Proposes a Gaussian process for Koopman mode decomposition.
problem Estimating Koopman mode decomposition quantities and latent variables.
method Unsupervised Gaussian process for simultaneous estimation.
result Efficient parameter estimation through low-rank approximations.
SRMD uses random features for efficient time-frequency analysis.
problem Efficiently analyzing time-series data with low computational cost.
method Sparse Random Mode Decomposition (SRMD) constructs a sparse approximation to the spectrogram.
result SRMD outperforms other methods in signal representation, outlier removal, and mode decomposition.
Review of algorithms for linear system approximations.
problem Linear approximation of high-dimensional dynamical systems.
method State-of-the-art algorithms for low-rank DMD.
result Provides additional details for comprehensive understanding.
Sparse-mode DMD disambiguates local and global modes in spatiotemporal data.
problem Disambiguating local and global modes in spatiotemporal data.
method Sparse-mode DMD with sparsity-promoting regularization.
result Explicitly constructs discrete and continuous spectra.
New algorithm improves dynamic mode decomposition for high-dimensional data.
problem Reduced modeling in high-dimensional spaces.
method Low rank constraint optimization and kernel-based computation.
result Gain in approximation accuracy and computational efficiency.
Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Reg…
Parsimonious Dynamic Mode Decomposition selects sparse modes robustly.
problem Manual tuning of sparsity parameters in traditional DMD.
method Time-delay embedding and Orthogonal Matching Pursuit.
result Autonomously determines optimally sparse subset of modes.
Enhances forecasting of complex systems using FKMD.
problem Forecasting high-dimensional dynamical systems with unknown features.
method Featurized Koopman Mode Decomposition (FKMD) using delay embedding and learned Mahalanobis distance.
result Improves prediction accuracy for various complex systems.
The paper finds shape modes for vortices in a specific sigma model.
problem Existence of internal modes in CP1 vortices. method Developed a geometric formalism based on the Bogomol'nyi decomposition of the energy functional.
result Proved the existence of at least one shape mode for a general CP1 vortex solution. New networks interpret kernel decompositions for signal analysis.
problem Mode decomposition in signal analysis.
method Programmable and interpretable regression networks using kernels and data.
result Near machine precision recovery of signal modes under regularity and separation assumptions.
Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlik…
Kernel Dynamic Mode Decomposition reconstructs dynamical systems using Laplacian kernel.
problem Reconstructing spatial-temporal dynamics of complex systems.
method Kernel Dynamic Mode Decomposition with Laplacian kernel.
result Laplacian kernel allows for the closability of Koopman operators in RKHS, enabling reconstruction.
Optimized DMD for fast atmospheric chemistry forecasting.
problem Forecasting global atmospheric chemistry dynamics efficiently.
method Optimized Dynamic Mode Decomposition (DMD) for reduced order modeling.
result Significant improvement in computational speed and interpretability.
New ADMM method for PARAFAC2 tensor decomposition with flexible regularization.
problem Challenges in applying regularisation to the evolving mode of PARAFAC2.
method Alternating Direction Method of Multipliers (AO-ADMM) for PARAFAC2 tensor fitting.
result The proposed ADMM-based approach accurately recovers underlying components from simulated data.
Paper proposes using DMD for feature extraction in image classification.
problem Lack of labelled data for machine learning.
method Dynamic Mode Decomposition (DMD) for feature extraction.
result DMD features with RKS give competitive results.
Paper uses DMD to embed time in spatiotemporal forecasting.
problem Forecasting long-range seasonal dependencies in spatiotemporal data.
method Dynamic Mode Decomposition (DMD) for time representation.
result DMD-based embedding improves long-horizon forecasting accuracy.
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank constrained optimisation problem. This problem is non-convex and state-of-the-art algor…
Study combines dynamic mode and wavelet decomposition for marketing time series analysis.
problem Insufficient quantitative studies in marketing literature.
method Dynamic mode decomposition and wavelet decomposition for marketing time series.
result Effect of time scale on brand sales persistence and forecasting.
Proposes neural dynamic mode decomposition for end-to-end modeling of nonlinear dynamics.
problem Understanding and modeling nonlinear dynamical systems.
method Trains neural networks to minimize forecast error based on spectral decomposition in the lifted space.
result Demonstrates effectiveness in eigenvalue estimation and forecast performance.
Adaptive tensor modeling preserves continuity in multidimensional data.
problem Discretization of continuous multidimensional data loses important information.
method Functional Tucker decomposition (FTD) with RKHS modeling.
result FTD enables adaptive and expressive tensor modeling.
We discuss structured Schatten norms for tensor decomposition that includes two recently proposed norms ("overlapped" and "latent") for convex-optimization-based tensor decomposition, and connect tensor decomposition with wider literature on structured sparsity. Based on the properties of the structured Schatten norms,…
Paper unifies subspace identification and DMD for dynamical systems.
problem Estimating dynamical models from data.
method Unified optimization and regression problems for SID and DMD.
result Proves equivalence of SID and DMD for optimal model construction.
We provide the proof that the space of time series data is a Kolmogorov space with T0-separation axiom using the loop space of time series data. In our approach we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes fro…
Study uses DMD to analyze oceanic features in Strait of Gibraltar.
problem Understanding complex oceanic features in Strait of Gibraltar.
method Dynamic Mode Decomposition (DMD) applied to 3D MIT general circulation model simulations.
result Unveiled new elements and dynamics of the Strait of Gibraltar, including a secondary gyre and wave propagation.
The Empirical Mode Decomposition (EMD) provides a tool to characterize time series in terms of its implicit components oscillating at different time-scales. We apply this decomposition to intraday time series of the following three financial indices: the S\&P 500 (USA), the IPC (Mexico) and the VIX (volatility index US…
This work improves tensor decomposition methods, especially for large datasets.
problem Lack of efficient methods for estimating Tucker decompositions.
method Applies Johnson-Lindenstrauss type guarantees to Tucker decompositions with random embeddings.
result Effective dimension reduction with minimal error for large tensors.
Study cryptocurrency price dynamics using adaptive EMD and spectral analysis.
problem Analyze the time-varying volatility of cryptocurrency prices.
method Adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis.
result Reveal the properties of various timescales in cryptocurrency price dynamics.
HHT feature generation enhances financial time series forecasting.
problem Forecasting nonstationary financial time series.
method CEEMD and HHT for decomposition, machine learning integration.
result HHT-enhanced models outperform traditional models in forecasting.
Paper uses AI methods to forecast Bitcoin prices.
problem Inaccurate Bitcoin price predictions in previous studies.
method Combines EEMD and LSTM for next-day price forecast.
result Improves Bitcoin price prediction accuracy.
The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a partition of the input space, while switching regression considers arbitrary switch…
The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis, the extracted dynamic modes are a generalization of global stability modes. We a…
Compact models learn photocurrent dynamics from radiation-induced excess carrier density.
problem Accurate but computationally expensive physics-based photocurrent models for semiconductor devices.
method Dynamic Mode Decomposition (DMD) for learning reduced order models from internal state data.
result Physics-aware, compact delayed photocurrent models accurately approximate internal excess carrier dynamics.
In this paper, a unified susceptible-exposed-infected-susceptible-aware (SEIS-A) framework is proposed to combine epidemic spreading with individuals' on-line self-consultation behaviors. An epidemic spreading prediction model is established based on the SEIS-A framework. The prediction process contains two phases. In …
Proposes using Dynamic Mode Decomposition with delays for short-term human motion anticipation.
problem Lack of interpretability and explainability in neural network-based motion anticipation methods.
method Dynamic Mode Decomposition with delays for motion representation and prediction.
result Anticipation errors comparable or better than recurrent neural networks for very short times.
This study proposes methods for multi-step-ahead stock price prediction using decomposition and neural networks.
problem Inaccurate one-step-ahead forecasting limits stock market decision-making.
method Two novel methods: DCT-MFRFNN and VMD-MFRFNN.
result VMD-MFRFNN outperforms other methods in multi-step-ahead stock price prediction.
A new method for decomposing non-negative tensors using energy-based modeling.
problem Challenges in traditional tensor decomposition methods, especially global optimization and rank selection.
method Energy-based modeling of tensors, considering interactions between modes for global optimization.
result Demonstrates effectiveness in tensor completion and approximation, revealing a relationship between many-body and low-rank approximations.
Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often need to prepare nonlinear observables manually according to the underlying dynami…
Develops SymGCP for tensor decompositions with general symmetry.
problem Handling symmetry in tensor decompositions for better model accuracy.
method Introduces SymGCP, a generalized CP decomposition that accounts for any subset of tensor modes' symmetry.
result SymGCP enables efficient and scalable tensor decomposition with improved model robustness and accuracy.
Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This extension is of particular interest for reduced-order modeling in various applicative …
We consider N-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces r-rank appr…
Hybrid model forecasts Bitcoin prices better than standard LSTM.
problem Forecasting Bitcoin price fluctuations.
method VMD for decomposition, LSTM for modeling IMFs, final prediction aggregation.
result Hybrid model outperforms standard LSTM in various metrics.
Empirical mode modeling improves state-space analysis of noisy data.
problem Analyzing nonlinear systems with noisy data.
method Combining empirical mode decomposition with empirical dynamic modeling.
result Empirical mode modeling enhances state-space representations in noisy data.
Proposes tPARAFAC2 for tracking evolving patterns in time-evolving data.
problem Lack of temporal regularization in tensor factorizations for capturing evolving patterns.
method Temporal PARAFAC2 (tPARAFAC2) with temporal regularization.
result tPARAFAC2 accurately captures evolving patterns better than existing methods.
New method decomposes KL error using refined information and mode interactions.
problem Learning probability distributions over discrete variables with higher-order interactions.
method Using information geometry, refined mode interactions, and a novel Monte-Carlo sampling technique.
result Complete decomposition of KL error and efficient data use.
New algorithms extract Koopman invariant subspaces from large-scale data.
problem Difficulty in discerning the Koopman invariant subspace from many Koopman eigenmodes.
method Multi-task feature learning and pruning procedure to remove spurious modes.
result Effective in approximating Koopman operator for complex flows.
This study applies EMD to MSCI World index and converts IMFs into graphs for GNN modeling.
problem Modeling financial time series with GNNs.
method EMD, CEEMDAN, graph transformations (natural visibility, horizontal visibility, recurrence, transition graphs), topological analysis.
result High-frequency IMFs yield dense, highly connected small-world graphs; low-frequency IMFs produce sparser networks.
Hybrid model for multimodal distributions using diffusion and classification.
problem Sampling from multimodal distributions with correct proportions.
method Divide-and-conquer strategy: identify modes, train classifiers, diffusion models, bridge sampling.
result Framework effectively handles multimodal distributions in high dimensions.
We demonstrate the application of an algorithmic trading strategy based upon the recently developed dynamic mode decomposition (DMD) on portfolios of financial data. The method is capable of characterizing complex dynamical systems, in this case financial market dynamics, in an equation-free manner by decomposing the s…