Related papers: Uniform Concentration Bounds toward a Unified Fram…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
We study the classic $k$-means/median clustering, which are fundamental problems in unsupervised learning, in the setting where data are partitioned across multiple sites, and where we are allowed to discard a small portion of the data by…
Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study…
An important issue in clustering concerns the avoidance of false positives while searching for clusters. This work addressed this problem considering agglomerative methods, namely single, average, median, complete, centroid and Ward's…
Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…
This paper presents a unified matrix factorization framework for classical and robust clustering. We begin by revisiting the well-known equivalence between crisp k-means clustering and matrix factorization, following and rigorously…
The Median of Means (MoM) is a mean estimator that has gained popularity in the context of heavy-tailed data. In this work, we analyze its performance in the task of simultaneously estimating the mean of each function in a class…
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…
In this work, we study the $k$-median and $k$-means clustering problems when the data is distributed across many servers and can contain outliers. While there has been a lot of work on these problems for worst-case instances, we focus on…
We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables. These estimators achieve optimal rates of convergence under minimal assumptions on the dataset.…
The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…
This paper provides new algorithms for distributed clustering for two popular center-based objectives, k-median and k-means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following…
Consensus clustering aggregates partitions in order to find a better fit by reconciling clustering results from different sources/executions. In practice, there exist noise and outliers in clustering task, which, however, may significantly…
Being robust to the presence of outliers is crucial for applying clustering algorithms in practice. In the $\textit{robust $k$-Means}$ problem (i.e., $k$-Means with outliers), the goal is to remove $z$ outliers and minimize the $k$-Means…
Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
The problem of linear predictions has been extensively studied for the past century under pretty generalized frameworks. Recent advances in the robust statistics literature allow us to analyze robust versions of classical linear models…
Clustering is a fundamental tool in unsupervised learning, used to group objects by distinguishing between similar and dissimilar features of a given data set. One of the most common clustering algorithms is k-means. Unfortunately, when…
Clustering is a central tool in biomedical research for discovering heterogeneous patient subpopulations, where group boundaries are often diffuse rather than sharply separated. Traditional methods produce hard partitions, whereas soft…
The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…