Related papers: Sparse Dynamic Distribution Decomposition: Efficie…
This paper introduces a fast algorithm for randomized computation of a low-rank Dynamic Mode Decomposition (DMD) of a matrix. Here we consider this matrix to represent the development of a spatial grid through time e.g. data from a static…
Sparse algorithms offer great flexibility for multi-view temporal perception tasks. In this paper, we present an enhanced version of Sparse4D, in which we improve the temporal fusion module by implementing a recursive form of multi-frame…
Tensor decomposition methods are popular tools for analysis of multi-way datasets from social media, healthcare, spatio-temporal domains, and others. Widely adopted models such as Tucker and canonical polyadic decomposition (CPD) follow a…
The generalized persistence diagram (GPD) is a natural extension of the classical persistence barcode to the setting of multi-parameter persistence and beyond. The GPD is defined as an integer-valued function whose domain is the set of…
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…
Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with…
In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…
The increasing deployment of distribution-level phasor measurement units (PMUs) calls for dynamic distribution state estimation (DDSE) approaches that tap into high-rate measurements to maintain a comprehensive view of the…
Given a time-evolving tensor with missing entries, how can we effectively factorize it for precisely predicting the missing entries? Tensor factorization has been extensively utilized for analyzing various multi-dimensional real-world data.…
This paper explores potential improvements to the Spatial-Temporal Matching algorithm for aligning the GPS trajectories to road networks. While this algorithm is effective, it presents some limitations in computational efficiency and the…
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…
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
Temporal graph signals are multivariate time series with individual components associated with nodes of a fixed graph structure. Data of this kind arises in many domains including activity of social network users, sensor network readings…
Dimension reduction is often needed in the area of data mining. The goal of these methods is to map the given high-dimensional data into a low-dimensional space preserving certain properties of the initial data. There are two kinds of…
This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called "Sparse Signal Subspace Decomposition" (or 3SD) method. This method makes use of a novel criterion based on the…
Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…
This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global…