Related papers: On Coreset Constructions for the Fuzzy $K$-Means P…

This paper presents an algorithm to solve the Soft k-Means problem globally. Unlike Fuzzy c-Means, Soft k-Means (SkM) has a matrix factorization-type objective and has been shown to have a close relation with the popular probability…

We study fair clustering problems in a setting where distance information is obtained from two sources: a strong oracle providing exact distances, but at a high cost, and a weak oracle providing potentially inaccurate distance estimates at…

Clustering is an extensive research area in data science. The aim of clustering is to discover groups and to identify interesting patterns in datasets. Crisp (hard) clustering considers that each data point belongs to one and only one…

K-means is an effective clustering technique used to separate similar data into groups based on initial centroids of clusters. In this paper, Normalization based K-means clustering algorithm(N-K means) is proposed. Proposed N-K means…

The $k$-median and $k$-means clustering objectives are classic objectives for modeling clustering in a metric space. Given a set of points in a metric space, the goal of the $k$-median (resp. $k$-means) problem is to find $k$ representative…

Constructing small-sized coresets for various clustering problems in different metric spaces has attracted significant attention for the past decade. A central problem in the coreset literature is to understand what is the best possible…

We design coresets for Ordered k-Median, a generalization of classical clustering problems such as k-Median and k-Center, that offers a more flexible data analysis, like easily combining multiple objectives (e.g., to increase fairness or…

K-means is one of the most widely used algorithms for clustering in Data Mining applications, which attempts to minimize the sum of the square of the Euclidean distance of the points in the clusters from the respective means of the…

Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…

This paper considers $k$-means clustering in the presence of noise. It is known that $k$-means clustering is highly sensitive to noise, and thus noise should be removed to obtain a quality solution. A popular formulation of this problem is…

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…

In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…

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…

Designing coresets--small-space sketches of the data preserving cost of the solutions within $(1\pm \epsilon)$-approximate factor--is an important research direction in the study of center-based $k$-clustering problems, such as $k$-means or…

The k-means method is one of the most widely used clustering algorithms, drawing its popularity from its speed in practice. Recently, however, it was shown to have exponential worst-case running time. In order to close the gap between…

The research interest of this paper is focused on the efficient clustering task for an arbitrary color data. In order to tackle this problem, we have tried to model the inherent uncertainty and vagueness of color data using fuzzy color…

Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…

Clustering of data points in metric space is among the most fundamental problems in computer science with plenty of applications in data mining, information retrieval and machine learning. Due to the necessity of clustering of large…

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

The Lloyd-Max algorithm is a classical approach to perform K-means clustering. Unfortunately, its cost becomes prohibitive as the training dataset grows large. We propose a compressive version of K-means (CKM), that estimates cluster…