Related papers: Probably certifiably correct k-means clustering

This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…

The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…

A robust clustering method for probabilities in Wasserstein space is introduced. This new "trimmed $k$-barycenters" approach relies on recent results on barycenters in Wasserstein space that allow intensive computation, as required by…

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…

Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…

Quantum Clustering is a powerful method to detect clusters in data with mixed density. However, it is very sensitive to a length parameter that is inherent to the Schr\"odinger equation. In addition, linking data points into clusters…

We consider the fundamental problem of balanced $k$-means clustering. In particular, we introduce an optimal transport approach to alternating minimization called BalLOT, and we show that it delivers a fast and effective solution to this…

Clustering is a widely used and powerful machine learning technique, but its effectiveness is often limited by the need to specify the number of clusters, k, or by relying on thresholds that implicitly determine k. We introduce k*-means, a…

We consider polynomial optimization problems on Cartesian products of basic compact semialgebraic sets. The solution of such problems can be approximated as closely as desired by hierarchies of semidefinite programming relaxations, based on…

Sum-of-norms clustering is a clustering formulation based on convex optimization that automatically induces hierarchy. Multiple algorithms have been proposed to solve the optimization problem: subgradient descent by Hocking et al., ADMM and…

$K$-means clustering is one of the most widely-used partitioning algorithm in cluster analysis due to its simplicity and computational efficiency. However, $K$-means does not provide an appropriate clustering result when applying to data…

K-means is one of the most widely used clustering algorithms in various disciplines, especially for large datasets. However the method is known to be highly sensitive to initial seed selection of cluster centers. K-means++ has been proposed…

Clustering is a fundamental problem in unsupervised learning. Popular methods like K-means, may suffer from poor performance as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as the…

We consider a network of binary-valued sensors with a fusion center. The fusion center has to perform K-means clustering on the binary data transmitted by the sensors. In order to reduce the amount of data transmitted within the network,…

Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the…

Finding the number of meaningful clusters in an unlabeled dataset is important in many applications. Regularized k-means algorithm is a possible approach frequently used to find the correct number of distinct clusters in datasets. The most…

We introduce the ratio-cut polytope defined as the convex hull of ratio-cut vectors corresponding to all partitions of $n$ points in $\mathbb R^m$ into at most $K$ clusters. This polytope is closely related to the convex hull of the…

Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper…

In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and…

Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any…