Related papers: Fuzzy Clustering with Similarity Queries

Recent advances in center-based clustering continue to improve upon the drawbacks of Lloyd's celebrated $k$-means algorithm over $60$ years after its introduction. Various methods seek to address poor local minima, sensitivity to outliers,…

Gaussian mixture models (GMM) are the most widely used statistical model for the $k$-means clustering problem and form a popular framework for clustering in machine learning and data analysis. In this paper, we propose a natural semi-random…

Clustering is an important facet of explorative data mining and finds extensive use in several fields. In this paper, we propose an extension of the classical Fuzzy C-Means clustering algorithm. The proposed algorithm, abbreviated as VFC,…

Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption…

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…

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…

Clustering is a key task in machine learning, with $k$-means being widely used for its simplicity and effectiveness. While 1D clustering is common, existing methods often fail to exploit the structure of 1D data, leading to inefficiencies.…

Clustering is one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\dots,v_n]\in\mathbb{R}^{d\times…

We study in this paper the problem of maintaining a solution to $k$-median and $k$-means clustering in a fully dynamic setting. To do so, we present an algorithm to efficiently maintain a coreset, a compressed version of the dataset, that…

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…

Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct…

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…

Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the…

K-means -- and the celebrated Lloyd algorithm -- is more than the clustering method it was originally designed to be. It has indeed proven pivotal to help increase the speed of many machine learning and data analysis techniques such as…

The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown…

Metric based comparison operations such as finding maximum, nearest and farthest neighbor are fundamental to studying various clustering techniques such as $k$-center clustering and agglomerative hierarchical clustering. These techniques…

We present a $k$-means-based clustering algorithm, which optimizes the mean square error, for given cluster sizes. A straightforward application is balanced clustering, where the sizes of each cluster are equal. In the $k$-means assignment…

Metric $k$-center clustering is a fundamental unsupervised learning primitive. Although widely used, this primitive is heavily affected by noise in the data, so that a more sensible variant seeks for the best solution that disregards a…

Given a point set S and an unknown metric d on S, we study the problem of efficiently partitioning S into k clusters while querying few distances between the points. In our model we assume that we have access to one versus all queries that…

Correlation clustering is a flexible framework for partitioning data based solely on pairwise similarity or dissimilarity information, without requiring the number of clusters as input. However, in many practical scenarios, these pairwise…