6 papers
Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation
Xiuyuan Cheng, Nan Wu
This work studies the spectral convergence of graph Laplacian to the Laplace-Beltrami operator when the graph affinity matrix is constructed from random samples on a -dimens…
Computing high-dimensional optimal transport by flow neural networks
Chen Xu, Xiuyuan Cheng, Yao Xie
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods h…
Deep graph kernel point processes
Zheng Dong, Matthew Repasky, Xiuyuan Cheng +1
Point process models are widely used for continuous asynchronous event data, where each data point includes time and additional information called "marks", which can be locations,…
G-invariant diffusion maps
Eitan Rosen, Xiuyuan Cheng, Yoel Shkolnisky
The diffusion maps embedding of data lying on a manifold has shown success in tasks such as dimensionality reduction, clustering, and data visualization. In this work, we consider…
Bi-stochastically normalized graph Laplacian: convergence to manifold Laplacian and robustness to outlier noise
Xiuyuan Cheng, Boris Landa
Bi-stochastic normalization provides an alternative normalization of graph Laplacians in graph-based data analysis and can be computed efficiently by Sinkhorn-Knopp (SK) iterations…
The G-invariant graph Laplacian
Eitan Rosen, Paulina Hoyos, Xiuyuan Cheng +2
Graph Laplacian based algorithms for data lying on a manifold have been proven effective for tasks such as dimensionality reduction, clustering, and denoising. In this work, we con…