45 citations · 273 across the 45 of their papers we have counts for
5 papers · 1 filter
Robust Inference of Manifold Density and Geometry by Doubly Stochastic Scaling
Boris Landa, Xiuyuan Cheng
The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate und…
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…
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…
Convergence of Graph Laplacian with kNN Self-tuned Kernels
Xiuyuan Cheng, Hau-Tieng Wu
Kernelized Gram matrix constructed from data points as is widely used in graph-based geometric data analysis…
Marchenko-Pastur Law for Tyler's M-estimator
Teng Zhang, Xiuyuan Cheng, Amit Singer
This paper studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples and their dimension both go to infinity, an…