Related papers: Recovery guarantees for exemplar-based clustering

Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…

We consider the problem of clustering in the learning-augmented setting, where we are given a data set in $d$-dimensional Euclidean space, and a label for each data point given by an oracle indicating what subsets of points should be…

The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been…

Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…

We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…

Motivated by the increasing availability of low- and mixed-precision arithmetic on modern hardware, we develop mixed-precision variants of Lloyd's algorithm for k-means clustering. The main ingredient is a family of mixed-precision kernels…

Clustering is one of the most important unsupervised problems in machine learning and statistics. Among many existing algorithms, kernel k-means has drawn much research attention due to its ability to find non-linear cluster boundaries and…

Sample reuse techniques have significantly reduced the numerical complexity of probabilistic robustness analysis. Existing results show that for a nested collection of hyper-spheres the complexity of the problem of performing $N$ equivalent…

Random restart of a given algorithm produces many partitions to yield a consensus clustering. Ensemble methods such as consensus clustering have been recognized as more robust approaches for data clustering than single clustering…

Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…

Convex clustering is an attractive clustering algorithm with favorable properties such as efficiency and optimality owing to its convex formulation. It is thought to generalize both k-means clustering and agglomerative clustering. However,…

We consider the problem of testing for a difference in means between clusters of observations identified via k-means clustering. In this setting, classical hypothesis tests lead to an inflated Type I error rate. To overcome this problem, we…

Over the last few years Explainable Clustering has gathered a lot of attention. Dasgupta et al. [ICML'20] initiated the study of explainable $k$-means and $k$-median clustering problems where the explanation is captured by a threshold…

Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…

Determining the number of clusters is a fundamental issue in data clustering. Several algorithms have been proposed, including centroid-based algorithms using the Euclidean distance and model-based algorithms using a mixture of probability…

We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight,…

We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

We introduce the ratio-cut polytope defined as the convex hull of ratio-cut vectors corresponding to all partitions of $n$ points in $\mathbb R^m$ into at most $K$ clusters. This polytope is closely related to the convex hull of the…

Quick Shift is a popular mode-seeking and clustering algorithm. We present finite sample statistical consistency guarantees for Quick Shift on mode and cluster recovery under mild distributional assumptions. We then apply our results to…