相关论文: A New Relaxation Approach to Normalized Hypergraph…

The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases…

Graph Neural Networks (GNNs) are popular machine learning methods for modeling graph data. A lot of GNNs perform well on homophily graphs while having unsatisfactory performance on heterophily graphs. Recently, some researchers turn their…

These are notes on the method of normalized graph cuts and its applications to graph clustering. I provide a fairly thorough treatment of this deeply original method due to Shi and Malik, including complete proofs. I include the necessary…

Networks with higher-order interactions, prevalent in biological, social, and information systems, are naturally represented as hypergraphs, yet their structural complexity poses fundamental challenges for geometric characterization. While…

The increasing prevalence of large-scale graphs poses a significant challenge for graph neural network training, attributed to their substantial computational requirements. In response, graph condensation (GC) emerges as a promising…

The increasing prevalence of large-scale hypergraphs poses significant computational challenges for hypergraph neural network (HNN) training. To address this, hypergraph condensation (HGC) distills large real hypergraphs into compact yet…

Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…

Graph Neural Networks (GNNs) are effective for processing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum Computing (QC) offers a…

Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges…

The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…

Graph Convolutional Networks (GCNs) have received increasing attention in the machine learning community for effectively leveraging both the content features of nodes and the linkage patterns across graphs in various applications. As…

Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…

Inspired by the recently remarkable successes of Sparse Representation (SR), Collaborative Representation (CR) and sparse graph, we present a novel hypergraph model named Regression-based Hypergraph (RH) which utilizes the regression models…

Convolutional Neural Networks (CNN) have been rigorously studied for Hyperspectral Image Classification (HSIC) and are known to be effective in exploiting joint spatial-spectral information with the expense of lower generalization…

We consider the following natural graph cut problem called Critical Node Cut (CNC): Given a graph $G$ on $n$ vertices, and two positive integers $k$ and $x$, determine whether $G$ has a set of $k$ vertices whose removal leaves $G$ with at…

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

Support vector classification (SVC) is an effective tool for classification tasks in machine learning. Its performance relies on the selection of appropriate hyperparameters. This paper focuses on optimizing the regularization…

Image Representation Learning is an important problem in Computer Vision. Traditionally, images were processed as grids, using Convolutional Neural Networks or as a sequence of visual tokens, using Vision Transformers. Recently, Vision…

The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…

Self-supervised heterogeneous graph learning (SHGL) has shown promising potential in diverse scenarios. However, while existing SHGL methods share a similar essential with clustering approaches, they encounter two significant limitations:…