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Department of Mathematics,
University of California San Diego

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Final Defense

Dhruv Kohli

UCSD

Geometry-Aware Bottom-Up Manifold Learning with Distortion Bounds

Abstract:

High-dimensional datasets often reside on a low-dimensional geometrical manifold. Manifold learning algorithms aim to retrieve this underlying structure by mapping the data into lower dimensions while minimizing some measure of local (and possibly global) distortion incurred by the map. Bottom-up  approaches address this problem by first constructing low-distortion low-dimensional local views of the data and then integrating them together to obtain a global embedding.

In our work, we investigate the following questions:

1. How to obtain low-distortion low-dimensional local views of high-dimensional data that are robust to noise.

2. How to integrate these local views in an efficient manner to produce a low-dimensional global embedding with distortion guarantees.

3. How does the distortion incurred in the low-dimensional embedding impacts the performance of the downstream tasks.

Advisors: Alex Cloninger and Gal Mishne

July 11, 2025

11:00 AM

APM 2402 & Zoom - For zoom link, please email at dhkohli@ucsd.edu.

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