LDLE: Low Distortion Local Eigenmaps

• URL: http://arxiv.org/abs/2101.11055v1
• Date: Tue, 26 Jan 2021 19:55:05 GMT
• Title: LDLE: Low Distortion Local Eigenmaps
• Authors: Dhruv Kohli, Alexander Cloninger, Gal Mishne
• Abstract summary: We present Low Distortion Local Eigenmaps (LDLE), a 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. The local views are constructed using the global eigenvectors of the graph Laplacian and are registered using Procrustes analysis.
• Score: 77.02534963571597
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present Low Distortion Local Eigenmaps (LDLE), a 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. The local views are constructed using the global eigenvectors of the graph Laplacian and are registered using Procrustes analysis. The choice of these eigenvectors may vary across the regions. In contrast to existing techniques, LDLE is more geometric and can embed manifolds without boundary as well as non-orientable manifolds into their intrinsic dimension.

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