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Chromatic Correlation Clustering
"... We study a novel clustering problem in which the pairwise relations between objects are categorical. This problem can be viewed as clustering the vertices of a graph whose edges are of different types (colors). We introduce an objective function that aims at partitioning the graph such that the edge ..."
Abstract

Cited by 4 (3 self)
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We study a novel clustering problem in which the pairwise relations between objects are categorical. This problem can be viewed as clustering the vertices of a graph whose edges are of different types (colors). We introduce an objective function that aims at partitioning the graph such that the edges within each cluster have, as much as possible, the same color. We show that the problem is NPhard and propose a randomized algorithm with approximation guarantee proportional to the maximum degree of the input graph. The algorithm iteratively picks a random edge as pivot, builds a cluster around it, and removes the cluster from the graph. Although being fast, easytoimplement, and parameter free, this algorithm tends to produce a relatively large number of clusters. To overcome this issue we introduce a variant algorithm, which modifies how the pivot is chosen and and how the cluster is built around the pivot. Finally, to address the case where a fixed number of output clusters is required, we devise a third algorithm that directly optimizes the objective function via a strategy based on the alternating minimization paradigm. We test our algorithms on synthetic and real data from the domains of proteininteraction networks, social media, and bibliometrics. Experimental evidence show that our algorithms outperform a baseline algorithm both in the task of reconstructing a groundtruth clustering and in terms of objective function value.