Related papers: Explicit agreement extremes for a $2\times2$ table…
We study a variant of classical clustering formulations in the context of algorithmic fairness, known as diversity-aware clustering. In this variant we are given a collection of facility subsets, and a solution must contain at least a…
In this work we focus on efficient heuristics for solving a class of stochastic planning problems that arise in a variety of business, investment, and industrial applications. The problem is best described in terms of future buy and sell…
We call a coupling of two stochastic processes which maximizes the time until the first disagreement a maximal agreement coupling. We show that such a coupling always exists. Furthermore, it is possible to construct a lower bound on the…
This paper introduces the equiwide clustering problem, where valid partitions must satisfy intra-cluster dissimilarity constraints. Unlike most existing clustering algorithms, equiwide clustering relies neither on density nor on a…
The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the…
Fair clustering is the process of grouping similar entities together, while satisfying a mathematically well-defined fairness metric as a constraint. Due to the practical challenges in precise model specification, the prescribed fairness…
We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific…
Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the…
In correlation clustering, we are given $n$ objects together with a binary similarity score between each pair of them. The goal is to partition the objects into clusters so to minimise the disagreements with the scores. In this work we…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the…
Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario,…
The price of explainability for a clustering task can be defined as the unavoidable loss,in terms of the objective function, if we force the final partition to be explainable. Here, we study this price for the following clustering problems:…
Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$…
We address the problem of clustering a set of points in $\mathbb{R}^d$ with axis-parallel clusters. Previous exact approaches to this problem are mostly based on integer programming formulations and can only solve to optimality instances of…
In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in…
Consensus clustering aggregates partitions in order to find a better fit by reconciling clustering results from different sources/executions. In practice, there exist noise and outliers in clustering task, which, however, may significantly…
We consider inapproximability of the correlation clustering problem defined as follows: Given a graph $G = (V,E)$ where each edge is labeled either "+" (similar) or "-" (dissimilar), correlation clustering seeks to partition the vertices…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…