Related papers: Axioms for Distanceless Graph Partitioning

Steinerberger proposed a notion of curvature on graphs involving the graph distance matrix (J. Graph Theory, 2023). We show that nonnegative curvature is almost preserved under three graph operations. We characterize the distance matrix and…

We propose a graph-based clustering method based on Cluster Catch Digraphs (CCDs) that extends their applicability to moderate-dimensional data settings. Existing CCD variants, such as RK-CCDs, rely on spatial randomness tests based on…

Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…

We study a family of graph clustering problems where each cluster has to satisfy a certain local requirement. Formally, let $\mu$ be a function on the subsets of vertices of a graph $G$. In the $(\mu,p,q)$-PARTITION problem, the task is to…

Motivated by applications in social and biological network analysis, we introduce a new form of agnostic clustering termed~\emph{motif correlation clustering}, which aims to minimize the cost of clustering errors associated with both edges…

We consider a large class of random geometric graphs constructed from samples $\mathcal{X}_n = \{X_1,X_2,\ldots,X_n\}$ of independent, identically distributed observations of an underlying probability measure $\nu$ on a bounded domain…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

We develop an algorithm that finds the consensus of many different clustering solutions of a graph. We formulate the problem as a median set partitioning problem and propose a greedy optimization technique. Unlike other approaches that find…

Determining the quality of the results obtained by clustering techniques is a key issue in unsupervised machine learning. Many authors have discussed the desirable features of good clustering algorithms. However, Jon Kleinberg established…

We study the balanced $k$-way hypergraph partitioning problem, with a special focus on its practical applications to manycore scheduling. Given a hypergraph on $n$ nodes, our goal is to partition the node set into $k$ parts of size at most…

We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use of quantum approximate counting, and all of…

Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…

The well-known clustering algorithm of Miller, Peng, and Xu (SPAA 2013) is useful for many applications, including low-diameter decomposition and low-energy distributed algorithms. One nice property of their clustering, shown in previous…

Integral to the problem of detecting communities through graph clustering is the expectation that they are "well connected". In this respect, we examine five different community detection approaches optimizing different criteria: the Leiden…

Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…

This article empirically examines the computational cost of solving a known hard problem, graph clustering, using novel purpose-built computer hardware. We express the graph clustering problem as an intra-cluster distance or dissimilarity…

Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…

We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…

Higher-order graph clustering aims to partition the graph using frequently occurring subgraphs. Motif conductance is one of the most promising higher-order graph clustering models due to its strong interpretability. However, existing motif…

In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and…