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Yu-Chia Chen

2 accepted papers

2021

The decomposition of the higher-order homology embedding constructed from the $k$-Laplacian

NeurIPS 2021oral

The null space of the $k$-th order Laplacian $\mathbf{\mathcal L}_k$, known as the {\em $k$-th homology vector space}, encodes the non-trivial topology of a manifold or a network. Understanding the structure of the homology embedding can thus disclose geometric or topological information from the da…

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2019

Selecting the independent coordinates of manifolds with large aspect ratios

NeurIPS 2019poster

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 finding a smooth embedding, showing also that the problem is pervasive and more complex than previously recognized. Math…