Related papers: Fast approximate $\ell$-center clustering in high …

$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…

We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the…

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable…

$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are…

In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…

This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…

The k-means objective is arguably the most widely-used cost function for modeling clustering tasks in a metric space. In practice and historically, k-means is thought of in a continuous setting, namely where the centers can be located…

The failure of the Euclidean norm to reliably distinguish between nearby and distant points in high dimensional space is well-known. This phenomenon of distance concentration manifests in a variety of data distributions, with iid or…

Clustering high-dimensional data is especially challenging when cluster distributions are heavy tailed and only approximately elliptical. Existing high-dimensional methods are largely built for Gaussian or other light-tailed models, whereas…

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…

We initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…

Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along…

This paper studies the large-scale subspace clustering (LSSC) problem with million data points. Many popular subspace clustering methods cannot directly handle the LSSC problem although they have been considered as state-of-the-art methods…

We provide efficient constant factor approximation algorithms for the problems of finding a hierarchical clustering of a point set in any metric space, minimizing the sum of minimimum spanning tree lengths within each cluster, and in the…

Clustering is a basic task in data analysis and machine learning, and the optimization of clustering objectives are well-studied optimization problems; amongst these, the $k$-Means objective is arguably the most well known. Given a…

We present a new technique for visualizing high-dimensional data called cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality reduction methods: preserving both local and global structures of the original sample in a…

For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least…

Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…

We give an efficient algorithm for Centroid-Linkage Hierarchical Agglomerative Clustering (HAC), which computes a $c$-approximate clustering in roughly $n^{1+O(1/c^2)}$ time. We obtain our result by combining a new Centroid-Linkage HAC…