Clustering with Label Consistency

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 real-world need for stable point labels, i.e., stable assignments of points to named sets (clusters). In this paper, we address this gap by initiating the study of label-consistent metric clustering. We first introduce a new notion of consistency, measuring the label distance between two consecutive solutions. Then, armed with this new definition, we design new consistent approximation algorithms for the classical $k$-center and $k$-median problems.

Generalizing Fair Clustering to Multiple Groups: Algorithms and Applications

Clustering is a fundamental task in machine learning and data analysis, but it frequently fails to provide fair representation for various marginalized communities defined by multiple protected attributes -- a shortcoming often caused by biases in the training data. As a result, there is a growing need to enhance the fairness of clustering outcomes, ideally by making minimal modifications, possibly as a post-processing step after conventional clustering. Recently, Chakraborty et al. [COLT'25] initiated the study of \emph{closest fair clustering}, though in a restricted scenario where data points belong to only two groups. In practice, however, data points are typically characterized by many groups, reflecting diverse protected attributes such as age, ethnicity, gender, etc. In this work, we generalize the study of the \emph{closest fair clustering} problem to settings with an arbitrary number (more than two) of groups. We begin by showing that the problem is NP-hard even when all groups are of equal size -- a stark contrast with the two-group case, for which an exact algorithm exists. Next, we propose near-linear time approximation algorithms that efficiently handle arbitrary-sized multiple groups, thereby answering an open question posed by Chakraborty et al. [COLT'25]. Leveraging our closest fair clustering algorithms, we further achieve improved approximation guarantees for the \emph{fair correlation clustering} problem, advancing the state-of-the-art results established by Ahmadian et al. [AISTATS'20] and Ahmadi et al. [2020]. Additionally, we are the first to provide approximation algorithms for the \emph{fair consensus clustering} problem involving multiple (more than two) groups, thus addressing another open direction highlighted by Chakraborty et al. [COLT'25].

Towards Fair Representation: Clustering and Consensus

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 represents the collective structure of the data. In this work, we study this fundamental problem through the lens of fair clustering, as introduced by Chierichetti et al. [NeurIPS'17], which incorporates the disparate impact doctrine to ensure proportional representation of each protected group in the dataset within every cluster. Our objective is to find a consensus clustering that is not only representative but also fair with respect to specific protected attributes. To the best of our knowledge, we are the first to address this problem and provide a constant-factor approximation. As part of our investigation, we examine how to minimally modify an existing clustering to enforce fairness -- an essential postprocessing step in many clustering applications that require fair representation. We develop an optimal algorithm for datasets with equal group representation and near-linear time constant factor approximation algorithms for more general scenarios with different proportions of two group sizes. We complement our approximation result by showing that the problem is NP-hard for two unequal-sized groups. Given the fundamental nature of this problem, we believe our results on Closest Fair Clustering could have broader implications for other clustering problems, particularly those for which no prior approximation guarantees exist for their fair variants.