534 citations · 2k across the 96 of their papers we have counts for
15 papers · 1 filter
Impact of signal-to-noise ratio and bandwidth on graph Laplacian spectrum from high-dimensional noisy point cloud
Xiucai Ding, Hau-Tieng Wu
We systematically study the spectrum of kernel-based graph Laplacian (GL) constructed from high-dimensional and noisy random point cloud in the nonnull setup. The problem is motive…
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…
Strong Uniform Consistency with Rates for Kernel Density Estimators with General Kernels on Manifolds
Hau-Tieng Wu, Nan Wu
When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be…
Scalability and robustness of spectral embedding: landmark diffusion is all you need
Chao Shen, Hau-Tieng Wu
While spectral embedding is a widely applied dimension reduction technique in various fields, so far it is still challenging to make it scalable to handle ``big data''. On the othe…
Spectral Convergence of Graph Laplacian and Heat Kernel Reconstruction in from Random Samples
David B Dunson, Hau-Tieng Wu, Nan Wu
In the manifold setting, we provide a series of spectral convergence results quantifying how the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions…
On the spectral property of kernel-based sensor fusion algorithms of high dimensional data
Xiucai Ding, Hau-Tieng Wu
We apply local laws of random matrices and free probability theory to study the spectral properties of two kernel-based sensor fusion algorithms, nonparametric canonical correlatio…
Asymptotic analysis of synchrosqueezing transform -- toward statistical inference with nonlinear-type time-frequency analysis
Matt Sourisseau, Hau-Tieng Wu, Zhou Zhou
We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate non…
Optimal Recovery of Precision Matrix for Mahalanobis Distance from High Dimensional Noisy Observations in Manifold Learning
Matan Gavish, Ronen Talmon, Pei-Chun Su +1
Motivated by establishing theoretical foundations for various manifold learning algorithms, we study the problem of Mahalanobis distance (MD), and the associated precision matrix,…
When Locally Linear Embedding Hits Boundary
Hau-tieng Wu, Nan Wu
Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud i…
Think globally, fit locally under the Manifold Setup: Asymptotic Analysis of Locally Linear Embedding
Hau-Tieng Wu, Nan Wu
Since its introduction in 2000, the locally linear embedding (LLE) has been widely applied in data science. We provide an asymptotical analysis of the LLE under the manifold setup.…
ConceFT: Concentration of Frequency and Time via a multitapered synchrosqueezed transform
Ingrid Daubechies, Yi Wang, Hau-tieng Wu
A new method is proposed to determine the time-frequency content of time-dependent signals consisting of multiple oscillatory components, with time-varying amplitudes and instantan…
Connection graph Laplacian methods can be made robust to noise
Noureddine El Karoui, Hau-tieng Wu
Recently, several data analytic techniques based on connection graph laplacian (CGL) ideas have appeared in the literature. At this point, the properties of these methods are start…
A New Test for One-Way ANOVA with Functional Data and Application to Ischemic Heart Screening
Jin-Ting Zhang, Ming-Yen Cheng, Chi-Jen Tseng +1
We propose and study a new global test, namely the -test, for the one-way ANOVA problem in functional data analysis. The test statistic is taken as the maximum value of t…
Nonparametric and adaptive modeling of dynamic seasonality and trend with heteroscedastic and dependent errors
Yu-Chun Chen, Ming-Yen Cheng, Hau-tieng Wu
Seasonality (or periodicity) and trend are features describing an observed sequence, and extracting these features is an important issue in many scientific fields. However, it is n…
Local Linear Regression on Manifolds and its Geometric Interpretation
Ming-Yen Cheng, Hau-tieng Wu
High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables a…