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The pairwise similarity information is given as a weighted graph G with edges labeled as either “positive/similar” or as “negative/dissimilar” by a noisy binary classifier

# Local Correlation Clustering with Asymmetric Classification Errors

ICML, pp.4677-4686, (2021)

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In the Correlation Clustering problem, we are given a complete weighted graph $G$ with its edges labeled as "similar" and "dissimilar" by a noisy binary classifier. For a clustering $\mathcal{C}$ of graph $G$, a similar edge is in disagreement with $\mathcal{C}$, if its endpoints belong to distinct clusters; and a dissimilar edge is in ...更多

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• Grouping objects based on the similarity between them is a ubiquitous and important task in machine learning
• Blum, and Chawla (2004) introduced the Correlation Clustering problem, a versatile model that elegantly captures this task of grouping objects based on similarity information
• The pairwise similarity information is given as a weighted graph G with edges labeled as either “positive/similar” or as “negative/dissimilar” by a noisy binary classifier
• For a clustering C, a positive edge is in disagreement with C, if its endpoints belong to distinct clusters; and a negative edge is in disagreement with C if its endpoints belong to the same cluster
• The first quantity, disu(P, E+, E−), is the total weight of edges incident on u that are in disagreement with P. We show that this quantity can be charged to the convex programming (CP) cost of u and is at most A∞ ·yu

• Jafar Jafarov and Yury Makarychev were supported by NSF CCF-1718820, CCF-1955173, and NSF TRIPODS CCF-1934843/CCF-1934813
• Sanchit Kalhan and Konstantin Makarychev were supported by NSF CCF-1955351 and NSF TRIPODS CCF-1934931

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