534 citations · 2k across the 96 of their papers we have counts for
15 papers · 1 filter
Central and Non-central Limit Theorems arising from the Scattering Transform and its Neural Activation Generalization
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
Motivated by analyzing complicated and non-stationary time series, we study a generalization of the scattering transform (ST) that includes broad neural activation functions, which…
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…
Decomposing non-stationary signals with time-varying wave-shape functions
Marcelo A. Colominas, Hau-Tieng Wu
Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is furthe…
Graph Based Gaussian Processes on Restricted Domains
David B Dunson, Hau-Tieng Wu, Nan Wu
In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic…
Denoising Click-evoked Otoacoustic Emission Signals by Optimal Shrinkage
Tzu-Chi Liu, Yi-Wen Liu, Hau-Tieng Wu
Click-evoked otoacoustic emissions (CEOAEs) are clinically used as an objective way to infer whether cochlear functions are normal. However, because the sound pressure level of CEO…
Airflow recovery from thoracic and abdominal movements using Synchrosqueezing Transform and Locally Stationary Gaussian Process Regression
Whitney K. Huang, Yu-Min Chung, Yu-Bo Wang +2
Airflow signal encodes rich information about respiratory system. While the gold standard for measuring airflow is to use a spirometer with an occlusive seal, this is not practical…
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…
Convergence analysis of Adaptive Locally Iterative Filtering and SIFT method
Antonio Cicone, Hau-Tieng Wu
Adaptive Local Iterative Filtering (ALIF) is a currently proposed novel time-frequency analysis tool. It has been empirically shown that ALIF is able to separate components and ove…
Frequency Detection and Change Point Estimation for Time Series of Complex Oscillation
Hau-Tieng Wu, Zhou Zhou
We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A hig…
Current state of nonlinear-type time-frequency analysis and applications to high-frequency biomedical signals
Hau-Tieng Wu
Motivated by analyzing complicated time series, nonlinear-type time-frequency analysis became an active research topic in the past decades. Those developed tools have been applied…
When Ramanujan meets time-frequency analysis in complicated time series analysis
Ziyu Chen, Hau-Tieng Wu
To handle time series with complicated oscillatory structure, we propose a novel time-frequency (TF) analysis tool that fuses the short time Fourier transform (STFT) and periodic t…
An Adaptive QRS Detection Algorithm for Ultra-Long-Term ECG Recordings
John Malik, Elsayed Z Soliman, Hau-Tieng Wu
Background: Accurate detection of QRS complexes during mobile, ultra-long-term ECG monitoring is challenged by instances of high heart rate, dramatic and persistent changes in sign…
On the behavior of -Laplacian Ratio Cuts on nearly rectangular domains
Wesley Hamilton, Jeremy L. Marzuola, Hau-tieng Wu
Given a connected set , define a sequence of sets where is the subset of where the first eigenfunction of the (prop…
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…