Related papers: Faster Clustering via Preprocessing

We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…

Clustering ensemble is one of the most recent advances in unsupervised learning. It aims to combine the clustering results obtained using different algorithms or from different runs of the same clustering algorithm for the same data set,…

Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…

$k$-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,…

This paper presents universal algorithms for clustering problems, including the widely studied $k$-median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must…

Two important optimization problems in the analysis of geometric data sets are clustering and sketching. Here, clustering refers to the problem of partitioning some input metric measure space (mm-space) into k clusters, minimizing some…

We provide the first coreset for clustering points in $\mathbb{R}^d$ that have multiple missing values (coordinates). Previous coreset constructions only allow one missing coordinate. The challenge in this setting is that objective…

Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…

K-means plays a vital role in data mining and is the simplest and most widely used algorithm under the Euclidean Minimum Sum-of-Squares Clustering (MSSC) model. However, its performance drastically drops when applied to vast amounts of…

Inferring cluster structure in microarray datasets is a fundamental task for the -omic sciences. A fundamental question in Statistics, Data Analysis and Classification, is the prediction of the number of clusters in a dataset, usually…

In this short communication we introduce the quick clustering algorithm (QUIST), an efficient hierarchical clustering algorithm based on sorting. QUIST is a poly-logarithmic divisive clustering algorithm that does not assume the number of…

In this brief paper, we go through the theoretical steps of the spectral clustering on quantum computers by employing the phase estimation and the amplitude amplification algorithms. We discuss circuit designs for each step and show how to…

Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering…

We study two generalizations of classic clustering problems called dynamic ordered $k$-median and dynamic $k$-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between…

This paper introduces k-splits, an improved hierarchical algorithm based on k-means to cluster data without prior knowledge of the number of clusters. K-splits starts from a small number of clusters and uses the most significant data…

Though mostly used as a clustering algorithm, k-means are originally designed as a quantization algorithm. Namely, it aims at providing a compression of a probability distribution with k points. Building upon [21, 33], we try to investigate…

Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused…

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…

There has been considerable work on improving popular clustering algorithm `K-means' in terms of mean squared error (MSE) and speed, both. However, most of the k-means variants tend to compute distance of each data point to each cluster…

Center-based clustering (e.g., $k$-means, $k$-medians) and clustering using linear subspaces are two most popular techniques to partition real-world data into smaller clusters. However, when the data consists of sensitive demographic…