534 citations · 2k across the 96 of their papers we have counts for
97 papers
Gaussian Approximation for the Moving Averaged Modulus Wavelet Transform and its Variants
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
The moving average of the complex modulus of the analytic wavelet transform provides a robust time-scale representation for signals to small time shifts and deformation. In this wo…
Geometric Scattering on Measure Spaces
Joyce Chew, Matthew Hirn, Smita Krishnaswamy +5
The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in o…
An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal
Marcelo A. Colominas, Hau-Tieng Wu
Nonsinusoidal oscillatory signals are everywhere. In practice, the nonsinusoidal oscillatory pattern, modeled as a 1-periodic wave-shape function (WSF), might vary from cycle to cy…
Data-Driven optimal shrinkage of singular values under high-dimensional noise with separable covariance structure with application
Pei-Chun Su, Hau-Tieng Wu
We develop a data-driven optimal shrinkage algorithm for matrix denoising in the presence of high-dimensional noise with a separable covariance structure; that is, the noise is col…
The Manifold Scattering Transform for High-Dimensional Point Cloud Data
Joyce Chew, Holly R. Steach, Siddharth Viswanath +5
The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-l…
Application of de-shape synchrosqueezing to estimate gait cadence from a single-sensor accelerometer placed in different body locations
Hau-Tieng Wu, Jacek Urbanek
Objective: Commercial and research-grade wearable devices have become increasingly popular over the past decade. Information extracted from devices using accelerometers is frequent…
Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operators
Tal Shnitzer, Hau-Tieng Wu, Ronen Talmon
Multivariate time-series have become abundant in recent years, as many data-acquisition systems record information through multiple sensors simultaneously. In this paper, we assume…
When Scattering Transform Meets Non-Gaussian Random Processes, a Double Scaling Limit Result
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
We explore the finite dimensional distributions of the second-order scattering transform of a class of non-Gaussian processes when all the scaling parameters go to infinity simulta…
Fundamental component enhancement via adaptive nonlinear activation functions
Stefan Steinerberger, Hau-Tieng Wu
In many real world oscillatory signals, the fundamental component of a signal might be weak or does not exist. This makes it difficult to estimate the instantaneous frequenc…
Disentangling modes with crossover instantaneous frequencies by synchrosqueezed chirplet transforms, from theory to application
Ziyu Chen, Hau-Tieng Wu
Analysis of signals with oscillatory modes with crossover instantaneous frequencies is a challenging problem in time series analysis. One way to handle this problem is lifting the…
How do kernel-based sensor fusion algorithms behave under high dimensional noise?
Xiucai Ding, Hau-Tieng Wu
We study the behavior of two kernel based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) and alternating diffusion (AD), under the nonnull setting th…
Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries
Stefan Steinerberger, Hau-Tieng Wu
We consider the eigenvalue problem where and the eigenvalue is also real . If we are given , and, additionally, th…
Asymptotic Analysis of Higher-order Scattering Transform of Gaussian Processes
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
We analyze the scattering transform with the quadratic nonlinearity (STQN) of Gaussian processes without depth limitation. STQN is a nonlinear transform that involves a sequential…
Prenatal stress perturbs fetal iron homeostasis in a sex-specific manner
Peter Zimmermann, Marta C. Antonelli, Ritika Sharma +7
What is the influence of chronic maternal prenatal stress (PS) on fetal iron homeostasis? In a prospective case-control study in 164 pregnant women, we show that cord blood transfe…
An Efficient Forecasting Approach to Reduce Boundary Effects in Real-Time Time-Frequency Analysis
Adrien Meynard, Hau-Tieng Wu
Time-frequency (TF) representations of time series are intrinsically subject to the boundary effects. As a result, the structures of signals that are highlighted by the representat…
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…