Better Private Algorithms for Correlation Clustering

In machine learning, correlation clustering is an important problem whose goal is to partition the individuals into groups that correlate with their pairwise similarities as much as possible. In this work, we revisit the correlation clustering under the differential privacy constraints. Particularly, we improve previous results and achieve an TildeO(n1.5) additive error compared to the optimal cost in expectation on general graphs. As for unweighted complete graphs, we improve the results further and propose a more involved algorithm which achieves TildeO(n √Delta^*) additive error, where Delta^* is the maximum degrees of positive edges among all nodes.