Related papers: Functional Continuous Decomposition
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
Understanding associations between paired high-dimensional longitudinal datasets is a fundamental yet challenging problem that arises across scientific domains, including longitudinal multi-omic studies. The difficulty stems from the…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…
Since Huang proposed the Empirical Mode Decomposition (EMD) in 1998, mode decomposition has been widely studied, but EMD and relative developed algorithms are still generally lack of adaptability and mathematical theory. This paper propose…
Dynamic mode decomposition (DMD) is a data-driven method that models high-dimensional time series as a sum of spatiotemporal modes, where the temporal modes are constrained by linear dynamics. For nonlinear dynamical systems exhibiting…
In this work we propose a novel approach to utilize convolutional neural networks for time series forecasting. The time direction of the sequential data with spatial dimensions $D=1,2$ is considered democratically as the input of a…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
While time-frequency analysis provides rich representations of multicomponent signals, current decomposition methods often overlook the morphological structure where components manifest as distinct regions. This study introduces…
We present a new convolutional neural network-based time-series model. Typical convolutional neural network (CNN) architectures rely on the use of max-pooling operators in between layers, which leads to reduced resolution at the top layers.…
Spatial convolution is fundamental in constructing deep Convolutional Neural Networks (CNNs) for visual recognition. While dynamic convolution enhances model accuracy by adaptively combining static kernels, it incurs significant…
Multimodal MRIs play a crucial role in clinical diagnosis and treatment. Feature disentanglement (FD)-based methods, aiming at learning superior feature representations for multimodal data analysis, have achieved significant success in…
In time series forecasting, effectively disentangling intricate temporal patterns is crucial. While recent works endeavor to combine decomposition techniques with deep learning, multiple frequencies may still be mixed in the decomposed…
The recently proposed fully-connected tensor network (FCTN) decomposition has demonstrated significant advantages in correlation characterization and transpositional invariance, and has achieved notable achievements in multi-dimensional…
Functional brain dynamics is supported by parallel and overlapping functional network modes that are associated with specific neural circuits. Decomposing these network modes from fMRI data and finding their temporal characteristics is…
The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…
Since many decades, there is a general perception in literature that the Fourier methods are not suitable for the analysis of nonlinear and nonstationary data. In this paper, we propose a Fourier Decomposition Method (FDM) and demonstrate…
We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is…
Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker…