Abstract: Many problems in science and engineering involve the sorting, or ordering, of large amounts of multi-variate data. A common sorting technique is to arrange the data into layers by repeatedly removing extremal points. Different notions of extremality lead to different sorting algorithms. Two common examples are non-dominated sorting and convex hull peeling, both of which are widely used in science and engineering, ranging from multi-objective optimization to machine learning and robust statistics. In this talk, I will present PDE continuum limits for nondominated sorting and convex hull peeling, and demonstrate how to use the continuum limits for fast online anomaly detection and classification. The talk will be accessible to graduate students.
Biography: Calder received his Ph.D. in Applied and Interdisciplinary Mathematics from the University of Michigan in 2014, and was a Morrey Assistant Professor of Mathematics at the University of California Berkeley from 2014-2016. He is currently an Assistant Professor of Mathematics at the University of Minnesota. Calder's research interests include partial differential equations and applied probability, with applications to machine learning. He is also interested in mathematical problems in computer vision and image processing.