Correlation Clustering (CC) is a foundational problem in unsupervised learning that models binary similarity relations using labeled graphs. While classical CC has been widely studied, many real-world applications involve more nuanced relationships, either multi-class categorical interactions or varying confidence levels in edge labels. To address these, two natural generalizations have been proposed: Chromatic Correlation Clustering, which assigns semantic colors to edge labels, and pseudometric-weighted Correlation Clustering, which allows edge weights satisfying the triangle inequality. In this paper, we develop improved approximation algorithms for both settings. Our approach leverages LP-based pivoting techniques combined with problem-specific rounding functions. For the pseudometric-weighted correlation clustering problem, we present a tight 103 approximation algorithm, matching the best possible bound achievable within the framework of standard LP relaxation combined with specialized rounding. For the Chromatic Correlation Clustering (CCC) problem, we improve the approximation ratio from the previous best of 2.5 to 2.15, and we establish a lower bound of 2.11within the same analytical framework, highlighting the near-optimality of our result.

We study streaming algorithms for Correlation Clustering. Given a graph as an arbitrary-order stream of edges, with each edge labeled as positive or negative, the goal is to partition the vertices into disjoint clusters, such that the number of disagreements is minimized. In this paper, we give the first learning-augmented streaming algorithms for the problem on both complete and general graphs, improving the best-known space-approximation tradeoffs. Based on the works of Cambus et al. (SODA'24) and Ahn et al. (ICML'15), our algorithms use the predictions of pairwise distances between vertices provided by a predictor. For complete graphs, our algorithm achieves a better-than-3 approximation under good prediction quality, while using O(n)total space. For general graphs, our algorithm achieves an O(log|E |)approximation under good prediction quality using O(n) total space, improving the best-known non-learning algorithm in terms of space efficiency. Experimental results on synthetic and real-world datasets demonstrate the superiority of our proposed algorithms over their non-learning counterparts.

Correlation Clustering (CC) is a foundational problem in unsupervised learning that models binary similarity relations using labeled graphs. While classical CC has been well studied, many real-world applications involve more nuanced relationships--either multi-class categorical interactions or varying confidence levels in edge labels. To address these, two natural generalizations have been proposed: Chromatic Correlation Clustering (CCC), which assigns semantic colors to edge labels, and pseudometric-weighted CC, which allows edge weights satisfying the triangle inequality. In this paper, we develop improved approximation algorithms for both settings. Our approach leverages LP-based pivoting techniques combined with problem-specific rounding functions. For the pseudometric-weighted correlation clustering problem, we present a tight $\frac{10}{3}$-approximation algorithm, matching the best possible bound achievable within the framework of standard LP relaxation combined with specialized rounding. For the Chromatic Correlation Clustering (CCC) problem, we improve the approximation ratio from the previous best of $2.5$ to $2.15$, and we establish a lower bound of $2.11$ within the same analytical framework, highlighting the near-optimality of our result.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

In this paper, we provide a simple single-pass streaming algorithm for Correlation Clustering.

In correlation clustering, we are given $n$ objects together with a binary similarity score between each pair of them. The goal is to partition the objects into clusters so to minimise the disagreements with the scores. In this work we investigate correlation clustering as an active learning problem: each similarity score can be learned by making a query, and the goal is to minimise both the disagreements and the total number of queries. On the one hand, we describe simple active learning algorithms, which provably achieve an almost optimal trade-off while giving cluster recovery guarantees, and we test them on different datasets. On the other hand, we prove information-theoretical bounds on the number of queries necessary to guarantee a prescribed disagreement bound. These results give a rich characterization of the trade-off between queries and clustering error.

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].

We study streaming algorithms for Correlation Clustering. Given a graph as an arbitrary-order stream of edges, with each edge labeled as positive or negative, the goal is to partition the vertices into disjoint clusters, such that the number of disagreements is minimized. In this paper, we give the first learning-augmented streaming algorithms for the problem on both complete and general graphs, improving the best-known space-approximation tradeoffs. Based on the works of Cambus et al. (SODA'24) and Ahn et al. (ICML'15), our algorithms use the predictions of pairwise distances between vertices provided by a predictor. For complete graphs, our algorithm achieves a better-than-$3$ approximation under good prediction quality, while using $\tilde{O}(n)$ total space. For general graphs, our algorithm achieves an $O(\log |E^-|)$ approximation under good prediction quality using $\tilde{O}(n)$ total space, improving the best-known non-learning algorithm in terms of space efficiency. Experimental results on synthetic and real-world datasets demonstrate the superiority of our proposed algorithms over their non-learning counterparts.