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The Taub Faculty of Computer Science Events and Talks

Identifying Underlying Geometry To Analyze High-Dimensional Data: Images And Shape Spaces As A Case Study
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Shira Faigenbaum-Golovin
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Wednesday, 21.02.2024, 15:00
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Zoom Lecture:93613579310 Passcode: 652820
High-dimensional data is increasingly available in diverse applications, ranging from images to shapes represented as point clouds. Such data raises novel questions and offers a unique opportunity to study them by developing new machine-learning tools. While the analysis of an individual sample may be challenging, leveraging the power of the data collection can be effective in tackling complex tasks. This talk delves into the challenges associated with studying such data, particularly focusing on learning from limited, non-labeled, noisy data in high dimensions. The discussion centers on the assumption that high-dimensional data represents an embedding of a low-dimensional manifold.

First, I will introduce a rigorous framework designed for denoising and reconstructing a low-dimensional manifold in a high-dimensional space from scattered data, by solving a non-convex optimization problem. Next, we will examine scatter data that has its own geometry (i.e. deal with manifold of manifolds), and address questions related to shape registration and variation within the realm of shape spaces. I will demonstrate the methodology on manifolds of various dimensions, as well as on a collection of anatomical surfaces pertaining to evolutionary anthropology. Lastly, I will underscore the importance of manifold learning in the realm of image processing. I will illustrate this through a novel method for comparing handwriting, which has revolutionized the study of ancient inscriptions (published in PNAS).

Short Bio: Shira Faigenbaum-Golovin is an Assistant Research Professor at Duke University, working with Ingrid Daubechies. Currently, her work ranges between understanding the theoretical properties of Neural networks and developing computational algorithms to address questions in shape space. Shira received her B.S.c in Mathematics with a major in Computer Science, as well as an M.Sc (in 2014, Magna Cum Laude) and Ph.D. (2021) in Applied Mathematics all from Tel-Aviv University. In parallel to her Ph.D. Shira held an algorithmic expert position in the Image Signal Processor team at Intel. Shira is a recipient of the 2016 Tel-Aviv Dean’s Excellence Scholarship, the 2017 Minerva Research Grant, and the 2021-2023 Zuckerman Postdoctoral Fellowship, as well as has also received generous support from the Schmidt Postdoctoral Award for women in mathematical and computing sciences during 2021-2023. Her research spans from low and high-dimensional approximation, theoretical and applicative machine learning, data science, and image processing.