Gal Mishne, “Looking deep into the spectrum of the Graph Laplacian”
Gal Mishne, PhD
Assistant Professor
Halıcıoğlu Data Science Institute (HDSI)
UC San Diego
“Looking deep into the spectrum of the Graph Laplacian”
Abstract: In this talk, I introduce new unsupervised geometric approaches for extracting structure from large-scale high-dimensional data. The traditional viewpoint of spectral approaches to clustering and manifold learning is to construct a data-driven graph on the data-points and use the top eigenvectors of the graph Laplacian matrix to embed the data. However, in recent work we have shown the benefit of looking deep within the spectrum of the graph-Laplacian to identify subsets of eigenvectors that characterize the data locally. First, I will present a new robust measure, the Spectral Embedding Norm, to separate clusters from background, and demonstrate its application to both outlier detection and image segmentation. Second, I will present Low Distortion Local Eigenmaps (LDLE), a “bottom-up” manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers them to obtain a global embedding. In contrast to existing data visualization techniques, LDLE is more geometric and can embed manifolds without boundary as well as non-orientable manifolds into their intrinsic dimension.
* Joint work with Xiuyuan Cheng, Alex Cloninger, Shahar Dror and Dhruv Kohli.
Biography: Gal Mishne, PhD is an assistant professor in the Halıcıoğlu Data Science Institute (HDSI) at UC San Diego, and affiliated with the ECE department, the CSE department and the Neurosciences Graduate program. Gal is part of the Neurotheory Network and Pathways 2 AI. Before joining UCSD, she was a Gibbs Assistant Professor in the Applied Math program at Yale University, with Prof. Ronald Coifman’s research group. Gal completed her PhD in 2017 at the Technion at the Faculty of Electrical Engineering under the supervision of Prof. Israel Cohen. Gal’s research interests are manifold learning, diffusion geometry computational neuroscience, image processing and biomedical signal processing, and applied harmonic analysis.
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Meeting ID: 688 650 7095