Given a set of $ n $ points in $ d $ dimensions, the Euclidean $ k $-means problem (resp.
Euclidean $ k $-median) consists of finding $ k $ centers such that the sum of squared …

Given a metric space, the (k, z)-clustering problem consists of finding k centers such that the
sum of the of distances raised to the power z of every point to its closest center is minimized …

The (k, z)-clustering problem consists of finding a set of k points called centers, such that the
sum of distances raised to the power of z of every data point to its closest center is …

Motivated by practical generalizations of the classic k-median and k-means objectives, such
as clustering with size constraints, fair clustering, and Wasserstein barycenter, we introduce …

Given a collection of n points in ℝ d, the goal of the (k, z)-clustering problem is to find a
subset of k “centers” that minimizes the sum of the z-th powers of the Euclidean distance of …

In this paper, we consider the problem of finding high dimensional power means: given a set
$ A $ of $ n $ points in $\R^ d $, find the point $ m $ that minimizes the sum of Euclidean …

We show that for n points in d-dimensional Euclidean space, a data oblivious random
projection of the columns onto m∈ O ((log k+ loglog n) ε− 6log1/ε) dimensions is sufficient to …

Clustering is an important technique for identifying structural information in large-scale data
analysis, where the underlying dataset may be too large to store. In many applications …

We study the complexity of the classic capacitated k-median and k-means problems
parameterized by the number of centers, k. These problems are notoriously difficult since the …

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 …