Related papers: Label-consistent clustering for evolving data
In this paper we give the first efficient algorithms for the $k$-center problem on dynamic graphs undergoing edge updates. In this problem, the goal is to partition the input into $k$ sets by choosing $k$ centers such that the maximum…
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…
Common clustering algorithms require multiple scans of all the data to achieve convergence, and this is prohibitive when large databases, with data arriving in streams, must be processed. Some algorithms to extend the popular K-means method…
In the standard planar $k$-center clustering problem, one is given a set $P$ of $n$ points in the plane, and the goal is to select $k$ center points, so as to minimize the maximum distance over points in $P$ to their nearest center. Here we…
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…
Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously…
Estimating the number of clusters (K) is a critical and often difficult task in cluster analysis. Many methods have been proposed to estimate K, including some top performers using resampling approach. When performing cluster analysis in…
Fair clustering enjoyed a surge of interest recently. One appealing way of integrating fairness aspects into classical clustering problems is by introducing multiple covering constraints. This is a natural generalization of the robust (or…
We consider the approximability of center-based clustering problems where the points to be clustered lie in a metric space, and no candidate centers are specified. We call such problems "continuous", to distinguish from "discrete"…
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…
We study discrete k-clustering problems in general metric spaces that are constrained by a combination of two different fairness conditions within the demographic fairness model. Given a metric space (P,d), where every point in P is…
Many approximation algorithms and heuristic algorithms to find a fair clustering have emerged. In this paper we define a new and natural variant of fair clustering problem and design a polynomial time algorithm to compute an optimal fair…
\textit{Clustering problems} often arise in the fields like data mining, machine learning etc. to group a collection of objects into similar groups with respect to a similarity (or dissimilarity) measure. Among the clustering problems,…
The $k$-means algorithm is a prevalent clustering method due to its simplicity, effectiveness, and speed. However, its main disadvantage is its high sensitivity to the initial positions of the cluster centers. The global $k$-means is a…
An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius \r{ho} such that there exist…
Fast and high quality document clustering is an important task in organizing information, search engine results obtaining from user query, enhancing web crawling and information retrieval. With the large amount of data available and with a…
The problem of data clustering is one of the most important in data analysis. It can be problematic when dealing with experimental data characterized by measurement uncertainties and errors. Our paper proposes a recursive scheme for…
In this paper, we study the fundamental problems of maintaining the diameter and a $k$-center clustering of a dynamic point set $P \subset \mathbb{R}^d$, where points may be inserted or deleted over time and the ambient dimension $d$ is not…
We study the fair variant of the classic $k$-median problem introduced by Chierichetti et al. [2017]. In the standard $k$-median problem, given an input pointset $P$, the goal is to find $k$ centers $C$ and assign each input point to one of…