Clark Hall, Room 316
?Looking deep into the spectrum of the Graph Laplacian?
Abstract: In this talk, Iintroduce new unsupervised geometric approaches for extracting structure fromlarge-scale high-dimensional data. The traditional viewpoint of spectralapproaches to clustering and manifold learning is to construct a data-drivengraph on the data-points and use the top eigenvectors of the graph Laplacianmatrix to embed the data. However, in recent work we have shown the benefit oflooking deep within the spectrum of the graph-Laplacian to identify subsets ofeigenvectors that characterize the data locally. First, I will present a newrobust measure, the Spectral Embedding Norm, to separate clusters frombackground, and demonstrate its application to both outlier detection and imagesegmentation. Second, I will present Low Distortion Local Eigenmaps (LDLE), a”bottom-up” manifold learning technique which constructs a set of lowdistortion local views of a dataset in lower dimension and registers them toobtain a global embedding. In contrast to existing data visualizationtechniques, LDLE is more geometric and can embed manifolds without boundary aswell as non-orientable manifolds into their intrinsic dimension.
* Joint workwith XiuyuanCheng, Alex Cloninger, Shahar Dror and Dhruv Kohli.
Biography:GalMishne, PhD is an assistant professor in the Hal?c?o?lu Data Science Institute (HDSI) at UC San Diego, and affiliated with the ECEdepartment, the CSE department and the Neurosciences Graduate program. Gal ispart of the NeurotheoryNetwork and Pathways 2 AI. Before joining UCSD, she was a Gibbs Assistant Professor inthe Applied Math program at Yale University, with Prof. Ronald Coifman‘s research group. Gal completed her PhD in 2017 at theTechnion at the Faculty of Electrical Engineering under thesupervision of Prof. Israel Cohen. Gal’s interests are manifold learning, diffusiongeometry
computationalneuroscience, image processing and biomedical signal processing, and