Related papers: Consistency of modularity clustering on random geo…

Modularity was introduced as a measure of goodness for the community structure induced by a partition of the set of vertices in a graph. Then, it also became an objective function used to find good partitions, with high success.…

This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on…

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…

In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…

Segmentation of a colour image composed of different kinds of texture regions can be a hard problem, namely to compute for an exact texture fields and a decision of the optimum number of segmentation areas in an image when it contains…

In this paper we consider discrete robot path planning problems on metric graphs. We propose a clustering method, Gamma-Clustering for the planning graph that significantly reduces the number of feasible solutions, yet retains a solution…

Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…

An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…

The theoretical analysis of spectral clustering mainly focuses on consistency, while there is relatively little research on its generalization performance. In this paper, we study the excess risk bounds of the popular spectral clustering…

A relational dataset is often analyzed by optimally assigning a label to each element through clustering or ordering. While similar characterizations of a dataset would be achieved by both clustering and ordering methods, the former has…

We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…

In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…

We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization…

We study a discrete version of a geometric stable marriage problem originally proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which points in the plane are stably matched to cluster centers, as prioritized by their…

In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…

Community detection, which involves partitioning nodes within a network, has widespread applications across computational sciences. Modularity-based algorithms identify communities by attempting to maximize the modularity function across…

Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…

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…

In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…

Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…