## Correlation Clustering (2002)

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Venue: | MACHINE LEARNING |

Citations: | 232 - 4 self |

### BibTeX

@INPROCEEDINGS{Bansal02correlationclustering,

author = {Nikhil Bansal and Avrim Blum and Shuchi Chawla},

title = {Correlation Clustering},

booktitle = {MACHINE LEARNING},

year = {2002},

pages = {238--247},

publisher = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider the following clustering problem: we have a complete graph on # vertices (items), where each edge ### ## is labeled either # or depending on whether # and # have been deemed to be similar or different. The goal is to produce a partition of the vertices (a clustering) that agrees as much as possible with the edge labels. That is, we want a clustering that maximizes the number of # edges within clusters, plus the number of edges between clusters (equivalently, minimizes the number of disagreements: the number of edges inside clusters plus the number of # edges between clusters). This formulation is motivated from a document clustering problem in which one has a pairwise similarity function # learned from past data, and the goal is to partition the current set of documents in a way that correlates with # as much as possible; it can also be viewed as a kind of "agnostic learning" problem. An interesting

### Citations

1717 | The Probabilistic Method
- Alon, Spencer
- 2000
(Show Context)
Citation Context ... partition. Next we will show that if the algorithm finds good partitions for most �, then it achieves at least agreements. We will need the following results from probability theory. Please refer to =-=[2]-=- for a proof. Fact 1: Let � � be the hypergeometric distribution with parameters � and (choosing samples from points without replacement with the random variable taking a value of 1 on exactly out of ... |

431 | Property testing and its connection to learning and approximation
- Goldreich, Ron
- 1996
(Show Context)
Citation Context ... clustering with at least �� agreements, this means it suffices to approximate agreements to within an additive factor of . This problem is also closely related to work on testing graph properties of =-=[13, 19, 1]-=-. In fact, we show how we can use the General Partition Property Tester of [13] as a subroutine to get a PTAS with running time � . Unfortunately, this is doubly exponential in , so we also present an... |

325 | Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation
- Jain, Vazirani
(Show Context)
Citation Context ...interesting about the clustering problem defined here is that unlike most clustering formulations, we do not need to specify the number of clusters � as a separate parameter. For example, in �-median =-=[7, 15]-=- or min-sum clustering [20] or min-max clustering [14], one can always get a perfect score by putting each node into its own cluster — the question is how well one can do with only � clusters. In our ... |

301 | Efficient noise-tolerant learning from statistical queries
- Kearns
- 1999
(Show Context)
Citation Context ...one can (whp) produce a clustering that is quite close to , much closer than the number of disagreements between and �. The analysis is fairly standard (much like the generic transformation of Kearns =-=[16]-=- in the machine learning context, and even closer to the analysis of Condon and Karp for graph partitioning [11]). In fact, this problem nearly matches a special case of the plantedpartition problem o... |

209 | Improved combinatorial algorithms for facility location problems
- Charikar, Guha
(Show Context)
Citation Context ...interesting about the clustering problem defined here is that unlike most clustering formulations, we do not need to specify the number of clusters � as a separate parameter. For example, in �-median =-=[7, 15]-=- or min-sum clustering [20] or min-max clustering [14], one can always get a perfect score by putting each node into its own cluster — the question is how well one can do with only � clusters. In our ... |

201 | Towards efficient agnostic learning
- Kearns, Schapire, et al.
- 1992
(Show Context)
Citation Context ...represent � perfectly. This sort of problem — trying to find the (nearly) best representation of some arbitrary target � in a given limited hypothesis language — is sometimes called agnostic learning =-=[17, 6]-=-. The observation that one can trivially agree with at least half the edge labels is equivalent to the standard machine learning fact that one can always achieve error at most � using either the all p... |

172 | Approximation schemes for dense instances of np-hard problems
- Arora, Karpinski
- 1995
(Show Context)
Citation Context ...is fact is used in our constant-factor approximation algorithm. For maximizing agreements, our PTAS is quite similar to the PTAS developed by [12] for MAX-CUT on dense graphs, and related to PTASs of =-=[4, 3]-=-. Notice that since there must exist a clustering with at least �� agreements, this means it suffices to approximate agreements to within an additive factor of . This problem is also closely related t... |

163 | Efficient testing of large graphs
- Alon, Fischer, et al.
(Show Context)
Citation Context ... clustering with at least �� agreements, this means it suffices to approximate agreements to within an additive factor of . This problem is also closely related to work on testing graph properties of =-=[13, 19, 1]-=-. In fact, we show how we can use the General Partition Property Tester of [13] as a subroutine to get a PTAS with running time � . Unfortunately, this is doubly exponential in , so we also present an... |

136 | Learning to match and cluster large high-dimensional data sets for data integration
- Cohen, Richman
- 2002
(Show Context)
Citation Context ...al-valued edge weights. This problem formulation is motivated in part by some clustering problems at Whizbang Labs in which learning algorithms have been trained to help with various clustering tasks =-=[8, 9, 10]-=-. 1 What is interesting about the clustering problem defined here is that unlike most clustering formulations, we do not need to specify the number of clusters � as a separate parameter. For example, ... |

92 |
A unified approach to approximation algorithms for bottleneck problems
- Hochbaum, Shmoys
- 1986
(Show Context)
Citation Context ...that unlike most clustering formulations, we do not need to specify the number of clusters � as a separate parameter. For example, in �-median [7, 15] or min-sum clustering [20] or min-max clustering =-=[14]-=-, one can always get a perfect score by putting each node into its own cluster — the question is how well one can do with only � clusters. In our clustering formulation, there is just a single objecti... |

90 | Spectral partitioning of random graphs
- McSherry
- 2001
(Show Context)
Citation Context ...hine learning context, and even closer to the analysis of Condon and Karp for graph partitioning [11]). In fact, this problem nearly matches a special case of the plantedpartition problem of McSherry =-=[18]-=-. We present our analysis anyway since the algorithms are so simple. One-sided noise: As an easier special case, let us consider only one-sided noise in which each true “ ” edge is flipped to “ ” with... |

78 | A new rounding procedure for the assignment problem with applications to dense graph arrangement problems
- Arora, Frieze, et al.
(Show Context)
Citation Context ...is fact is used in our constant-factor approximation algorithm. For maximizing agreements, our PTAS is quite similar to the PTAS developed by [12] for MAX-CUT on dense graphs, and related to PTASs of =-=[4, 3]-=-. Notice that since there must exist a clustering with at least �� agreements, this means it suffices to approximate agreements to within an additive factor of . This problem is also closely related t... |

42 | Algorithms for graph partitioning on the planted partition model. Random Struct
- Condon, Karp
(Show Context)
Citation Context ... and �. The analysis is fairly standard (much like the generic transformation of Kearns [16] in the machine learning context, and even closer to the analysis of Condon and Karp for graph partitioning =-=[11]-=-). In fact, this problem nearly matches a special case of the plantedpartition problem of McSherry [18]. We present our analysis anyway since the algorithms are so simple. One-sided noise: As an easie... |

33 | Learning to match and cluster entity names
- Cohen, Richman
- 2001
(Show Context)
Citation Context ...al-valued edge weights. This problem formulation is motivated in part by some clustering problems at Whizbang Labs in which learning algorithms have been trained to help with various clustering tasks =-=[8, 9, 10]-=-. 1 What is interesting about the clustering problem defined here is that unlike most clustering formulations, we do not need to specify the number of clusters � as a separate parameter. For example, ... |

31 | Clustering for Edge-Cost Minimization
- Schulman
- 2002
(Show Context)
Citation Context ...ng problem defined here is that unlike most clustering formulations, we do not need to specify the number of clusters � as a separate parameter. For example, in �-median [7, 15] or min-sum clustering =-=[20]-=- or min-max clustering [14], one can always get a perfect score by putting each node into its own cluster — the question is how well one can do with only � clusters. In our clustering formulation, the... |

30 | Testing the diameter of graphs
- Parnas, Ron
- 2002
(Show Context)
Citation Context ... clustering with at least �� agreements, this means it suffices to approximate agreements to within an additive factor of . This problem is also closely related to work on testing graph properties of =-=[13, 19, 1]-=-. In fact, we show how we can use the General Partition Property Tester of [13] as a subroutine to get a PTAS with running time � . Unfortunately, this is doubly exponential in , so we also present an... |

29 | Martingale Boosting
- Long, Servedio
- 2005
(Show Context)
Citation Context ...represent � perfectly. This sort of problem — trying to find the (nearly) best representation of some arbitrary target � in a given limited hypothesis language — is sometimes called agnostic learning =-=[17, 6]-=-. The observation that one can trivially agree with at least half the edge labels is equivalent to the standard machine learning fact that one can always achieve error at most � using either the all p... |

12 |
MAX-CUT has a randomized approximation scheme in dense graphs. Random Structures and Algorithms
- VEGA, W
- 1996
(Show Context)
Citation Context ... the number of disagreements of the optimal clustering. This fact is used in our constant-factor approximation algorithm. For maximizing agreements, our PTAS is quite similar to the PTAS developed by =-=[12]-=- for MAX-CUT on dense graphs, and related to PTASs of [4, 3]. Notice that since there must exist a clustering with at least �� agreements, this means it suffices to approximate agreements to within an... |

1 |
Correlation clustering (http://www.cs.cmu.edu/˜shuchi/papers/clusteringfull.ps
- Bansal, Blum, et al.
- 2002
(Show Context)
Citation Context ...ments, getting a -approximation is easy (note: we will show a PTAS). In general, finding the optimal clustering is NP-hard, which can be seen via a tedious reduction from X3C (details can be found in =-=[5]-=-). Another simple fact to notice is that if the graph contains a triangle in which two edges are labeled and one is labeled , then no clustering can be perfect. More generally, the number of edge-disj... |