Clustering is an essential data mining tool that aims to discover inherent cluster structure in
data. For most applications, applying clustering is only appropriate when cluster structure is …

Hierarchical clustering is a recursive partitioning of a dataset into clusters at an increasingly
finer granularity. Motivated by the fact that most work on hierarchical clustering was based …

Clustering is a classic topic in optimization with k-means being one of the most fundamental
such problems. In the absence of any restrictions on the input, the best-known algorithm for k …

We investigate variants of Lloyd's heuristic for clustering high-dimensional data in an attempt
to explain its popularity (a half century after its introduction) among practitioners, and in …

We present a novel approximation algorithm for k-median that achieves an approximation
guarantee of 1+√ 3+ ε, improving upon the decade-old ratio of 3+ ε. Our approach is based …

We give the first polynomial-time approximation schemes (PTASs) for the following
problems:(1) uniform facility location in edge-weighted planar graphs;(2) k-median and k …

Motivated by data analysis and machine learning applications, we consider the popular high-
dimensional Euclidean k-median and k-means problems. We propose a new primal-dual …

In this paper, we present a new iterative rounding framework for many clustering problems.
Using this, we obtain an (α1+ є≤ 7.081+ є)-approximation algorithm for k-median with …

The most well-known and ubiquitous clustering problem encountered in nearly every branch
of science is undoubtedly k-means: given a set of data points and a parameter k, select k …

The k-means algorithm is one of the most widely used clustering heuristics. Despite its
simplicity, analyzing its running time and quality of approximation is surprisingly difficult and …