Related papers: Multiscale Graph Reduction for Heterogeneous and A…
$\textbf{Graph Coarsening (GC)}$ is a prominent graph reduction technique that compresses large graphs to enable efficient learning and inference. However, existing GC methods generate only one coarsened graph per run and must recompute…
In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…
We introduce a framework for joint grounded scene graph - image generation, a challenging task involving high-dimensional, multi-modal structured data. To effectively model this complex joint distribution, we adopt a factorized approach:…
The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that…
We consider image denoising using a nonlinear diffusion process, where we solve unsteady partial differential equations with nonlinear coefficients. The noised image is given as an initial condition, and nonlinear coefficients are used to…
Spectral graph sparsification aims to find ultra-sparse subgraphs whose Laplacian matrix can well approximate the original Laplacian eigenvalues and eigenvectors. In recent years, spectral sparsification techniques have been extensively…
Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…
We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on…
The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on…
Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium…
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…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
Recently, graph mining approaches have become very popular, especially in domains such as bioinformatics, chemoinformatics and social networks. In this scope, one of the most challenging tasks is frequent subgraph discovery. This task has…
How might one "reduce" a graph? That is, generate a smaller graph that preserves the global structure at the expense of discarding local details? There has been extensive work on both graph sparsification (removing edges) and graph…
The objective of graph coarsening is to generate smaller, more manageable graphs while preserving key information of the original graph. Previous work were mainly based on the perspective of spectrum-preserving, using some predefined…
Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…
We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…
This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…