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Found 12 papers, 0 papers with code
Identifying manifolds underlying group motion in Vicsek agents
In a topological sense, we describe these changes as switching between low-dimensional embedding manifolds underlying a group of evolving agents.
Dimensionality Reduction of Collective Motion by Principal Manifolds
Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates.
Detecting phase transitions in collective behavior using manifold's curvature
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure.
A Nonlinear Dimensionality Reduction Framework Using Smooth Geodesics
Herein, we propose a framework for nonlinear dimensionality reduction that generates a manifold in terms of smooth geodesics that is designed to treat problems in which manifold measurements are either sparse or corrupted by noise.
Bounded Manifold Completion
Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research.
A Patch-based Image Denoising Method Using Eigenvectors of the Geodesics' Gramian Matrix
Thus, here we propose a novel and computationally efficient image denoising method that is capable of producing accurate images.
Reconstruction of Fragmented Trajectories of Collective Motion using Hadamard Deep Autoencoders
Learning dynamics of collectively moving agents such as fish or humans is an active field in research.
Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling
Specifically, we analyze the performance of RNNs applied to three tasks: reconstruction of correct Lorenz solutions for a system with a formulation error, reconstruction of corrupted collective motion trajectories, and forecasting of streamflow time series possessing spikes, representing three fields, namely, ordinary differential equations, collective motion, and hydrological modeling, respectively.
Geodesic Gramian Denoising Applied to the Images Contaminated With Noise Sampled From Diverse Probability Distributions
As quotidian use of sophisticated cameras surges, people in modern society are more interested in capturing fine-quality images.
Real-time Forecasting of Time Series in Financial Markets Using Sequentially Trained Many-to-one LSTMs
People have been using learning tools from diverse fields such as financial mathematics and machine learning in the attempt of making trustworthy predictions on such markets.
Fraud Detection Using Optimized Machine Learning Tools Under Imbalance Classes
For both phishing website URLs and credit card fraud transaction datasets, the results indicate that extreme gradient boost trained on the original data shows trustworthy performance in the imbalanced dataset and manages to outperform the other three methods in terms of both AUC ROC and AUC PR.
Efficient Noise Filtration of Images by Low-Rank Singular Vector Approximations of Geodesics' Gramian Matrix
The applicability of GDD is limited as it encounters $\mathcal{O}(n^6)$ when denoising a given image of size $n\times n$ since GGD computes the prominent singular vectors of a $n^2 \times n^2$ data matrix that is implemented by singular value decomposition (SVD).
