2 citations · 3 across the 2 of their papers we have counts for
4 papers
The decomposition of the higher-order homology embedding constructed from the -Laplacian
Yu-Chia Chen, Marina Meilă
The null space of the -th order Laplacian , known as the {\em -th homology vector space}, encodes the non-trivial topology of a manifold or a network.…
Helmholtzian Eigenmap: Topological feature discovery & edge flow learning from point cloud data
Yu-Chia Chen, Weicheng Wu, Marina Meilă +1
The manifold Helmholtzian (1-Laplacian) operator elegantly generalizes the Laplace-Beltrami operator to vector fields on a manifold . In this work, we propose the…
Selecting the independent coordinates of manifolds with large aspect ratios
Yu-Chia Chen, Marina Meilă
Many manifold embedding algorithms fail apparently when the data manifold has a large aspect ratio (such as a long, thin strip). Here, we formulate success and failure in terms of…
Manifold Coordinates with Physical Meaning
Samson Koelle, Hanyu Zhang, Marina Meila +1
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinat…