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24 June 2024
 
  » arxiv » 2302.00263

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Dictionary-based Manifold Learning
Hanyu Zhang ; Samson Joelle ; Marina Meila ;
Date 1 Feb 2023
AbstractWe propose a paradigm for interpretable Manifold Learning for scientific data analysis, whereby we parametrize a manifold with $d$ smooth functions from a scientist-provided dictionary of meaningful, domain-related functions. When such a parametrization exists, we provide an algorithm for finding it based on sparse non-linear regression in the manifold tangent bundle, bypassing more standard manifold learning algorithms. We also discuss conditions for the existence of such parameterizations in function space and for successful recovery from finite samples. We demonstrate our method with experimental results from a real scientific domain.
Source arXiv, 2302.00263
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