Related papers: Multilayer hypergraph clustering using the aggrega…
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.…
The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…
In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously,…
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…
We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is…
We present a shared-memory algorithm to compute high-quality solutions to the balanced $k$-way hypergraph partitioning problem. This problem asks for a partition of the vertex set into $k$ disjoint blocks of bounded size that minimizes the…
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…
We consider the community recovery problem on a one-dimensional random geometric graph where every node has two independent labels: an observed location label and a hidden community label. A geometric kernel maps the locations of pairs of…
Stochastic block models (SBMs) are often used to find assortative community structures in networks, such that the probability of connections within communities is higher than in between communities. However, classic SBMs are not limited to…
The graph projection of a hypergraph is a simple graph with the same vertex set and with an edge between each pair of vertices that appear in a hyperedge. We consider the problem of reconstructing a random $d$-uniform hypergraph from its…
We propose a new hierarchy of semidefinite programming relaxations for inference problems. As test cases, we consider the problem of community detection in block models. The vertices are partitioned into $k$ communities, and a graph is…
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…
We consider the problem of clustering a graph $G$ into two communities by observing a subset of the vertex correlations. Specifically, we consider the inverse problem with observed variables $Y=B_G x \oplus Z$, where $B_G$ is the incidence…
Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…
Community detection, which aims to cluster $N$ nodes in a given graph into $r$ distinct groups based on the observed undirected edges, is an important problem in network data analysis. In this paper, the popular stochastic block model (SBM)…
The overlap gap property (OGP) is a statement about the geometry of near-optimal solutions. Exhibiting OGP implies failure of a class of local algorithms; and has been observed to coincide with conjectured algorithmic limits in problems…
We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing…
Maximum A posteriori Probability (MAP) inference in graphical models amounts to solving a graph-structured combinatorial optimization problem. Popular inference algorithms such as belief propagation (BP) and generalized belief propagation…
The problem of community detection in multi-layer undirected networks has received considerable attention in recent years. However, practical scenarios often involve multi-layer bipartite networks, where each layer consists of two distinct…
Existing deep learning approaches for image super-resolution, particularly those based on CNNs and attention mechanisms, often suffer from structural inflexibility. Although graph-based methods offer greater representational adaptability,…