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Found 22 papers, 10 papers with code
Transfer operators on graphs: Spectral clustering and beyond
Graphs and networks play an important role in modeling and analyzing complex interconnected systems such as transportation networks, integrated circuits, power grids, citation graphs, and biological and artificial neural networks.
Koopman-based spectral clustering of directed and time-evolving graphs
While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and social network analysis, clustering directed graphs remains notoriously difficult.
A Dynamic Mode Decomposition Approach for Decentralized Spectral Clustering of Graphs
Our proposed method uses the existing wave equation clustering algorithm that is based on propagating waves through the graph.
Deeptime: a Python library for machine learning dynamical models from time series data
Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics.
Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry
We derive symmetric and antisymmetric kernels by symmetrizing and antisymmetrizing conventional kernels and analyze their properties.
Data-driven model reduction of agent-based systems using the Koopman generator
The dynamical behavior of social systems can be described by agent-based models.
Feature space approximation for kernel-based supervised learning
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning.
GraphKKE: Graph Kernel Koopman Embedding for Human Microbiome Analysis
We demonstrate that our method can capture temporary changes in the time-evolving graph on both created synthetic data and real-world data.
Kernel-based approximation of the Koopman generator and Schrödinger operator
Furthermore, we exploit that, under certain conditions, the Schr\"odinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa.
Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergence
We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space.
Tensor-based algorithms for image classification
The interest in machine learning with tensor networks has been growing rapidly in recent years.
Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition).
Tensor-based computation of metastable and coherent sets
Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches.
Kernel Conditional Density Operators
The proposed model is based on a novel approach to the reconstruction of probability densities from their kernel mean embeddings by drawing connections to estimation of Radon-Nikodym derivatives in the reproducing kernel Hilbert space (RKHS).
Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems.
Kernel methods for detecting coherent structures in dynamical data
In particular, we show that kernel canonical correlation analysis (CCA) can be interpreted in terms of kernel transfer operators and that it can be obtained by optimizing the variational approach for Markov processes (VAMP) score.
Learning chemical reaction networks from trajectory data
We develop a data-driven method to learn chemical reaction networks from trajectory data.
Optimization and Control 92C42, 62M86
A kernel-based approach to molecular conformation analysis
We present a novel machine learning approach to understanding conformation dynamics of biomolecules.
Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions.
Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions
Kernel transfer operators, which can be regarded as approximations of transfer operators such as the Perron-Frobenius or Koopman operator in reproducing kernel Hilbert spaces, are defined in terms of covariance and cross-covariance operators and have been shown to be closely related to the conditional mean embedding framework developed by the machine learning community.
Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces
Transfer operators such as the Perron--Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems.
Variational Koopman models: slow collective variables and molecular kinetics from short off-equilibrium simulations
Recently, a powerful generalization of MSMs has been introduced, the variational approach (VA) of molecular kinetics and its special case the time-lagged independent component analysis (TICA), which allow us to approximate slow collective variables and molecular kinetics by linear combinations of smooth basis functions or order parameters.
