Related papers: Diffusion maps for changing data
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…
The Diffusion Map is a nonlinear dimensionality reduction technique used to analyze high-dimensional data, with recent applications extending to datasets from the social sciences. Previous research has given little attention to how the…
The ability of Graph Neural Networks (GNNs) to capture long-range and global topology information is limited by the scope of conventional graph Laplacian, leading to unsatisfactory performance on some datasets, particularly on heterophilic…
Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism,…
Distance plays a fundamental role in measuring similarity between objects. Various visualization techniques and learning tasks in statistics and machine learning such as shape matching, classification, dimension reduction and clustering…
This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the…
High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
We introduce {\em vector diffusion maps} (VDM), a new mathematical framework for organizing and analyzing massive high dimensional data sets, images and shapes. VDM is a mathematical and algorithmic generalization of diffusion maps and…
Diffusion maps (DMAP) are often used as a dimensionality-reduction tool, but more precisely they provide a spectral representation of the intrinsic geometry rather than a complete charting method. To illustrate this distinction, we study a…
Networks are important structures used to model complex systems where interactions take place. In a basic network model, entities are represented as nodes, and interaction and relations among them are represented as edges. However, in a…
This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation…
Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational…
This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…
In this paper, we design distributed multi-modal localization approaches for Connected and Automated vehicles. We utilize information diffusion on graphs formed by moving vehicles, based on Adapt-then-Combine strategies combined with the…
Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a…
We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…
This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…