Related papers: A Nonlocal Graph-PDE and Higher-Order Geometric In…
Document Image Enhancement (DIE) serves as a critical component in Document AI systems, where its performance substantially determines the effectiveness of downstream tasks. To address the limitations of existing methods confined to…
We introduce a novel algorithm for estimating optimal parameters of linearized assignment flows for image labeling. An exact formula is derived for the parameter gradient of any loss function that is constrained by the linear system of ODEs…
Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…
In this paper we present a non-local numerical scheme based on the Local Discontinuous Galerkin method for a non-local diffusive partial differential equation with application to traffic flow. In this model, the velocity is determined by…
Graph structure expression plays a vital role in distinguishing various graphs. In this work, we propose a Structure-Sensitive Graph Dictionary Embedding (SS-GDE) framework to transform input graphs into the embedding space of a graph…
One of the main challenges in solving time-dependent partial differential equations is to develop computationally efficient solvers that are accurate and stable. Here, we introduce a graph neural network approach to finding efficient PDE…
Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…
Recently a variety of methods have been developed to encode graphs into low-dimensional vectors that can be easily exploited by machine learning algorithms. The majority of these methods start by embedding the graph nodes into a…
Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical…
Learning universal graph representations across heterogeneous domains is difficult because graph datasets differ in topology, node-attribute semantics, feature dimensions, and even attribute availability. We propose GraphVec, a…
Nonlocally related partial differential equation (PDE) systems are useful in the analysis of a given PDE system. It is known that each local conservation law of a given PDE system systematically yields a nonlocally related system. In this…
We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a…
Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world…
Nonlocal metric dimension ${\rm dim}_{\rm n\ell}(G)$ of a graph $G$ is introduced as the cardinality of a smallest nonlocal resolving set, that is, a set of vertices which resolves each pair of non-adjacent vertices of $G$. Graphs $G$ with…
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…
We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph…
In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann…
Graph data widely exist in many high-impact applications. Inspired by the success of deep learning in grid-structured data, graph neural network models have been proposed to learn powerful node-level or graph-level representation. However,…
Recently, there has been a strong ambition to translate models and algorithms from traditional image processing to non-Euclidean domains, e.g., to manifold-valued data. While the task of denoising has been extensively studied in the last…
Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and…