Correlation Clustering with Noisy Input

Correlation clustering is a type of clustering that uses a basic form of input data: For every pair of data items, the input specifies whether they are similar (belonging to the same cluster) or dissimilar (belonging to different clusters). This information may be inconsistent, and the goal is to find a clustering (partition of the vertices) that disagrees with as few pieces of information as possible. Correlation clustering is APX-hard for worst-case inputs. We study the following semi-random noisy model to generate the input: start from an arbitrary partition of the vertices into clusters. Then, for each pair of vertices, the similarity information is corrupted (noisy) independently with probability p. Finally, an adversary generates the input by choosing similarity/dissimilarity information arbitrarily for each corrupted pair of vertices. In this model, our algorithm produces a clustering with cost at most 1 + O(n-1/6 ) times the cost of the optimal clustering, as long as p 1/2 - ...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Claire Mathieu, Warren Schudy
• Keywords: Correlation Clustering, Discrete Algorithms, Optimal Clustering, Planted Clustering, SODA 2010