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This paper presents a thorough evaluation of the existing methods that accelerate Lloyd's algorithm for fast k-means clustering. To do so, we analyze the pruning mechanisms of existing methods, and summarize their common pipeline into a…
There is no, nor will there ever be, single best clustering algorithm. Nevertheless, we would still like to be able to distinguish between methods that work well on certain task types and those that systematically underperform. Clustering…
The $k$-means is a popular clustering objective, although it is inherently non-robust and sensitive to outliers. Its popular seeding or initialization called $k$-means++ uses $D^{2}$ sampling and comes with a provable $O(\log k)$…
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…
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…
We study anomaly clustering, grouping data into coherent clusters of anomaly types. This is different from anomaly detection that aims to divide anomalies from normal data. Unlike object-centered image clustering, anomaly clustering is…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
The recent framework of compressive statistical learning aims at designing tractable learning algorithms that use only a heavily compressed representation-or sketch-of massive datasets. Compressive K-Means (CKM) is such a method: it…
Deep image clustering methods are typically evaluated on small-scale balanced classification datasets while feature-based $k$-means has been applied on proprietary billion-scale datasets. In this work, we explore the performance of…
In sensor networks, it is not always practical to set up a fusion center. Therefore, there is need for fully decentralized clustering algorithms. Decentralized clustering algorithms should minimize the amount of data exchanged between…
We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number…
We propose a graph-based clustering method based on Cluster Catch Digraphs (CCDs) that extends their applicability to moderate-dimensional data settings. Existing CCD variants, such as RK-CCDs, rely on spatial randomness tests based on…
Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and…
The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its…
Density-based clustering methods often surpass centroid-based counterparts, when addressing data with noise or arbitrary data distributions common in real-world problems. In this study, we reveal a key property intrinsic to density-based…
Centroid-based clustering algorithms, such as hard K-means (HKM) and fuzzy K-means (FKM), have suffered from learning bias towards large clusters. Their centroids tend to be crowded in large clusters, compromising performance when the true…
We propose efficient algorithms for two key tasks in the analysis of large nonuniform networks: uniform node sampling and cluster detection. Our sampling technique is based on augmenting a simple, but slowly mixing uniform MCMC sampler with…
Existing approaches remain largely constrained by traditional distance metrics, limiting their effectiveness in handling random data. In this work, we introduce the first k-means variant in the literature that operates within a…
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.…
The fairness of clustering algorithms has gained widespread attention across various areas, including machine learning, In this paper, we study fair $k$-means clustering in Euclidean space. Given a dataset comprising several groups, the…