3b6ea058d3401410VgnVCM100000c2b1d38dRCRDapproved/UMICH/stats/Home/News & Events/Dissertations and Oral Preliminary ExaminationsHossein Keshavarz###@###(Fri, 6 Sep 2013)Hossein Keshavarz###@###(Fri, 6 Sep 2013)438 WHOn the anomaly detection in the spatio-temporal datastats137849040000013784904000002:00PM<p>Contextual anomaly and outlier detection is about to finding the peculiar phenomenons<br> which don’t conform the normal pattern. Anomaly detection has vast applications<br> in many areas such as fraud detection for credit cards, disease outbreak detection,<br> sensor networks and environmental science. We address the anomaly detection<br> problem in high dimensional spatio-temporal data. This study is motivated by finding<br> non-conforming patterns in environmental data sets such as NDVI and CO2 flux<br> linkage. In the first part, we propose two class of detection algorithms based on the<br> low rank and sparse Fourier representation of data. The simulation studies show<br> that the suggested algorithms can efficiently detect the abnormal patterns. We also<br> state the theoretical conditions under which the sparse Fourier anomaly detection<br> scheme attains the minimax consistency rate. The second part is devoted to study<br> the fused lasso signal approximator (FLSA) as a change point detection algorithm.<br> We present some upper bounds on `1 and `2 norm of estimation error of convex and<br> non-convex FLSA under possible model mismatch.</p>Njkmcdonjkmcdon13787562362330b6ea058d3401410VgnVCM100000c2b1d38d____once11112newnewOn the anomaly detection in the spatio-temporal data/UMICH/stats/Home/News & Events/Dissertations and Oral Preliminary Examinations/Hossein Keshavarz PreLim Flyer.pdf