Related papers: Consistency of Spectral Hypergraph Partitioning un…

In this paper, we consider the planted partition model, in which $n = ks$ vertices of a random graph are partitioned into $k$ "clusters," each of size $s$. Edges between vertices in the same cluster and different clusters are included with…

Component-centric distributed graph processing platforms that use a bulk synchronous parallel (BSP) programming model have gained traction. These address the short-comings of Big Data abstractions/platforms like MapReduce/Hadoop for…

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take…

Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…

Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task…

Unsupervised semantic segmentation aims to discover groupings within and across images that capture object and view-invariance of a category without external supervision. Grouping naturally has levels of granularity, creating ambiguity in…

Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…

We investigate the unsupervised node classification problem on random hypergraphs under the non-uniform Hypergraph Stochastic Block Model (HSBM) with two equal-sized communities. In this model, edges appear independently with probabilities…

The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a…

We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…

Spectral clustering views the similarity matrix as a weighted graph, and partitions the data by minimizing a graph-cut loss. Since it minimizes the across-cluster similarity, there is no need to model the distribution within each cluster.…

We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, a standard recursive bi-partitioning algorithm is…

The balanced hypergraph partitioning problem (HGP) is to partition the vertex set of a hypergraph into k disjoint blocks of bounded weight, while minimizing an objective function defined on the hyperedges. Whereas real-world applications…

We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…

Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…

We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as…

The problem of multiway partitioning of an undirected graph is considered. A spectral method is used, where the k > 2 largest eigenvalues of the normalized adjacency matrix (equivalently, the k smallest eigenvalues of the normalized graph…

This work develops a distributed graph neural network (GNN) methodology for mesh-based modeling applications using a consistent neural message passing layer. As the name implies, the focus is on enabling scalable operations that satisfy…

We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…