Geometric harmonics: A novel tool for multiscale out-of-sample extension of empirical functions

By Ronald R. Coifman, Stéphane Lafon. 2006

262 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Geophysics

View Paper: https://www.semanticscholar.org/paper/37b13a08bfd5a1edfb468c6c7fbe0505d09c6c93

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Geophysics

Citations in the corpus

Anisotropic diffusion on sub-manifolds with application to Earth structure classification (2012, background): “1 is based on the reproducibility property [7] and given in various papers such as [9].”
On Learning with Integral Operators (2010, methodology): “In a slightly differentco text Coifman and Lafon (2006) showed the connection between the Nyström method and the set of eigenfunctions of LK , which are calledgeometric harmonics.”
A spectral notion of Gromov–Wasserstein distance and related methods (2011, methodology): “Coifman and collaborators [17,28–30,41,44,52], and recently in the shape analysis community by Sun et al.”
Learning Sets with Separating Kernels (2012, background): “The adjoint of S n is and S ∗ n can be interpreted as the out-of-sample extension operator [18, 53].”
Riemannian Manifold Learning (2008, background): “Note that for a manifold with complex topology, for example, a torus, multiple normal coordinate charts, rather than one single chart, are needed to cover the whole manifold.”
Diffusion polynomial frames on metric measure spaces (2008, methodology): “This can be done in at least two ways: by adding the new points to the graph, and updating the eigenfunctions (for example by feeding the existing eigenfunctions as “initial conditions” to the eigensolver), or by using the geometric harmonic extensions described in [12].”
Data Fusion and Multicue Data Matching by Diffusion Maps (2006, methodology): “We start by reviewing the density-invariant embedding and out-of-sample extension schemes (previously introduced in [5] and [9]) in Sections 2.”
SpectralNet: Spectral Clustering using Deep Neural Networks (2018, methodology): “Our preference to use k -means is based on the interpretation (for normalized Laplacian matrices) of the Euclidean distance in the embedding space as diffusion distance in the input space (Nadler et al., 2006; Coifman & Lafon, 2006a).”