4 papers
Differentially Private Manifold Denoising
Jiaqi Wu, Yiqing Sun, Zhigang Yao
We introduce a differentially private manifold denoising framework that allows users to exploit sensitive reference datasets to correct noisy, non-private query points without comp…
Ridge Estimation with Nonlinear Transformations
Zheng Zhai, Hengchao Chen, Zhigang Yao
Ridge estimation is an important manifold learning technique. The goal of this paper is to examine the effects of nonlinear transformations on the ridge sets. The main result prove…
Manifold Fitting under Unbounded Noise
Zhigang Yao, Yuqing Xia
There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Re…
Principal Sub-manifolds
Zhigang Yao, Benjamin Eltzner, Tung Pham
We propose a novel method of finding principal components in multivariate data sets that lie on an embedded nonlinear Riemannian manifold within a higher-dimensional space. Our aim…