Related papers: Fast and Accurate $k$-means++ via Rejection Sampli…

We introduce an evolutionary algorithm called recombinator-$k$-means for optimizing the highly non-convex kmeans problem. Its defining feature is that its crossover step involves all the members of the current generation, stochastically…

There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between…

k-means has recently been recognized as one of the best algorithms for clustering unsupervised data. Since k-means depends mainly on distance calculation between all data points and the centers, the time cost will be high when the size of…

We consider the problem of clustering a sample of probability distributions from a random distribution on $\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing…

We propose a new algorithm for k-means clustering in a distributed setting, where the data is distributed across many machines, and a coordinator communicates with these machines to calculate the output clustering. Our algorithm guarantees…

The k-means++ algorithm of Arthur and Vassilvitskii (SODA 2007) is a state-of-the-art algorithm for solving the k-means clustering problem and is known to give an O(log k)-approximation in expectation. Recently, Lattanzi and Sohler (ICML…

Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…

This paper investigates the capability of correctly recovering well-separated clusters by various brands of the $k$-means algorithm. The concept of well-separatedness used here is derived directly from the common definition of clusters,…

Since its introduction in 1957, Lloyd's algorithm for $k$-means clustering has been extensively studied and has undergone several improvements. While in its original form it does not guarantee any approximation factor at all, Arthur and…

Kernel $k$-means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear $k$-means clustering algorithm. However, kernel $k$-means clustering is computationally expensive when the…

$k$-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,…

We present a new clustering algorithm called k-means-u* which in many cases is able to significantly improve the clusterings found by k-means++, the current de-facto standard for clustering in Euclidean spaces. First we introduce the…

Clustering is one of the most fundamental tools in the artificial intelligence area, particularly in the pattern recognition and learning theory. In this paper, we propose a simple, but novel approach for variance-based k-clustering tasks,…

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 $k$-means with a provable guarantee is a simple…

Bateni et al. has recently introduced the weak-strong distance oracle model to study clustering problems in settings with limited distance information. Given query access to the strong-oracle and weak-oracle in the weak-strong oracle model,…

We propose k^2-means, a new clustering method which efficiently copes with large numbers of clusters and achieves low energy solutions. k^2-means builds upon the standard k-means (Lloyd's algorithm) and combines a new strategy to accelerate…

Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of…

The k-means algorithm is one of the most common clustering algorithms and widely used in data mining and pattern recognition. The increasing computational requirement of big data applications makes hardware acceleration for the k-means…

Being robust to the presence of outliers is crucial for applying clustering algorithms in practice. In the $\textit{robust $k$-Means}$ problem (i.e., $k$-Means with outliers), the goal is to remove $z$ outliers and minimize the $k$-Means…

In this paper, we propose an acceleration of the exact k-means++ algorithm using geometric information, specifically the Triangle Inequality and additional norm filters, along with a two-step sampling procedure. Our experiments demonstrate…