Cluster-Centric Anomaly Detection and Characterization in Spatial Time

Anomaly detection in spatial time series is a challenging problem with numerous potential applications. A comprehensive anomaly detection approach not only should be able to detect and identify the emerging anomalies, but it also has to characterize the essence of these anomalies by visualizing the structures revealed within data in a way, which is understandable to the end-user. In this study, a cluster-centric framework for anomaly detection and characterization in spatial time series has been developed. For this purpose, the time series part of data is divided into a set of subsequences and the available spatio-temporal structures within the generated subsequences are discovered through a fuzzy clustering technique. Since in spatial time series, each datum is composed of features dealing with the spatial and the temporal (one or more time series) components, clustering of data of this nature poses some significant challenges, especially in terms of a suitable treatment of different components of the data. We propose an extended version of the Fuzzy C-Means (FCM) clustering by introducing a composite distance function with adjustable weights (parameters) controlling the impact of different components in the clustering process. Three optimization criteria-a reconstruction error, a prediction error, and an agreement level are introduced and used as a vehicle to quantify the performance of the clustering method. By comparing the revealed structures (clusters) in spatial time series in successive time intervals, one assigns an anomaly score to each cluster measuring the level of unexpected changes in data. Moreover, through developing some fuzzy relational iii dependencies, the propagation of anomalies can be visualized in an understandable way to the end-user. To illustrate the proposed technique in this study, several datasets including synthetic and real-world data have been investigated. Experimental studies show that the proposed technique is able to find incident anomalies and quantify the propagation of anomalies over time. Acknowledgments I would like to express my deepest respect and gratitude to my supervisor, Professor Witold Pedrycz, for his patience, innovations, enthusiasm, and supports during the four years Ph.D. study. It has been an honor to be his Ph.D. student.