69 citations · 518 across the 94 of their papers we have counts for
7 papers · 1 filter
Deep Residual Learning and PDEs on Manifold
Zhen Li, Zuoqiang Shi
In this paper, we formulate the deep residual network (ResNet) as a control problem of transport equation. In ResNet, the transport equation is solved along the characteristics. Ba…
Sparse Time-Frequency decomposition for multiple signals with same frequencies
Thomas Y. Hou, Zuoqiang Shi
In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of th…
Convergence of Laplacian spectra from random samples
Zuoqiang Shi
Eigenvectors and eigenvalues of discrete graph Laplacians are often used for manifold learning and nonlinear dimensionality reduction. It was previously proved by Belkin and Niyogi…
Extracting a shape function for a signal with intra-wave frequency modulation
Thomas Y. Hou, Zuoqiang Shi
In this paper, we consider signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using…
On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data
Chunguang Liu, Thomas Y. Hou, Zuoqiang Shi
In this paper, we analyze the uniqueness of the sparse time frequency decomposition and investigate the efficiency of the nonlinear matching pursuit method. Under the assumption of…
Sparse Time Frequency Representations and Dynamical Systems
T. Y. Hou, Z. Shi, P. Tavallali
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations…