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13 February 2025 |
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Article overview
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Dictionary-based Manifold Learning | | Hanyu Zhang
; Samson Joelle
; Marina Meila
; | | Date: |
1 Feb 2023 | | Abstract: | We 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 | | Services: | Forum | Review | PDF | Favorites | |
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