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Gal Mishne (UCSD)

Time: 11:30 am on Thursday, October 6th, 2022

LDLE: Low Distortion Local Eigenmaps

In this talk I will present Low Distortion Local Eigenmaps (LDLE), a "bottom-up" manifold learning approach which constructs a set of low distortion local views of a dataset in lower dimensions and registers them to obtain a global embedding. The local views are constructed by selecting subsets of the global eigenvectors of the graph Laplacian such that they are locally orthogonal and form a local near-orthogonal basis for the data. Aligning the local views using Procrustes analysis, we obtain state-of-the-art low-distortion low-dimensional embeddings of manifolds. In contrast to existing techniques, LDLE can embed manifolds without boundary as well as non-orientable manifolds into their intrinsic dimension by tearing them apart.

Joint work with Dhruv Kohli and Alex Cloninger.