Related papers: Explicit agreement extremes for a $2\times2$ table…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a…
In this paper we study the problem of correlation clustering under fairness constraints. In the classic correlation clustering problem, we are given a complete graph where each edge is labeled positive or negative. The goal is to obtain a…
In Bipartite Correlation Clustering (BCC) we are given a complete bipartite graph $G$ with `+' and `-' edges, and we seek a vertex clustering that maximizes the number of agreements: the number of all `+' edges within clusters plus all `-'…
Numerous algorithms have been produced for the fundamental problem of clustering under many different notions of fairness. Perhaps the most common family of notions currently studied is group fairness, in which proportional group…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
Generalized from the concept of consensus, this paper considers a group of edge agreements, i.e. constraints defined for neighboring agents, in which each pair of neighboring agents is required to satisfy one edge agreement constraint. Edge…
Many-to-many matching with contracts is studied in the framework of revealed preferences. All preferences are described by choice functions that satisfy natural conditions. Under a no-externality assumption individual preferences can be…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of…
Clustering is an unsupervised machine learning task that consists of identifying groups of similar objects. It has numerous applications and is increasingly used in fairness-sensitive domains where objects represent individuals, such as…
Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
Correlation clustering is a fundamental combinatorial optimization problem arising in many contexts and applications that has been the subject of dozens of papers in the literature. In this problem we are given a general weighted graph…
We consider the clustering aggregation problem in which we are given a set of clusterings and want to find an aggregated clustering which minimizes the sum of mismatches to the input clusterings. In the binary case (each clustering is a…
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…