17 citations · 20 across the 11 of their papers we have counts for
12 papers
On Random Fields Associated with Analytic Wavelet Transform
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
Despite the broad application of the analytic wavelet transform (AWT), a systematic statistical characterization of its magnitude and phase as inhomogeneous random fields on the ti…
Probabilistic Analysis of Scalogram Ridges in Signal Processing
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
While ridges in the scalogram, determined by the squared modulus of analytic wavelet transform (AWT), is a widely accepted concept and utilized in nonstationary time series analysi…
Ridge detection for nonstationary multicomponent signals with time-varying wave-shape functions and its applications
Yan-Wei Su, Gi-Ren Liu, Yuan-Chung Sheu +1
We introduce a novel ridge detection algorithm for time-frequency (TF) analysis, particularly tailored for intricate nonstationary time series encompassing multiple non-sinusoidal…
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…
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…
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…
Matrix Deviation Inequality for -Norm
Te-Chun Wang, Yuan-Chung Sheu
Motivated by the general matrix deviation inequality for i.i.d ensemble Gaussian matrix, we study its universality property. As a starting point for this problem, we show that this…
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…
Explore intrinsic geometry of sleep dynamics and predict sleep stage by unsupervised learning techniques
Gi-Ren Liu, Yu-Lun Lo, Yuan-Chung Sheu +1
We propose a novel unsupervised approach for sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools. Specifically, we apply diffusion-based…
Diffuse to fuse EEG spectra -- intrinsic geometry of sleep dynamics for classification
Gi-Ren Liu, Yu-Lun Lo, John Malik +2
We propose a novel algorithm for sleep dynamics visualization and automatic annotation by applying diffusion geometry based sensor fusion algorithm to fuse spectral information fro…
The -cutoffs for reversible Markov chains
Guan-Yu Chen, Jui-Ming Hsu, Yuan-Chung Sheu
In this article, we considers reversible Markov chains of which -distances can be expressed in terms of Laplace transforms. The cutoff of Laplace transforms was first discusse…
Disorder chaos in the spherical mean-field model
Wei-Kuo Chen, Hsi-Wei Hsieh, Chii-Ruey Hwang +1
We consider the problem of disorder chaos in the spherical mean-field model. It is concerned about the behavior of the overlap between two independently sampled spin configurations…