Related papers: Hamiltonian formulations of centroid-based cluster…

Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…

$k$-means clustering is NP-hard in the worst case but previous work has shown efficient algorithms assuming the optimal $k$-means clusters are \emph{stable} under additive or multiplicative perturbation of data. This has two caveats. First,…

$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…

Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…

We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior combinatorial optimization…

In correlation clustering, we are given $n$ objects together with a binary similarity score between each pair of them. The goal is to partition the objects into clusters so to minimise the disagreements with the scores. In this work we…

Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together. Among various clustering methods, the Minimum Sum-of-Squares Clustering (MSSC) is one of the most widely used. MSSC…

Currently, data-driven discovery in biological sciences resides in finding segmentation strategies in multivariate data that produce sensible descriptions of the data. Clustering is but one of several approaches and sometimes falls short…

The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…

Numerous papers ask how difficult it is to cluster data. We suggest that the more relevant and interesting question is how difficult it is to cluster data sets {\em that can be clustered well}. More generally, despite the ubiquity and the…

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 on providing algorithms, rather than optimizing a…

Clustering is a fundamental analysis tool aiming at classifying data points into groups based on their similarity or distance. It has found successful applications in all natural and social sciences, including biology, physics, economics,…

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…

A key issue in cluster analysis is the choice of an appropriate clustering method and the determination of the best number of clusters. Different clusterings are optimal on the same data set according to different criteria, and the choice…

Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…

Advances made to the traditional clustering algorithms solves the various problems such as curse of dimensionality and sparsity of data for multiple attributes. The traditional H-K clustering algorithm can solve the randomness and apriority…

Fast and high quality document clustering is an important task in organizing information, search engine results obtaining from user query, enhancing web crawling and information retrieval. With the large amount of data available and with a…

Clustering data objects into homogeneous groups is one of the most important tasks in data mining. Spectral clustering is arguably one of the most important algorithms for clustering, as it is appealing for its theoretical soundness and is…

Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of $n$ agents located in an underlying metric space, our goal is to partition them into $k$ clusters,…