Related papers: Faster Coreset Construction for Projective Cluster…
We demonstrate an implementation for an approximate rank-k SVD factorization, combining well-known randomized projection techniques with previously known paralel solutions in order to compute steps of the random projection based SVD…
Constructing a similarity graph from a set $X$ of data points in $\mathbb{R}^d$ is the first step of many modern clustering algorithms. However, typical constructions of a similarity graph have high time complexity, and a quadratic space…
We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for…
A coreset for a set of points is a small subset of weighted points that approximately preserves important properties of the original set. Specifically, if $P$ is a set of points, $Q$ is a set of queries, and $f:P\times Q\to\mathbb{R}$ is a…
$\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}} \newcommand{\eps}{{\varepsilon}} \newcommand{\Coreset}{{\mathcal{S}}} $ In this paper, we show the existence of small coresets for the problems of computing $k$-median and $k$-means…
We develop and analyze a method to reduce the size of a very large set of data points in a high dimensional Euclidean space R d to a small set of weighted points such that the result of a predetermined data analysis task on the reduced set…
In a recent work, [19] studied the following "fair" variants of classical clustering problems such as $k$-means and $k$-median: given a set of $n$ data points in $\mathbb{R}^d$ and a binary type associated to each data point, the goal is to…
We present algorithms for the computation of $\varepsilon$-coresets for $k$-median clustering of point sequences in $\mathbb{R}^d$ under the $p$-dynamic time warping (DTW) distance. Coresets under DTW have not been investigated before, and…
A \emph{strong coreset} for the mean queries of a set $P$ in ${\mathbb{R}}^d$ is a small weighted subset $C\subseteq P$, which provably approximates its sum of squared distances to any center (point) $x\in {\mathbb{R}}^d$. A \emph{weak…
Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably…
Finding a good clustering of vertices in a network, where vertices in the same cluster are more tightly connected than those in different clusters, is a useful, important, and well-studied task. Many clustering algorithms scale well,…
In this paper we are going to introduce a new nearest neighbours based approach to clustering, and compare it with previous solutions; the resulting algorithm, which takes inspiration from both DBscan and minimum spanning tree approaches,…
Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster…
In computer vision, the estimation of the fundamental matrix is a basic problem that has been extensively studied. The accuracy of the estimation imposes a significant influence on subsequent tasks such as the camera trajectory…
We study coresets for clustering with capacity and fairness constraints. Our main result is a near-linear time algorithm to construct $\tilde{O}(k^2\varepsilon^{-2z-2})$-sized $\varepsilon$-coresets for capacitated $(k,z)$-clustering which…
We investigate coresets - succinct, small summaries of large data sets - so that solutions found on the summary are provably competitive with solution found on the full data set. We provide an overview over the state-of-the-art in coreset…
We study the theoretical and practical runtime limits of k-means and k-median clustering on large datasets. Since effectively all clustering methods are slower than the time it takes to read the dataset, the fastest approach is to quickly…
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…
Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…