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Consensus clustering, a fundamental task in machine learning and data analysis, aims to aggregate multiple input clusterings of a dataset, potentially based on different non-sensitive attributes, into a single clustering that best…
In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…
It is well known that the classical single linkage algorithm usually fails to identify clusters in the presence of outliers. In this paper, we propose a new version of this algorithm, and we study its mathematical performances. In…
We initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…
In this paper we introduce and study the online consistent $k$-clustering with outliers problem, generalizing the non-outlier version of the problem studied in [Lattanzi-Vassilvitskii, ICML17]. We show that a simple local-search based…
Clustering is an unsupervised machine learning task that consists of identifying groups of similar objects. It has numerous applications and is increasingly used in fairness-sensitive domains where objects represent individuals, such as…
Diversity is an important principle in data selection and summarization, facility location, and recommendation systems. Our work focuses on maximizing diversity in data selection, while offering fairness guarantees. In particular, we offer…
Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on fairness in machine learning and AI; one representative notion of fairness is that no single demographic group should be over-represented among…
In the Priority $k$-Supplier problem the input consists of a metric space $(F \cup C, d)$ over set of facilities $F$ and a set of clients $C$, an integer $k > 0$, and a non-negative radius $r_v$ for each client $v \in C$. The goal is to…
In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious…
We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a…
We consider the problem of approximate $K$-means clustering with outliers and side information provided by same-cluster queries and possibly noisy answers. Our solution shows that, under some mild assumptions on the smallest cluster size,…
The fair $k$-median problem is one of the important clustering problems. The current best approximation ratio is 4.675 for this problem with 1-fair violation, which was proposed by Bercea et al. [APPROX-RANDOM'2019]. As far as we know,…
We consider clustering in the perturbation resilience model that has been studied since the work of Bilu and Linial [ICS, 2010] and Awasthi, Blum and Sheffet [Inf. Proc. Lett., 2012]. A clustering instance $I$ is said to be…
We consider the problem of whether a given decision model, working with structured data, has individual fairness. Following the work of Dwork, a model is individually biased (or unfair) if there is a pair of valid inputs which are close to…
The $k$-center problem is a classical combinatorial optimization problem which asks to find $k$ centers such that the maximum distance of any input point in a set $P$ to its assigned center is minimized. The problem allows for elegant…
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,…
Fair clustering has traditionally focused on ensuring equitable group representation or equalizing group-specific clustering costs. However, Dickerson et al. (2025) recently showed that these fairness notions may yield undesirable or…
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…
In recent years, the capacitated center problems have attracted a lot of research interest. Given a set of vertices $V$, we want to find a subset of vertices $S$, called centers, such that the maximum cluster radius is minimized. Moreover,…