6 papers
Transform-Based Multilinear Algebra via Tensor Decomposition
Yidan Mei, Shenghan Mei, Ziqin He +1
Transform-based tensor products, including the T-product and its more general form, namely the higher-order tensor-tensor product, have become fundamental tools for multilinear dat…
Quadratic Formula-based Nonlinear Approximation
Ziqin He, Can Chen, Min Hyung Cho +2
This paper presents a quadratic formula-based nonlinear representation for a given single-variable function f(x), . First, we construct the explicit polynomial co…
Tensor Dynamic Mode Decomposition
Ziqin He, Mengqi Hu, Yifei Lou +1
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD…
Data-driven model order reduction for T-Product-Based dynamical systems
Shenghan Mei, Ziqin He, Yidan Mei +4
Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of…
Tensor-based homogeneous polynomial dynamical system analysis from data
Xin Mao, Anqi Dong, Ziqin He +3
Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamic…
Data-driven Analysis of T-Product-based Dynamical Systems
Xin Mao, Anqi Dong, Ziqin He +2
A wide variety of data can be represented using third-order tensors, spanning applications in chemometrics, psychometrics, and image processing. However, traditional data-driven fr…