4 papers
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…
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…