Frequent Closed Itemset

A Frequent Closed Itemset is a Frequent Itemset that …

• AKA: Closed Frequent Itemset, Closed Itemset.
• See: Association Rule.

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References

2007

• Yoshifumi Okada, Wataru Fujibuchi, and Paul Horton. (2007). “A Biclustering Method for Gene Expression Module Discovery Using a Closed Itemset Enumeration Algorithm.” In: IPSJ Transactions on Bioinformatics, vol. 48, no. SIG 5(TBIO2).
  • QUOTE: [math]\displaystyle{ P }[/math] is a closed itemset if there exists no itemset. P such that P?P and supp(P)=supp(P)
  • ABSTRACT: Abstract: A gene expression module (module for short) is a set of genes with shared expression behavior under certain experimental conditions. Discovering of modules enables us to uncover the function of uncharacterized genes or genetic networks. In recent years, several biclustering methods have been suggested to discover modules from gene expression data matrices, where a bicluster is defined as a subset of genes that exhibit a highly correlated expression pattern over a subset of conditions. Biclustering however involves combinatorial optimization in selecting the rows and columns composing modules. Hence most existing algorithms are based on heuristic or stochastic approaches and produce possibly sub-optimal solutions. In this paper, we propose a novel biclustering method, BiModule, based on a closed itemset enumeration algorithm. By exhaustive enumeration of such biclusters, it is possible to select only biclusters satisfying certain criteria such as a user-specified bicluster size, an enrichment of functional annotation terms, etc. We performed comparative experiments to existing salient biclustering methods to test the validity of biclusters extracted by BiModule using synthetic data and real expression data. We show that BiModule provides high performance compared to the other methods in extracting artificially-embedded modules as well as modules strongly related to GO annotations, protein-protein interactions and metabolic pathways

2005

• Tian-rui Li, Da Ruan, Tianmin Huang, and Yang Xu. (2005). “On a Mathematical Relationship Between the Fixed Point and the Closed Itemset in Association Rule Mining.” In: International Journal of Mathematics and Analysis, 1:1. doi:10.1007/11589990
  • QUOTE: … is a closed itemset if there exists no itemset [math]\displaystyle{ Y }[/math] such that [math]\displaystyle{ Y }[/math] is a proper superset of [math]\displaystyle{ X }[/math] and every transaction containing [math]\displaystyle{ X }[/math] also contains [math]\displaystyle{ Y }[/math] [4].
  • ABSTRACT: Association rule mining is one of important research topics in knowledge discovery and data mining. Recent promising direction of association rule mining is mainly to mine closed itemsets. Based on the Galois closed operators, a mathematical relationship between the fixed point and closed itemset in association rule mining is discussed and several properties are obtained. To mine all frequent closed itemsets is equal to build the fixed point lattice and mine its all points that satisfy support constraints. A new method for visualization of association rules based on the generalized association rule base is also proposed.

2004

• (Sivanandam et al., 2004) ⇒ S. N. Sivanandam, D. Sumathi, T. Hamsapriya, and K. Babu. (2004). “Parallel Buddy Prima – A Hybrid Parallel Frequent itemset mining algorithm for very large databases." Retrieved from http://www.acadjournal.com.
  • A frequent itemset is called closed if it does not have any superset with the same support. A frequent itemset is said to be maximal if it has no supersets that are frequent. The collection of maximal frequent itemsets is a subset of the collection of closed frequent itemsets, which is a subset of the collection of all frequent itemsets. Maximal frequent itemsets are necessary for generating association rules.

2000

• (Pei et al., 2000) ⇒ Jian Pei, Jiawei Han, and Runying Mao. (2000). “CLOSET: An efficient algorithm for mining frequent closed itemsets.” In: Proceedings of the 2000 ACM SIGMOD Workshop Data Mining and Knowledge Discovery (DMKD 2000).
  • Presentation slides: http://www.cs.ualberta.ca/~zaiane/courses/cmput695-02/slides/gradP1-695-02.pdf

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