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Anti-monotonic Overlap-Graph Support Measures

Toon Calders, Jan Ramon, Dries Van Dyck
2008 2008 Eighth IEEE International Conference on Data Mining  
In graph mining, a frequency measure is anti-monotonic if the frequency of a pattern never exceeds the frequency of a subpattern.  ...  Vanetik, Gudes and Shimony already gave sufficient and necessary conditions for anti-monotonicity of measures depending only on the edge-overlaps between the intances of the pattern in a labeled graph.  ...  Let us now return to the connection between measures with this property and anti-monotonic graph support measures based on overlap graphs.  ... 
doi:10.1109/icdm.2008.114 dblp:conf/icdm/CaldersRD08 fatcat:z5bpb5655rhbfns7xl5oflerhq

An Efficiently Computable Support Measure for Frequent Subgraph Pattern Mining [chapter]

Yuyi Wang, Jan Ramon
2012 Lecture Notes in Computer Science  
Graph support measures are functions measuring how frequently a given subgraph pattern occurs in a given database graph. An important class of support measures relies on overlap graphs.  ...  A major advantage of the overlap graph based approaches is that they combine anti-monotonicity with counting occurrences of a pattern which are independent according to certain criteria.  ...  This work was supported by ERC Starting Grant 240186 "MiGraNT: Mining Graphs and Networks: a Theory-based appraoch".  ... 
doi:10.1007/978-3-642-33460-3_29 fatcat:nutejpfsszemlc2v7ahoodcfca

An efficiently computable subgraph pattern support measure: counting independent observations

Yuyi Wang, Jan Ramon, Thomas Fannes
2013 Data mining and knowledge discovery  
Graph support measures are functions measuring how frequently a given subgraph pattern occurs in a given database graph. An important class of support measures relies on overlap graphs.  ...  A major advantage of overlap-graph based approaches is that they combine anti-monotonicity with counting the occurrences of a subgraph pattern which are independent according to certain criteria.  ...  Acknowledgements This work was supported by ERC Starting Grant 240186 "MiGraNT: Mining Graphs and Networks: a Theory-based approach".  ... 
doi:10.1007/s10618-013-0318-x fatcat:udmiepun2jfvzispm3wjowucra

Flexible and Feasible Support Measures for Mining Frequent Patterns in Large Labeled Graphs

Jinghan Meng, Yi-cheng Tu
2017 Proceedings of the 2017 ACM International Conference on Management of Data - SIGMOD '17  
It is known, however, that the count of instances as a support measure is not anti-monotonic, in this paper we present two anti-monotonic support measures that achieve counts that are closer to the number  ...  THEOREM 4. 2 2 The MIES measure is anti-monotonic.  ... 
doi:10.1145/3035918.3035936 dblp:conf/sigmod/MengT17 fatcat:52hj5twrhjekpns5ojplx7p3l4

All normalized anti-monotonic overlap graph measures are bounded

Toon Calders, Jan Ramon, Dries Van Dyck
2011 Data mining and knowledge discovery  
In that way, we obtain that all normalized anti-monotonic overlap graph measures are bounded from above and below.  ...  In graph mining, a frequency measure for graphs is anti-monotonic if the frequency of a pattern never exceeds the frequency of a subpattern.  ...  Acknowledgements This work is supported by the FWO project 'Graph logic: Representation, Inference and Learning'.  ... 
doi:10.1007/s10618-011-0217-y fatcat:ddw232qyifbbvceazpl26oswka

Optimizing Frequent Subgraph Mining for Single Large Graph

Aarzoo Dhiman, S.K. Jain
2016 Procedia Computer Science  
When the input to FSM algorithm is a single graph, calculating support of subgraph needs identifying its isomorphisms in the input graph. Identifying subgraph isomorphisms is NP-Complete problem.  ...  Evidently, fewer the number of candidates, fewer the support computations needed.  ...  An anti-monotone support metric is the one that follows anti-monotone property.  ... 
doi:10.1016/j.procs.2016.06.085 fatcat:zdraoylkknewxk6oovgtsbkvhi

Report on the First International Workshop on Mining Graphs and Complex Structures (MGCS'07)

Lawrence B. Holder, Xifeng Yan
2008 SIGMOD record  
They also provide a clear proof of the anti-monotonicity of the MIS-support proposed in previous work.  ...  Specifically, some overlapping embeddings can be considered harmless, in that counting them all will not violate the anti-monotone property and therefore increase the set of frequent subgraphs for a given  ... 
doi:10.1145/1374780.1374795 fatcat:lyebwlg5yfb5rkwkddzqn2hqdq

Support Measure Admissibility Based on Operations on Instance Graphs

Ford Lumban Gaol
2007 Journal of Computer Science  
Most mining algorithms require the support of a pattern to be no grater than that of its subpatterns, a property called anti-monotonicity or admissibility.  ...  Support measure for mining graphs are usually based on the notion of an instance graph-a graph representing all the instances of the pattern in a database and their intersection properties.  ...  This property is the defacto standard assumption for algorithms, which relay heavily on anti-monotonicity.  ... 
doi:10.3844/jcssp.2007.708.716 fatcat:bg5sbaeqljbfde7zu7pulrdpvm

Finding the Most Descriptive Substructures in Graphs with Discrete and Numeric Labels [chapter]

Michael Davis, Weiru Liu, Paul Miller
2013 Lecture Notes in Computer Science  
We support our findings with experiments on transaction graphs and single large graphs from the domains of physical building security and digital forensics, measuring the effect on runtime, memory requirements  ...  Many graph datasets are labelled with discrete and numeric attributes.  ...  Support is an anti-monotone property: the support of a graph cannot exceed that of its subgraphs.  ... 
doi:10.1007/978-3-642-37382-4_10 fatcat:hvz3v7p3orbwnofe5dv5je7mre

Finding the most descriptive substructures in graphs with discrete and numeric labels

Michael Davis, Weiru Liu, Paul Miller
2013 Journal of Intelligent Information Systems  
We support our findings with experiments on transaction graphs and single large graphs from the domains of physical building security and digital forensics, measuring the effect on runtime, memory requirements  ...  Many graph datasets are labelled with discrete and numeric attributes.  ...  Support is an anti-monotone property: the support of a graph cannot exceed that of its subgraphs.  ... 
doi:10.1007/s10844-013-0299-7 fatcat:eqrepgrfi5bi3pwcoiol6ygura

SUBGRAPH WITH SET SIMILARITY IN ADATABASE

Vinjamuri Kantha Rao
2017 Asia-pacific Journal of Convergent Research Interchange  
To with efficiency method the SMS2 question, this paper styles a unique lattice-based index for knowledge graph, and light-weight signatures for each question vertices and knowledge vertices. supported  ...  , we have a tendency to study a subgraph matching with set similarity (SMS2) question over an outsized graph information, that retrieves subgraphs that ar structurally isomorphous to the question graph  ...  The set,similarity pruning includes anti-monotone pruning, vertical pruning, and horizontal pruning, that ar supported our projected inverted pattern lattice. supported the signature buckets, we have a  ... 
doi:10.21742/apjcri.2017.06.04 fatcat:x2x2hd3nuzadvfhkzbewjv3ssq

The Minimum Consistent Subset Cover Problem: A Minimization View of Data Mining

Byron J. Gao, Martin Ester, Hui Xiong, Jin-Yi Cai, Oliver Schulte
2013 IEEE Transactions on Knowledge and Data Engineering  
The MCSC problem generalizes the traditional set covering problem and has Minimum Clique Partition, a dual problem of graph coloring, as an instance.  ...  CAG starts by constructing a maximal optimal partial solution, then performs an example-driven specific-to-general search on a dynamically maintained bipartite assignment graph to simultaneously learn  ...  anti-monotonic constraints.  ... 
doi:10.1109/tkde.2011.260 fatcat:qxj7xzuucfbqfdkxzp4wgzkevy

The minimum consistent subset cover problem and its applications in data mining

Byron J. Gao, Martin Ester, Jin-Yi Cai, Oliver Schulte, Hui Xiong
2007 Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '07  
The MCSC problem generalizes the traditional set covering problem and has Minimum Clique Partition, a dual problem of graph coloring, as an instance.  ...  CAG starts by constructing a maximal optimal partial solution, then performs an example-driven specific-to-general search on a dynamically maintained bipartite assignment graph to simultaneously learn  ...  anti-monotonic constraints.  ... 
doi:10.1145/1281192.1281228 dblp:conf/kdd/GaoESCX07 fatcat:hedl4ciq4jd5jjctjo3nyvh7yi

Overlapping Community Extraction: A Link Hypergraph Partitioning Based Method

Haicheng Tao, Zhiang Wu, Jin Shi, Jie Cao, Xiaofeng Yu
2014 2014 IEEE International Conference on Services Computing  
Finally, based on extracted link communities, we restore the membership of nodes in the original graph owing to its links.  ...  In this paper, we explore overlapping community extraction from a link partitioning perspective.  ...  As is known, the anti-monotone property (AMP) held by the support measure determines it can be leveraged to reduce the search space of frequent patterns.  ... 
doi:10.1109/scc.2014.25 dblp:conf/IEEEscc/TaoWSCY14 fatcat:l2c5klg5zjbbtkorgwdzeec4dq

Support measures for graph data*

N. Vanetik, S. E. Shimony, E. Gudes
2006 Data mining and knowledge discovery  
Most mining algorithms require the support of a pattern to be no greater than that of its subpatterns, a property called admissibility (also called anti-monotonicity).  ...  Support measures for mining graphs are usually based on the notion of an instance graph -a graph representing all the instances of the pattern in a database and their intersection properties.  ...  The importance of the fundamental property of support measures (a.k.a. anti-monotonicity or downward closure) for itemsets indicates its general applicability, leading to the following definition: Definition  ... 
doi:10.1007/s10618-006-0044-8 fatcat:cdcfb63niva4fciqnc567xlt4a
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