Correlation Clustering and Biclustering with Locally Bounded Errors
Abstract
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$ edges between clusters or $-$ edges within clusters. Classically, one seeks to minimize the total number of such errors. We introduce a new framework that allows the objective to be a more general function of the number of errors at each vertex (for example, we may wish to minimize the number of errors at the worst vertex) and provide a rounding algorithm which converts "fractional clusterings" into discrete clusterings while causing only a constant-factor blowup in the number of errors at each vertex. This rounding algorithm yields constant-factor approximation algorithms for the discrete problem under a wide variety of objective functions.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2015
- DOI:
- 10.48550/arXiv.1506.08189
- arXiv:
- arXiv:1506.08189
- Bibcode:
- 2015arXiv150608189P
- Keywords:
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- Computer Science - Data Structures and Algorithms;
- Computer Science - Machine Learning
- E-Print:
- 20 pages, reorganized paper to emphasize the key properties of the rounding algorithm and the broader class of possible objective functions