Short Survey on Graph Correlation Clustering with Minimization Criteria

In clustering problems one has to partition a given set of objects into some subsets (called clusters) taking into consideration only similarity of the objects. One of the most visual formalizations of clustering is the graph clustering, that is, grouping the vertices of a graph into clusters taking into consideration the edge structure of the graph whose vertices are objects and edges represent similarities between the objects.

[1]  Amos Fiat,et al.  Correlation clustering in general weighted graphs , 2006, Theor. Comput. Sci..

[2]  Christian Komusiewicz,et al.  Cluster editing with locally bounded modifications , 2012, Discret. Appl. Math..

[3]  Roded Sharan,et al.  Cluster graph modification problems , 2002, Discret. Appl. Math..

[4]  Bassel Mannaa,et al.  Cluster editing problem for points on the real line: A polynomial time algorithm , 2010, Inf. Process. Lett..

[5]  Zhi-Zhong Chen,et al.  Computing Phylogenetic Roots with Bounded Degrees and Errors , 2003, SIAM J. Comput..

[6]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[8]  James Saunderson,et al.  A Local-Search 2-Approximation for 2-Correlation-Clustering , 2008, ESA.

[9]  Inderjit S. Dhillon,et al.  Semi-supervised graph clustering: a kernel approach , 2005, Machine Learning.

[10]  Xiao Xin,et al.  An FPT Algorithm for the Correlation Clustering Problem , 2011 .

[11]  Mirko Krivánek,et al.  NP-hard problems in hierarchical-tree clustering , 1986, Acta Informatica.

[12]  Ioan Tomescu,et al.  Note sur une caractérisation des graphes dont le degré de déséquilibre est maximal , 1973 .

[13]  A. Ageev,et al.  Computational complexity of the graph approximation problem , 2007 .

[14]  David P. Williamson,et al.  Deterministic pivoting algorithms for constrained ranking and clustering problems , 2007, SODA '07.

[15]  Nicholas R. Jennings,et al.  Coalition Structure Generation over Graphs , 2012, J. Artif. Intell. Res..

[16]  Venkatesan Guruswami,et al.  Clustering with qualitative information , 2005, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[17]  Ivan C. Martins,et al.  Efficient algorithms for cluster editing , 2016, J. Comb. Optim..

[18]  J. Zahn Approximating Symmetric Relations by Equivalence Relations , 1964 .

[19]  Christian Komusiewicz,et al.  Parameterizing Edge Modification Problems Above Lower Bounds , 2016, CSR.

[20]  Philip N. Klein,et al.  Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs , 2023, STACS.

[21]  Sven Rahmann,et al.  Exact and heuristic algorithms for weighted cluster editing. , 2007, Computational systems bioinformatics. Computational Systems Bioinformatics Conference.

[22]  Morteza Zadimoghaddam,et al.  Optimal Coalition Structure Generation in Cooperative Graph Games , 2013, AAAI.

[23]  Nir Ailon,et al.  Aggregating inconsistent information: Ranking and clustering , 2008 .

[24]  Avrim Blum,et al.  Correlation Clustering , 2004, Machine Learning.

[25]  Steven Skiena,et al.  Integrating microarray data by consensus clustering , 2003, Proceedings. 15th IEEE International Conference on Tools with Artificial Intelligence.

[26]  Venkatesan Guruswami,et al.  Correlation clustering with a fixed number of clusters , 2005, SODA '06.

[27]  Satu Elisa Schaeffer,et al.  Graph Clustering , 2017, Encyclopedia of Machine Learning and Data Mining.

[28]  Ron Shamir,et al.  Clustering Gene Expression Patterns , 1999, J. Comput. Biol..

[29]  Sergey Yekhanin,et al.  Towards 3-query locally decodable codes of subexponential length , 2008, JACM.

[30]  Paola Bonizzoni,et al.  On the Approximation of Correlation Clustering and Consensus Clustering , 2008, J. Comput. Syst. Sci..

[31]  Ioan Tomescu La reduction minimale d'un graphe a une reunion de cliques , 1974, Discret. Math..

[32]  F. Harary On the notion of balance of a signed graph. , 1953 .