# Correlation Clustering and Biclustering With Locally Bounded Errors

@article{Puleo2018CorrelationCA, title={Correlation Clustering and Biclustering With Locally Bounded Errors}, author={Gregory J. Puleo and Olgica Milenkovic}, journal={IEEE Transactions on Information Theory}, year={2018}, volume={64}, pages={4105-4119} }

We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> 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… Expand

#### Figures and Topics from this paper

#### 27 Citations

Motif and Hypergraph Correlation Clustering

- Computer Science
- IEEE Transactions on Information Theory
- 2020

This work introduces several variants of motif correlation clustering and then describes polynomial-time clustering algorithms that provide constant approximation guarantees for the problems at hand, and shows that these clustering problems are NP-hard. Expand

Ju n 20 19 Min-Max Correlation Clustering via MultiCut ⋆

- 2019

Correlation clustering is a fundamental combinatorial optimization problem arising in many contexts and applications that has been the subject of dozens of papers in the literature. In this problem… Expand

Faster Deterministic Approximation Algorithms for Correlation Clustering and Cluster Deletion

- Computer Science
- ArXiv
- 2021

This paper proves new relationships between correlation clustering problems and edge labeling problems related to the principle of strong triadic closure, and develops faster techniques that are purely combinatorial, based on computing maximal matchings in certain auxiliary graphs and hypergraphs. Expand

Local Guarantees in Graph Cuts and Clustering

- Computer Science, Mathematics
- IPCO
- 2017

This work presents an \(O(\sqrt{n})\)-approximation for the problem of minimizing the maximum total weight of disagreement edges incident on any node, providing the first known approximation for the above family of min-max graph cut problems. Expand

Approximation Algorithm for the Balanced 2-correlation Clustering Problem on Well-Proportional Graphs

- Computer Science, Mathematics
- AAIM
- 2020

This paper provides a \((3,\max \{4(M+1),16\})\)-balanced approximation algorithm for the balanced 2-correlation clustering problem on M-proportional graphs and returns the cost of the vertex partition at most three times the optimum solution. Expand

Exact Clustering via Integer Programming and Maximum Satisfiability

- Computer Science
- AAAI
- 2018

This study presents a novel integer linear programming (ILP) formulation that has far fewer constraints than the standard ILP formulation by Grötschel and Wakabayashi (1989), and proposes an ILP-based exact algorithm that solves anILP problem obtained by modifying the above ILP formulated and then performs simple post-processing to produce an optimal solution. Expand

Approximation Algorithm for the Correlation Clustering Problem with Non-uniform Hard Constrained Cluster Sizes

- Computer Science, Mathematics
- AAIM
- 2019

This paper provides a (2, 4)-bicriteria approximation algorithm for the correlation clustering problem with non-uniform hard constrained cluster sizes, and provides a solution that has the cost at most 4 times the optimum. Expand

Metric-Constrained Optimization for Graph Clustering Algorithms\ast

- 2019

We outline a new approach for solving linear programming relaxations of NP-hard graph clustering problems that enforce triangle inequality constraints on output variables. Extensive previous research… Expand

Improved algorithms for Correlation Clustering with local objectives

- Mathematics, Computer Science
- ArXiv
- 2019

The first known algorithm for minimizing the $\ell_q$ norm of the disagreements vector on arbitrary graphs is presented and an improved algorithm for minimize the $q \geq 1$ norm on complete graphs is provided. Expand

Correlation clustering with local objectives

- Computer Science, Mathematics
- NeurIPS
- 2019

This paper presents the first known algorithm for minimizing the \ell_q norm of the disagreements vector on arbitrary graphs and provides an improved algorithm for minimize the\ell-q norm (q >= 1) of the disagreement vector on complete graphs. Expand

#### References

SHOWING 1-10 OF 35 REFERENCES

Correlation clustering in general weighted graphs

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2006

An O(log n)-approximation algorithm is given for the general case based on a linear-programming rounding and the "region-growing" technique for Kr, r-minor-free graphs and it is proved that this linear program has a gap of Ω( log n), and therefore the approximation is tight under this approach. Expand

Correlation clustering

- Mathematics, Computer Science
- The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
- 2002

This formulation is motivated from a document clustering problem in which one has a pairwise similarity function f learned from past data, and the goal is to partition the current set of documents in a way that correlates with f as much as possible; it can also be viewed as a kind of "agnostic learning" problem. Expand

Parallel Correlation Clustering on Big Graphs

- Computer Science, Mathematics
- NIPS
- 2015

C4 and ClusterWild!, two algorithms for parallel correlation clustering that run in a polylogarithmic number of rounds and achieve nearly linear speedups, provably are presented. Expand

Cluster editing with locally bounded modifications

- Computer Science, Mathematics
- Discret. Appl. Math.
- 2012

This work studies how ''local degree bounds'' influence the complexity of Cluster Editing and of the related Cluster Deletion problem which allows only edge deletions, and presents a problem kernelization for the combined parameter ''number d of clusters and maximum number t of modifications incident with a vertex'' thus showing that Cluster edits become easier in case the number of clusters is upper-bounded. Expand

Deterministic pivoting algorithms for constrained ranking and clustering problems

- Mathematics, Computer Science
- SODA '07
- 2007

D deterministic algorithms for constrained weighted feedback arc set in tournaments, constrained correlation clustering, and constrained hierarchical clustering related to finding good ultrametrics and a combinatorial algorithm that improves on the best known factor given by deterministic combinatorsial algorithms for the unconstrained case are given. Expand

Local Guarantees in Graph Cuts and Clustering

- Computer Science, Mathematics
- IPCO
- 2017

This work presents an \(O(\sqrt{n})\)-approximation for the problem of minimizing the maximum total weight of disagreement edges incident on any node, providing the first known approximation for the above family of min-max graph cut problems. Expand

Improved Approximation Algorithms for Bipartite Correlation Clustering

- Mathematics, Computer Science
- ESA
- 2011

The analysis extends a method developed by Ailon, Charikar and Newman in 2008, where a randomized pivoting algorithm was analyzed for obtaining a 3-approximation algorithm for CC, and is presented, and the main contribution, is a simple randomized combinatorial algorithm. Expand

Near Optimal LP Rounding Algorithm for CorrelationClustering on Complete and Complete k-partite Graphs

- Computer Science, Mathematics
- STOC
- 2015

These results improve a long line of work on approximation algorithms for correlation clustering in complete graphs, previously culminating in a ratio of 2.5 by Ailon, Charikar and Newman. Expand

Clustering with qualitative information

- Computer Science, Mathematics
- J. Comput. Syst. Sci.
- 2005

A factor 4 approximation for minimization on complete graphs, and a factor O(logn) approximation for general graphs are demonstrated, and the APX-hardness of minimization of complete graphs is proved. Expand

Min-max Graph Partitioning and Small Set Expansion

- Computer Science, Mathematics
- 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
- 2011

An O(√log n log (1/p) bicriteria approximation algorithm for the general case of Small Set Expansion and O(1) approximation algorithms for graphs that exclude any fixed minor. Expand