Related papers: Min-Max Correlation Clustering via MultiCut
We initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…
The Max-Cut problem is a well known combinatorial optimization problem. In this paper we describe a fast approximation method. Given a graph G, we want to find a cut whose size is maximal among all possible cuts. A cut is a partition of the…
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…
In the Minimum Clique Routing Problem on Cycles \textsc{MCRPC} we are given a cycle together with a set of demands (weighted origin-destination pairs) and the goal is to route all the pairs minimizing the maximum weighted clique of the…
Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…
In a recent work, [19] studied the following "fair" variants of classical clustering problems such as $k$-means and $k$-median: given a set of $n$ data points in $\mathbb{R}^d$ and a binary type associated to each data point, the goal is to…
In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an…
The higher-order correlation clustering problem for a graph $G$ and costs associated with cliques of $G$ consists in finding a clustering of $G$ so as to minimize the sum of the costs of those cliques whose nodes all belong to the same…
Data de-duplication is the task of detecting multiple records that correspond to the same real-world entity in a database. In this work, we view de-duplication as a clustering problem where the goal is to put records corresponding to the…
Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating…
Clustering large datasets is a fundamental problem with a number of applications in machine learning. Data is often collected on different sites and clustering needs to be performed in a distributed manner with low communication. We would…
Graph routing problems have been investigated extensively in operations research, computer science and engineering due to their ubiquity and vast applications. In this paper, we study constant approximation algorithms for some variations of…
We consider the graph $k$-partitioning problem under the min-max objective, termed as Minmax $k$-cut. The input here is a graph $G=(V,E)$ with non-negative edge weights $w:E\rightarrow \mathbb{R}_+$ and an integer $k\geq 2$ and the goal is…
In Correlation Clustering, the input is a graph $G=(V,E)$ with weight function $\omega: {V \choose 2}\to Z$ and the task is to partition the vertex set into clusters such that the total weight of edges between clusters and missing edges…
Clustering bipartite graphs is a fundamental task in network analysis. In the high-dimensional regime where the number of rows $n_1$ and the number of columns $n_2$ of the associated adjacency matrix are of different order, existing methods…
We propose a novel approach for optimizing the graph ratio-cut by modeling the binary assignments as random variables. We provide an upper bound on the expected ratio-cut, as well as an unbiased estimate of its gradient, to learn the…
We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a $…
Graph clustering is a challenging pattern recognition problem whose goal is to identify vertex partitions with high intra-group connectivity. This paper investigates a bi-objective problem that maximizes the number of intra-cluster edges of…
Clustering is a widely-used data mining tool, which aims to discover partitions of similar items in data. We introduce a new clustering paradigm, \emph{accordant clustering}, which enables the discovery of (predefined) group level insights.…
Graph based clustering is one of the major clustering methods. Most of it work in three separate steps: similarity graph construction, clustering label relaxing and label discretization with k-means. Such common practice has three…