Related papers: A Polynomial-Time Approximation for Pairwise Fair …
Clustering is a fundamental problem in unsupervised machine learning, and fair variants of it have recently received significant attention due to its societal implications. In this work we introduce a novel definition of individual fairness…
We consider the classical $k$-Center problem in undirected graphs. The problem is known to have a polynomial-time 2-approximation. There are even $(2+\varepsilon)$-approximations running in near-linear time. The conventional wisdom is that…
Clustering is an important task with applications in many fields of computer science. We study the fully dynamic setting in which we want to maintain good clusters efficiently when input points (from a metric space) can be inserted and…
In this work, we study the $k$-median clustering problem with an additional equal-size constraint on the clusters, from the perspective of parameterized preprocessing. Our main result is the first lossy ($2$-approximate) polynomial kernel…
The $k$-median and $k$-means clustering objectives are classic objectives for modeling clustering in a metric space. Given a set of points in a metric space, the goal of the $k$-median (resp. $k$-means) problem is to find $k$ representative…
We study the problem of fairness in k-centers clustering on data with disjoint demographic groups. Specifically, this work proposes a variant of fairness which restricts each group's number of centers with both a lower bound…
A fair clustering instance is given a data set $A$ in which every point is assigned some color. Colors correspond to various protected attributes such as sex, ethnicity, or age. A fair clustering is an instance where membership of points in…
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…
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 the Max-k-diameter problem, we are given a set of points in a metric space, and the goal is to partition the input points into k parts such that the maximum pairwise distance between points in the same part of the partition is minimized.…
$k-$means Clustering requires as input the exact value of $k$, the number of clusters. Two challenges are open: (i) Is there a data-determined definition of $k$ which is provably correct and (ii) Is there a polynomial time algorithm to find…
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…
This paper studies the $k$-means++ algorithm for clustering as well as the class of $D^\ell$ sampling algorithms to which $k$-means++ belongs. It is shown that for any constant factor $\beta > 1$, selecting $\beta k$ cluster centers by…
Given two sets $S$ and $T$ of points in the plane, of total size $n$, a {many-to-many} matching between $S$ and $T$ is a set of pairs $(p,q)$ such that $p\in S$, $q\in T$ and for each $r\in S\cup T$, $r$ appears in at least one such pair.…
Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct…
We show that the popular k-means clustering algorithm (Lloyd's heuristic), used for a variety of scientific data, can result in outcomes that are unfavorable to subgroups of data (e.g., demographic groups). Such biased clusterings can have…
Traditionally, clustering algorithms focus on partitioning the data into groups of similar instances. The similarity objective, however, is not sufficient in applications where a fair-representation of the groups in terms of protected…
Clustering is a fundamental unsupervised learning problem where a dataset is partitioned into clusters that consist of nearby points in a metric space. A recent variant, fair clustering, associates a color with each point representing its…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
We present combinatorial approximation algorithms for the weighted correlation clustering problem. In this problem, we have a set of vertices and two weight values for each pair of vertices, denoting their difference and similarity. The…