Correlation Clustering and Biclustering with Locally Bounded Errors

Gregory Puleo, Olgica Milenkovic
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:869-877, 2016.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-puleo16, title = {Correlation Clustering and Biclustering with Locally Bounded Errors}, author = {Puleo, Gregory and Milenkovic, Olgica}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {869--877}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/puleo16.pdf}, url = {https://proceedings.mlr.press/v48/puleo16.html}, 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.} }
Endnote
%0 Conference Paper %T Correlation Clustering and Biclustering with Locally Bounded Errors %A Gregory Puleo %A Olgica Milenkovic %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-puleo16 %I PMLR %P 869--877 %U https://proceedings.mlr.press/v48/puleo16.html %V 48 %X 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.
RIS
TY - CPAPER TI - Correlation Clustering and Biclustering with Locally Bounded Errors AU - Gregory Puleo AU - Olgica Milenkovic BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-puleo16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 869 EP - 877 L1 - http://proceedings.mlr.press/v48/puleo16.pdf UR - https://proceedings.mlr.press/v48/puleo16.html AB - 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. ER -
APA
Puleo, G. & Milenkovic, O.. (2016). Correlation Clustering and Biclustering with Locally Bounded Errors. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:869-877 Available from https://proceedings.mlr.press/v48/puleo16.html.

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