Related papers: Fixed-sized clusters $k$-Means

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…

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…

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…

We study the fair variant of the classic $k$-median problem introduced by Chierichetti et al. [2017]. In the standard $k$-median problem, given an input pointset $P$, the goal is to find $k$ centers $C$ and assign each input point to one of…

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…

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…

We investigate $k$-means clustering in the online no-substitution setting when the input arrives in \emph{arbitrary} order. In this setting, points arrive one after another, and the algorithm is required to instantly decide whether to take…

Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…

Clustering is one of the widely used techniques to find out patterns from a dataset that can be applied in different applications or analyses. K-means, the most popular and simple clustering algorithm, might get trapped into local minima if…

Minimum sum-of-squares clustering (MSSC) is a widely used clustering model, of which the popular K-means algorithm constitutes a local minimizer. It is well known that the solutions of K-means can be arbitrarily distant from the true MSSC…

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…

As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…

This paper considers the well-studied algorithmic regime of designing a $(1+\epsilon)$-approximation algorithm for a $k$-clustering problem that runs in time $f(k,\epsilon)poly(n)$ (sometimes called an efficient parameterized approximation…

We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…

Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in…

This problem was solved within the framework of the grant project "Solving of problems of cluster analysis with application of parallel algorithms and cloud technologies" in the Institute of Mathematics and Mathematical Modelling in Almaty.…

Traditional k-means clustering underperforms on non-convex shapes and requires the number of clusters k to be specified in advance. We propose a simple geometric enhancement: after standard k-means, each cluster center is assigned a radius…

Big Data is a massive volume of both structured and unstructured data that is too large and it also difficult to process using traditional techniques. Clustering algorithms have developed as a powerful learning tool that can exactly analyze…

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…

Cluster analysis plays an important role in decision making process for many knowledge-based systems. There exist a wide variety of different approaches for clustering applications including the heuristic techniques, probabilistic models,…