Abstract:
Many big data applications involve difficult combinatorial optimization that can be cast as finding a minimal graph that covers a subset of data points. Examples include computing minimal spanning trees over visual features in computer vision, finding a shortest path over an image database between image pairs, or detecting non-dominated anti-chains in multi-objective database search. When the nodes are real-valued random vectors and the graph is constructed on the basis of Euclidean distance these minimal paths can have continuum limits as the number of nodes approaches infinity. Such continuum limits can lead to low complexity diffusion approximations to the solution of the associated combinatorial problem. We will present theory and application of continuum limits and illustrate how such limits can break the combinatorial bottleneck in large scale data analysis.
Biography:
Alfred O. Hero III received the B.S. (summa cum laude) from Boston University (1980) and the Ph.D from Princeton University (1984), both in Electrical Engineering. Since 1984 he has been with the University of Michigan, Ann Arbor, where he is the John H. Holland Distinguished University Professor of Electrical Engineering and Computer Science and the R. Jamison and Betty Williams Professor of Engineering. He is also the Co-Director of the University’s Michigan Institute for Data Science (MIDAS) . His primary appointment is in the Department of Electrical Engineering and Computer Science and he also has appointments, by courtesy, in the Department of Biomedical Engineering and the Department of Statistics. From 2008-2013 he held the Digiteo Chaire d’Excellence at the Ecole Superieure d’Electricite, Gif-sur-Yvette, France. He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and several of his research articles have received best paper awards. Alfred Hero was awarded the University of Michigan Distinguished Faculty Achievement Award (2011). He received the IEEE Signal Processing Society Meritorious Service Award (1998), the IEEE Third Millenium Medal (2000), and the IEEE Signal Processing Society Technical Achievement Award (2014). In 2015 he received the Society Award, which is the highest career award bestowed by the IEEE Signal Processing Society. Alfred Hero was President of the IEEE Signal Processing Society (2006-2008) and was on the Board of Directors of the IEEE (2009-2011) where he served as Director of Division IX (Signals and Applications). He served on the IEEE TAB Nominations and Appointments Committee (2012-2014). Alfred Hero is currently a member of the Big Data Special Interest Group (SIG) of the IEEE Signal Processing Society. Since 2011 he has been a member of the Committee on Applied and Theoretical Statistics (CATS) of the US National Academies of Science.
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