Ingrid Daubechies (Duke): Distinguished Speaker Series- Discovering low-dimensional manifolds in high-dimensional data
Abstract: This talk reviews diffusion methods to identify low-dimensional manifolds underlying high-dimensional datasets, and illustrates that by pinpointing additional mathematical structure, improved results can be obtained. Much of the talk draws on a case study from a collaboration with biological morphologists, who compare different phenotypical structures to study relationships of living or extinct animals with their surroundings and each other. This is typically done from carefully defined anatomical correspondence points (landmarks) on e.g. bones; such landmarking draws on highly specialized knowledge. To make possible more extensive use of large (and growing) databases, algorithms are required for automatic morphological correspondence maps, without any preliminary marking of special features or landmarks by the user.
Speakers
Ingrid Daubechies
Ingrid Daubechies is the James B. Duke Distinguished Professor Emeritus of Mathematics at Duke University. Her sprawling research career has touched fields as diverse as art restoration, evolutionary biology, electrical engineering and, most notably, image and data processing. Her most famous contributions concern wavelets, mathematical structures vital for modern signal processing.
She is a member of the National Academy of Engineering, the National Academy of Sciences, the American Academy of Arts and Sciences, and the Academia Europaea. She is a 1992 MacArthur Fellow and served as president of the International Mathematical Union from 2011 to 2014. She is the recipient of numerous awards, including the National Academy of Sciences Award in Mathematics, the Wolf Prize in Mathematics, the Bakerian Medal, the National Medal of Science, the Nemmers Prize, the Fudan-Zhongzhi Science Award and the Princess of Asturias Award for Technical and Scientific Research.
