HybridTreeMiner: an efficient algorithm for mining frequent rooted trees and free trees using canonical forms

Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. In this paper, we present HybridTreeMiner, a computationally efficient algorithm that discovers all frequently occurring subtrees in a database of rooted unordered trees. The algorithm mines frequent subtrees by traversing an enumeration tree that systematically enumerates all subtrees. The enumeration tree is defined based on a novel canonical form for rooted unordered trees - the breadth-first canonical form (BFCF). By extending the definitions of our canonical form and enumeration tree to free trees, our algorithm can efficiently handle databases of free trees as well. We study the performance of our algorithms through extensive experiments based on both synthetic data and datasets from real applications. The experiments show that our algorithm is competitive in comparison to known rooted tree mining algorithms and is faster by one to two orders of magnitudes compared to a known algorithm for mining frequent free trees.

[1]  Mario Gerla,et al.  Aggregated Multicast – A Comparative Study , 2002, Cluster Computing.

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  Alexandre Termier,et al.  TreeFinder: a first step towards XML data mining , 2002, 2002 IEEE International Conference on Data Mining, 2002. Proceedings..

[4]  Tao Jiang,et al.  On the Complexity of Comparing Evolutionary Trees , 1996, Discret. Appl. Math..

[5]  Roberto J. Bayardo,et al.  Efficiently mining long patterns from databases , 1998, SIGMOD '98.

[6]  Wei Wang,et al.  Efficient mining of frequent subgraphs in the presence of isomorphism , 2003, Third IEEE International Conference on Data Mining.

[7]  Hiroki Arimura,et al.  Efficient Substructure Discovery from Large Semi-Structured Data , 2001, IEICE Trans. Inf. Syst..

[8]  Mohammed J. Zaki.  Efficiently mining frequent trees in a forest , 2002, KDD.

[9]  Divesh Srivastava,et al.  Counting twig matches in a tree , 2001, Proceedings 17th International Conference on Data Engineering.

[10]  Joost N. Kok,et al.  Efficient discovery of frequent unordered trees , 2003 .

[11]  Kaizhong Zhang,et al.  ATreeGrep: approximate searching in unordered trees , 2002, Proceedings 14th International Conference on Scientific and Statistical Database Management.

[12]  Charu C. Aggarwal,et al.  XRules: an effective structural classifier for XML data , 2003, KDD '03.

[13]  George Karypis,et al.  Frequent subgraph discovery , 2001, Proceedings 2001 IEEE International Conference on Data Mining.

[14]  Yun Chi,et al.  Indexing and mining free trees , 2003, Third IEEE International Conference on Data Mining.

[15]  Dennis Shasha,et al.  TreeRank: a similarity measure for nearest neighbor searching in phylogenetic databases , 2003, 15th International Conference on Scientific and Statistical Database Management, 2003..

[16]  Anukool Lakhina,et al.  BRITE: Universal Topology Generation from a User''s Perspective , 2001 .

[17]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[18]  Ramakrishnan Srikant,et al.  Fast algorithms for mining association rules , 1998, VLDB 1998.

[19]  Robin Wilson,et al.  Graphs and Applications , 2000 .

[20]  Jiawei Han,et al.  CloseGraph: mining closed frequent graph patterns , 2003, KDD '03.

[21]  Hiroki Arimura,et al.  Optimized Substructure Discovery for Semi-structured Data , 2002, PKDD.

[22]  Mukkai S. Krishnamoorthy,et al.  WWWPal - A System for Analysis and Synthesis of Web Pages , 1998, WebNet.

[23]  Takashi Washio,et al.  An Apriori-Based Algorithm for Mining Frequent Substructures from Graph Data , 2000, PKDD.

[24]  Dennis Shasha,et al.  Algorithmics and applications of tree and graph searching , 2002, PODS.

[25]  Charu C. Aggarwal,et al.  A Tree Projection Algorithm for Generation of Frequent Item Sets , 2001, J. Parallel Distributed Comput..

[26]  Jiawei Han,et al.  gSpan: graph-based substructure pattern mining , 2002, 2002 IEEE International Conference on Data Mining, 2002. Proceedings..

[27]  Robin Wilson,et al.  Graphs and Applications_ An Introductory Approach , 2001 .

[28]  Hiroki Arimura,et al.  Discovering Frequent Substructures in Large Unordered Trees , 2003, Discovery Science.

[29]  Tyng-Luh Liu,et al.  Approximate tree matching and shape similarity , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.