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Graph-Modeled Data Clustering: Exact Algorithms for Clique Generation

Jens Gramm, Jiong Guo, Falk Hüffner, Rolf Niedermeier
2005 Theory of Computing Systems  
We present efficient fixed-parameter algorithms for the NP-complete edge modification problems CLUSTER EDITING and CLUSTER DELETION.  ...  Here, the goal is to make the fewest changes to the edge set of an input graph such that the new graph is a vertex-disjoint union of cliques.  ...  Acknowledgment We thank Jochen Alber (Tübingen) and Elena Prieto-Rodriguez (Newcastle, Australia) for inspiring discussions and two anonymous referees of Theory of Computing Systems for comments that helped  ... 
doi:10.1007/s00224-004-1178-y fatcat:yojzktpnkjdijmjif4gz7txjxq

Fixed-Parameter Algorithms for Graph-Modeled Data Clustering [chapter]

Falk Hüffner, Rolf Niedermeier, Sebastian Wernicke
2009 Clustering Challenges in Biological Networks  
Our investigations are circumstantiated by three concrete problems from the realm of graph-modeled data clustering for which fixed-parameter algorithms have been implemented and experimentally evaluated  ...  , namely Clique, Cluster Editing, and Clique Cover.  ...  g That is, the graph that contains exactly those edges that are not contained in the original graph. Fixed-Parameter Algorithms for Graph-Modeled Data Clustering  ... 
doi:10.1142/9789812771667_0001 fatcat:yv2okjnvjfblhlgit7cnawid4e

Graph-Modeled Data Clustering: Fixed-Parameter Algorithms for Clique Generation [chapter]

Jens Gramm, Jiong Guo, Falk Hüffner, Rolf Niedermeier
2003 Lecture Notes in Computer Science  
We present efficient fixed-parameter algorithms for the NPcomplete edge modification problems Cluster Editing and Cluster Deletion.  ...  Here, the goal is to make the fewest changes to the edge set of an input graph such that the new graph is a vertex-disjoint union of cliques.  ...  We thank Jochen Alber and Elena Prieto-Rodriguez for inspiring discussions.  ... 
doi:10.1007/3-540-44849-7_17 fatcat:l4keks55rfge5g22vzxgtgfuee

A More Relaxed Model for Graph-Based Data Clustering: s-Plex Cluster Editing

Jiong Guo, Christian Komusiewicz, Rolf Niedermeier, Johannes Uhlmann
2010 SIAM Journal on Discrete Mathematics  
Cliques are 1-plexes. The advantage of s-plexes for s ≥ 2 is that they allow to model a more relaxed cluster notion (s-plexes instead of cliques), better reflecting inaccuracies of the input data.  ...  Altogether, this yields efficient algorithms in case of moderate numbers of edge modifications, this often being a reasonable assumption under a maximum parsimony model for data clustering.  ...  We are grateful to Falk Hüffner for inspiring discussions in the early phase of this research and anonymous referees of SIAM Journal on Discrete Mathematics for detailed feedback improving our presentation  ... 
doi:10.1137/090767285 fatcat:dnkgz4fpgnf3lmcuenkg3p6kxe

A More Relaxed Model for Graph-Based Data Clustering: s-Plex Editing [chapter]

Jiong Guo, Christian Komusiewicz, Rolf Niedermeier, Johannes Uhlmann
2009 Lecture Notes in Computer Science  
The advantage of s-plexes for s ≥ 2 is that they allow to model a more relaxed cluster notion (s-plexes instead of cliques), which better reflects inaccuracies of the input data.  ...  We introduce the s-Plex Editing problem generalizing the well-studied Cluster Editing problem, both being NP-hard and both being motivated by graph-based data clustering.  ...  We are grateful to Falk Hüffner for inspiring discussions in the early phase of this research.  ... 
doi:10.1007/978-3-642-02158-9_20 fatcat:vjf7q4fnbrhkhk6lg5po2yeyk4

Graph-Based Data Selection for the Construction of Genomic Prediction Models

S. Maenhout, B. De Baets, G. Haesaert
2010 Genetics  
However, as the genotyping budget is generally limited, the genomic prediction model can only be constructed using a subset of the tested individuals and possibly a genome-covering subset of the molecular  ...  for hybrid maize.  ...  The authors thank the people from RAGT R2n for their unreserved and open-minded scientific contribution to this research.  ... 
doi:10.1534/genetics.110.116426 pmid:20479144 pmcid:PMC2927770 fatcat:gqvvk4jjbjeshca2gadj7aiajm

FLUID: A Common Model for Semantic Structural Graph Summaries Based on Equivalence Relations [article]

Till Blume, Ansgar Scherp
2020 arXiv   pre-print
We abstract from these patterns and provide for the first time a formally defined common model FLUID (FLexible graph sUmmarIes for Data graphs) that allows to flexibly define structural graph summaries  ...  As there are many tasks regarding what information is to be summarized from a graph, there is no single concept or model of graph summaries.  ...  We abstract these patterns in a common, formal model called FLUID (short for: FLexible graph sUmmarIes for Data graphs).  ... 
arXiv:1908.01528v2 fatcat:i75lscq2crd4fiuyqotqciwuse

Assortativity in Chung Lu Random Graph Models

Stephen Mussmann, John Moore, Joseph J. Pfeiffer, Jennifer Neville
2014 Proceedings of the 8th Workshop on Social Network Mining and Analysis - SNAKDD'14  
Due to the widespread interest in networks as a representation to investigate the properties of complex systems, there has been a great deal of interest in generative models of graph structure that can  ...  One exception is the BTER method [5], which generates graphs with positive assortativity (e.g., high degree nodes link to each other).  ...  For evaluation, we compared the graphs generated by the algorithms using different metrics.  ... 
doi:10.1145/2659480.2659495 dblp:conf/kdd/MussmannMPN14 fatcat:2ppgtpmgl5h43ff54t2t7rbwni

Algorithmic techniques for modeling and mining large graphs (AMAzING)

Alan Frieze, Aristides Gionis, Charalampos Tsourakakis
2013 Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '13  
Figure 2 :Figure 3 :Figure 7 : 237 Clusters for WordNet data, k = 12 (best viewed in color). Q versus k for the WordNet data. Q versus k for NIPS coauthorship data.  ...  Techniques for Modeling and Mining Large Graphs 199 / 277 streaming k-way graph partitioning • input is a data stream • graph is ordered • arbitrarily • breadth-first search • depth-first search • generate  ...  Repeat until no edges left Weight functions • s c : number of vertices in cluster c Greedy algorithm for densest subgraph [Charikar, 2000] input: undirected graph G = (V , E ) output: S, a dense sungraph  ... 
doi:10.1145/2487575.2506176 dblp:conf/kdd/FriezeGT13 fatcat:mp2uedrsbfewjjaar6jven43yq

Micro-Clustering: Finding Small Clusters in Large Diversity [article]

Takeaki Uno, Hiroki Maegawa, Takanobu Nakahara, Yukinobu Hamuro, Ryo Yoshinaka, Makoto Tatsuta
2016 arXiv   pre-print
The clusters are clarified as maximal cliques, thus the number of maximal cliques will be drastically reduced. We also propose an efficient algorithm applicable even for large scale data.  ...  The problem formulation of micro-clustering is non-trivial. Clique mining in a similarity graph is a typical approach, but it results in a huge number of cliques that are of many similar cliques.  ...  We also express our appreciation to Teikoku DataBank Limited, Japan, for supplying the Japanese company business relation data. This research is supported by JST CREST, Japan.  ... 
arXiv:1507.03067v2 fatcat:yhiiidb6qbarxf25x3av2qjtii

Next Generation Cluster Editing [article]

Thomas Bellitto and Tobias Marschall and Alexander Schönhuth and Gunnar W. Klau
2013 arXiv   pre-print
We suggest a new model based on cluster editing in weighted graphs and introduce a new heuristic algorithm that allows to solve this problem quickly and with a good approximation on the huge graphs that  ...  Acknowledgements The authors thank COST action BM1006 SeqAhead for supporting this work and Murray Patterson for his advice on an early version of this manuscript.  ...  Best clustering for a given order Looking back at algorithm 3, we realise that it solves a more general problem than just optimal clustering for one dimensional point graphs: given any kind of graph and  ... 
arXiv:1310.3353v1 fatcat:yxx7h3ygvbgv5gwgtvmrxtu7um

Circuit clustering using graph coloring

Amit Singh, Malgorzata Marek-Sadowska
1999 Proceedings of the 1999 international symposium on Physical design - ISPD '99  
We identify cliques in the graph and use these cliques, starting from the max_clique, as building blocks for our clusters. A cost function is derived using the cluster density notion and edge costs.  ...  We present a circuit clustering technique based on graph coloring. A given netlist is modeled as an undirected graph and its vertices are colored.  ...  Table 1 shows the size of the test cases on which we tried our clustering algorithm, as well as the exact coloring obtained for these circuits (based on our graph model).  ... 
doi:10.1145/299996.300055 dblp:conf/ispd/SinghM99 fatcat:c6utjhc7yndjfengp3flt2inhq

Modification-Fair Cluster Editing [article]

Vincent Froese, Leon Kellerhals, Rolf Niedermeier
2021 arXiv   pre-print
When applied to vertex-colored graphs (the colors representing subgroups), standard algorithms for the NP-hard Cluster Editing problem may yield solutions that are biased towards subgroups of data (e.g  ...  To start with, we study Modification-Fair Cluster Editing for graphs with two vertex colors.  ...  A more relaxed model for graph-based data clustering: s-plex cluster editing. SIAM J. Discret.  ... 
arXiv:2112.03183v1 fatcat:zdq24phxhrexxppuqzsej5prya

Clustering to the Fewest Clusters Under Intra-Cluster Dissimilarity Constraints

Jennie Andersen, Brice Chardin, Mohamed Tribak
2021 2021 IEEE 33rd International Conference on Tools with Artificial Intelligence (ICTAI)  
We review and evaluate suitable clustering algorithms to identify trade-offs between the various practical solutions for this clustering problem.  ...  Unlike most existing clustering algorithms, equiwide clustering relies neither on density nor on a predefined number of expected classes, but on a dissimilarity threshold.  ...  [17] . • Exact graph coloring, using the DSATUR-based implementation provided by Mehrotra and Trick [18] . • Graph coloring with minimization of the maximum diameter of clusters [8] (denoted CG, for  ... 
doi:10.1109/ictai52525.2021.00036 fatcat:kpp3njb4afa3vjsbjacvmo4q4y

Graph clustering

Satu Elisa Schaeffer
2007 Computer Science Review  
Then we present global algorithms for producing a clustering for the entire vertex set of an input graph, after which we discuss the task of identifying a cluster for a specific seed vertex by local computation  ...  Some ideas on the application areas of graph clustering algorithms are given. We also address the problematics of evaluating clusterings and benchmarking cluster algorithms.  ...  For their valuable comments, the author thanks Pekka Orponen, the editors and the anonymous reviewer, whose comments greatly improved the structure of the presentation.  ... 
doi:10.1016/j.cosrev.2007.05.001 fatcat:o2vpx2pgzndzjezuprkfzf5jsa
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