Related papers: Near-Optimal Clustering in the $k$-machine model
Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…
Recently, due to an increasing interest for transparency in artificial intelligence, several methods of explainable machine learning have been developed with the simultaneous goal of accuracy and interpretability by humans. In this paper,…
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"…
In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and…
We study $k$-clustering problems with lower bounds, including $k$-median and $k$-means clustering with lower bounds. In addition to the point set $P$ and the number of centers $k$, a $k$-clustering problem with (uniform) lower bounds gets a…
\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,…
We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the…
Center-based clustering techniques are fundamental in some areas of machine learning such as data summarization. Generic $k$-center algorithms can produce biased cluster representatives so there has been a recent interest in fair $k$-center…
Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering…
$k$-center is one of the most popular clustering models. While it admits a simple 2-approximation in polynomial time in general metrics, the Euclidean version is NP-hard to approximate within a factor of 1.93, even in the plane, if one…
We study the $k$-median with discounts problem, wherein we are given clients with non-negative discounts and seek to open at most $k$ facilities. The goal is to minimize the sum of distances from each client to its nearest open facility…
The $K$-nearest neighbors is a basic problem in machine learning with numerous applications. In this problem, given a (training) set of $n$ data points with labels and a query point $p$, we want to assign a label to $p$ based on the labels…
Clustering with capacity constraints is a fundamental problem that attracted significant attention throughout the years. In this paper, we give the first FPT constant-factor approximation algorithm for the problem of clustering points in a…
We study the $k$-center problem in the context of individual fairness. Let $P$ be a set of $n$ points in a metric space and $r_x$ be the distance between $x \in P$ and its $\lceil n/k \rceil$-th nearest neighbor. The problem asks to…
We study the consistent k-center clustering problem. In this problem, the goal is to maintain a constant factor approximate $k$-center solution during a sequence of $n$ point insertions and deletions while minimizing the recourse, i.e., the…
We consider the classical $k$-means clustering problem in the setting bi-criteria approximation, in which an algoithm is allowed to output $\beta k > k$ clusters, and must produce a clustering with cost at most $\alpha$ times the to the…
We study the classical metric $k$-median clustering problem over a set of input rankings (i.e., permutations), which has myriad applications, from social-choice theory to web search and databases. A folklore algorithm provides a…
In real applications, database systems should be able to manage and process data with uncertainty. Any real dataset may have missing or rounded values, also the values of data may change by time. So, it becomes important to handle these…
Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any…
Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the…