Related papers: Algorithms for finding $k$ in $k$-means

Center-based clustering is a fundamental primitive for data analysis and becomes very challenging for large datasets. In this paper, we focus on the popular $k$-center variant which, given a set $S$ of points from some metric space and a…

We present an asymptotic criterion to determine the optimal number of clusters in k-means. We consider k-means as data compression, and propose to adopt the number of clusters that minimizes the estimated description length after…

Application of K-Means algorithm is restricted by the fact that the number of clusters should be known beforehand. Previously suggested methods to solve this problem are either ad hoc or require parametric assumptions and complicated…

Clustering is an essential task to unsupervised learning. It tries to automatically separate instances into coherent subsets. As one of the most well-known clustering algorithms, k-means assigns sample points at the boundary to a unique…

We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task?…

In the Max-k-diameter problem, we are given a set of points in a metric space, and the goal is to partition the input points into k parts such that the maximum pairwise distance between points in the same part of the partition is minimized.…

The metric $k$-median problem is a textbook clustering problem. As input, we are given a metric space $V$ of size $n$ and an integer $k$, and our task is to find a subset $S \subseteq V$ of at most $k$ `centers' that minimizes the total…

The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is…

In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…

Mixed datasets consist of both numeric and categorical attributes. Various k-means-based clustering algorithms have been developed for these datasets. Generally, these algorithms use random partition as a starting point, which tends to…

Many clustering methods, including k-means, require the user to specify the number of clusters as an input parameter. A variety of methods have been devised to choose the number of clusters automatically, but they often rely on strong…

The most well known and ubiquitous clustering problem encountered in nearly every branch of science is undoubtedly $k$-means: given a set of data points and a parameter $k$, select $k$ centres and partition the data points into $k$ clusters…

Data summarization tasks are often modeled as $k$-clustering problems, where the goal is to choose $k$ data points, called cluster centers, that best represent the dataset by minimizing a clustering objective. A popular objective is to…

The purpose of this paper is to improve the traditional K-means algorithm. In the traditional K mean clustering algorithm, the initial clustering centers are generated randomly in the data set. It is easy to fall into the local minimum…

Individual fairness guarantees are often desirable properties to have, but they become hard to formalize when the dataset contains outliers. Here, we investigate the problem of developing an individually fair $k$-means clustering algorithm…

Deep learning models have become widely adopted in various domains, but their performance heavily relies on a vast amount of data. Datasets often contain a large number of irrelevant or redundant samples, which can lead to computational…

Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a…

In this paper, we propose a model-based clustering method (TVClust) that robustly incorporates noisy side information as soft-constraints and aims to seek a consensus between side information and the observed data. Our method is based on a…

The k-means clustering is one of the most popular clustering algorithms in data mining. Recently a lot of research has been concentrated on the algorithm when the dataset is divided into multiple parties or when the dataset is too large to…

Clustering is a fundamental task in unsupervised learning. Previous research has focused on learning-augmented $k$-means in Euclidean metrics, limiting its applicability to complex data representations. In this paper, we generalize…