulation has been widely used in both cardiac research and clinical study to investigate cardiac disease mechanisms and develop new treatment designs. However, existing cardiac models have a great level of complexity, and the simulation is often time-consuming. We propose a deep spatio-temporal sparse decomposition (DSTSD) approach to bypass the time-consuming cardiac partial differential equations with the deep spatio-temporal model and detect the time and location of the anomaly (i.e., malfunctioning cardiac cells). This approach is validated from the data set generated from the Courtemanche-Ramirez-Nattel (CRN) model, which is widely used to model the propagation of the transmembrane potential across the cross neuron membrane. The proposed DSTSD achieved the best accuracy in terms of spatio-temporal mean trend prediction and anomaly detection.
Deep learning approaches to anomaly detection have recently improved the state of the art in detection performance on complex datasets such as large collections of images or text. These results have sparked a renewed interest in the anomaly detection problem and led to the introduction of a great variety of new methods. With the emergence of numerous such methods, including approaches based on generative models, one-class classification, and reconstruction, there is a growing need to bring methods of this field into a systematic and unified perspective. In this review we aim to identify the common underlying principles as well as the assumptions that are often made implicitly by various methods. In particular, we draw connections between classic 'shallow' and novel deep approaches and show how this relation might cross-fertilize or extend both directions. We further provide an empirical assessment of major existing methods that is enriched by the use of recent explainability techniques, and present specific worked-through examples together with practical advice. Finally, we outline critical open challenges and identify specific paths for future research in anomaly detection.