BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jeff Calder (University of Minnesota) DTSTART:20210525T141500Z DTEND:20210525T154500Z DTSTAMP:20260423T022602Z UID:MathDeep/6 DESCRIPTION:Title: Random walks and PDEs in graph-based learning\nby Jeff Calder (Univer sity of Minnesota) as part of Mathematics of Deep Learning\n\n\nAbstract\n I will discuss some applications of random walks and PDEs in graph-based l earning\, both for theoretical analysis and algorithm development. Graph-b ased learning is a field within machine learning that uses similarities be tween datapoints to create efficient representations of high-dimensional d ata for tasks like semi-supervised classification\, clustering and dimensi on reduction. There has been considerable interest recently in semi-superv ised learning problems with very few labeled examples (e.g.\, 1 label per class). The widely used Laplacian regularization is ill-posed at low label rates and gives very poor classification results. In the first part of th e talk\, we will use the random walk interpretation of the graph Laplacian to precisely characterize the lowest label rate at which Laplacian regula rized semi-supervised learning is well-posed. At lower label rates\, where Laplace learning performs poorly\, we will show how our random walk analy sis leads to a new algorithm\, called Poisson learning\, that is probably more stable and informative than Laplace learning. We will conclude with s ome applications of Poisson learning to image classification and mesh segm entation of broken bone fragments of interest in anthropology.\n LOCATION:https://researchseminars.org/talk/MathDeep/6/ END:VEVENT END:VCALENDAR