TL;DR
This paper introduces Multilayer Correlation Clustering, extending correlation clustering to multiple layers with a focus on minimizing multilayer disagreements, and provides approximation algorithms with practical validation.
Contribution
It develops the first approximation algorithms for multilayer correlation clustering, including a general $O(L ext{log} n)$-approximation and specialized algorithms for probability constraints.
Findings
An $O(L ext{log} n)$-approximation algorithm for multilayer correlation clustering.
A $(eta+2)$-approximation algorithm for the probability constraint case, where $eta$ is the single-layer approximation ratio.
Experimental results demonstrate the effectiveness of the algorithms on real-world datasets.
Abstract
We establish Multilayer Correlation Clustering, a novel generalization of Correlation Clustering to the multilayer setting. In this model, we are given a series of inputs of Correlation Clustering (called layers) over the common set of elements. The goal is to find a clustering of that minimizes the -norm () of the multilayer-disagreements vector, which is defined as the vector (with dimension equal to the number of layers), each element of which represents the disagreements of the clustering on the corresponding layer. For this generalization, we first design an -approximation algorithm, where is the number of layers. We then study an important special case of our problem, namely the problem with the so-called probability constraint. For this case, we first give an -approximation algorithm, where is any possible…
Peer Reviews
Decision·Submitted to ICLR 2025
+cute problem for correlation clustering where multiple instances are present. This is a nice twist in a famous problem and I am curious if this has been studied for more traditional clustering problems like k-means or other graph partitioning problems. +overall, the statements are clean for approximation and interesting. +well-motivated problem.
-one major concern I have is that there is limited novelty. Introducing a new problem is always interesting however in terms of techniques the paper heavily relies on prior works. The L layers in the input are handled in a relatively straighforward way and the analysis is a bit incremental, given the large bode of works for correlation clustering. I like the paper, but this is an important concern that I have.
Well written paper Results are interesting from a theoretical perspective Paper could spark nice follow-up work as it leaves many interesting challenges open It is rare to find a theory paper run experiments of the kind this paper does, so much credit to the authors :)
Not sure how suitable the paper is for ICLR audience, as it is more of an SODA/ALENEX type paper in my humble opinion. (Not taking anything away from the technical merits!) In Section 5.1, Authors could do much more justice in explaining how they use Problem 2 to solve the general problem. In particular, what metric they use, what are x1, .., x_L and what is F? Are these the different solutions we get from the convex program? and metric space is the space of all solutions? Adding this details
The main contribution is to propose a polynomial time algorithm to output a solution of $O(L \log(n))$ accuracy for the generalized correlation clustering problem.
1, The proposed multilayer correlation clustering problem lacks motivations. The aggregation of information from multiple weight functions $w_{l}^{+}$, $w_{l}^{-}, l=1,2, \dots, L$ can be done through more convenient and efficient ways. For instance, one can aggregate information by aggregating the weight functions by considering $w^{+} = \max_l w_{l}^{+}$, $w^{-} = \max_l w_{l}^{-}$ or $w^{+} = \sum_l w_{l}^{+}$, $w^{-} = \sum_l w_{l}^{-}$ or $w^{+} = (\sum_l (w_{l}^{+})^p)^{1/p}$, $w^{-} = (
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Taxonomy
TopicsAdvanced Clustering Algorithms Research
MethodsSparse Evolutionary Training
