Related papers: On Optimal Coreset Construction for Euclidean $(k,…
Coresets are among the most popular paradigms for summarizing data. In particular, there exist many high performance coresets for clustering problems such as $k$-means in both theory and practice. Curiously, there exists no work on…
In a geometric $k$-clustering problem the goal is to partition a set of points in $\mathbb{R}^d$ into $k$ subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering…
In this paper, we consider the $k$-center/median/means clustering with outliers problems (or the $(k, z)$-center/median/means problems) in the distributed setting. Most previous distributed algorithms have their communication costs linearly…
The Euclidean $k$-center problem is a classical problem that has been extensively studied in computer science. Given a set $\mathcal{G}$ of $n$ points in Euclidean space, the problem is to determine a set $\mathcal{C}$ of $k$ centers (not…
We study the complexity of geometric problems on spaces of low fractal dimension. It was recently shown by [Sidiropoulos & Sridhar, SoCG 2017] that several problems admit improved solutions when the input is a pointset in Euclidean space…
We consider the problem of approximate $K$-means clustering with outliers and side information provided by same-cluster queries and possibly noisy answers. Our solution shows that, under some mild assumptions on the smallest cluster size,…
Bayesian coresets speed up posterior inference in the large-scale data regime by approximating the full-data log-likelihood function with a surrogate log-likelihood based on a small, weighted subset of the data. But while Bayesian coresets…
One of the most popular algorithms for clustering in Euclidean space is the $k$-means algorithm; $k$-means is difficult to analyze mathematically, and few theoretical guarantees are known about it, particularly when the data is {\em…
We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors facilitating…
The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes…
An $\varepsilon$-coreset for Least-Mean-Squares (LMS) of a matrix $A\in{\mathbb{R}}^{n\times d}$ is a small weighted subset of its rows that approximates the sum of squared distances from its rows to every affine $k$-dimensional subspace of…
In the (continuous) Euclidean $k$-center problem, given $n$ points in $\mathbb{R}^d$ and an integer $k$, the goal is to find $k$ center points in $\mathbb{R}^d$ that minimize the maximum Euclidean distance from any input point to its…
Motivated by an application from geodesy, we introduce a novel clustering problem which is a $k$-center (or k-diameter) problem with a side constraint. For the side constraint, we are given an undirected connectivity graph $G$ on the input…
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 consider the classic $k$-center problem {in the constant dimensional Euclidean space} under a parallel setting, on the low-local-space Massively Parallel Computation (MPC) model, with local space per machine of ${O}(n^{\delta})$, where…
We introduce a new $(\epsilon_p, \delta_p)$-differentially private algorithm for the $k$-means clustering problem. Given a dataset in Euclidean space, the $k$-means clustering problem requires one to find $k$ points in that space such that…
Motivated by many applications, we study clustering with a faulty oracle. In this problem, there are $n$ items belonging to $k$ unknown clusters, and the algorithm is allowed to ask the oracle whether two items belong to the same cluster or…
We present the first algorithm for fully dynamic $k$-centers clustering in an arbitrary metric space that maintains an optimal $2+\epsilon$ approximation in $O(k \cdot \operatorname{polylog}(n,\Delta))$ amortized update time. Here, $n$ is…
We study fair clustering problems in a setting where distance information is obtained from two sources: a strong oracle providing exact distances, but at a high cost, and a weak oracle providing potentially inaccurate distance estimates at…
Given a set of points in $d$-dimensional space, an explainable clustering is one where the clusters are specified by a tree of axis-aligned threshold cuts. Dasgupta et al. (ICML 2020) posed the question of the price of explainability: the…