Abstract
Clustering and classification hierarchies are organizational structures of a set of objects. Multiple hierarchies may be derived over the same set of objects, which makes distance computation between hierarchies an important task. In this paper, we model the classification and clustering hierarchies as rooted, leaf-labeled, unordered trees. We propose a novel distance metric Split-Order distance to evaluate the organizational structure difference between two hierarchies over the same set of leaf objects. Split-Order distance reflects the order in which subsets of the tree leaves are differentiated from each other and can be used to explain the relationships between the leaf objects. We also propose an efficient algorithm for computing Split-Order distance between two trees in O(n 2 d 4) time, where n is the number of leaves, and d is the maximum number of children of any node. Our experiments on both real and synthetic data demonstrate the efficiency and effectiveness of our algorithm.
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References
Allen, B.L., Steel, M.: Subtree transfer operations and their induced metrics on evolutionary trees. Annals of Combinatorics 5, 1–13 (2001)
Amir, A., Keselman, D.: Maximum agreement subtree in a set of evolutionary trees: metrics and efficient algorithms. Proc. of the SIAM Journal on Computing 26(6), 1656–1669 (1997)
Bille, P.: A survey on tree edit distance and related problems. Theoretical Computer Science, 217–239 (2005)
Demaine, E.D., Mozes, S., Rossman, B., Weimann, O.: An Optimal Decomposition Algorithm for Tree Edit Distance. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 146–157. Springer, Heidelberg (2007)
Eastabrook, G.F., McMorris, F.R., Meacham, C.A.: Comparison of undirected phylogenetic trees based on subtrees of four evolutionary units. Syst. Zool (1985)
Felsenstein, J.: Cases in which parsimony and compatibility methods will be positively misleading. Syst. Zool. 27, 401–410 (1978)
Iyer, V.R., Eisen, M.B., Ross, D.T., Schuler, G., Moore, T., Lee, J.C., Trent, J.M., Staudt, L.M., Hudson Jr., J., Boguski, M.S., Lashkari, D., Shalon, D., Botstein, D., Brown, P.O.: Transcriptional program in the response of human fibroblasts to serum. Science 283, 83–87 (1996)
Jiang, D., Pei, J., Zhang, A.: DHC: a density-based hierarchical clustering method for time series gene expression data. In: Proc. of the The Third Symposium on Bioinformatics and Bioengineering, pp. 393–400 (2003)
Karypis, G.: CLUTO - A Clustering Toolkit. Tech Report, Dept. of Computer Science, University of Minnesota (2002)
Klein, P.N.: Computing the edit-distance between unrooted ordered trees. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, p. 91. Springer, Heidelberg (1998)
Lu, S.Y.: A tree-to-tree distance and its application to cluster analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI) (1979)
Robinson, D.F., Foulds, L.R.: Comparison of weighted labeled trees. Combinatorial mathematics VI, 119–126 (1979)
Robinson, D.F., Foulds, L.: Comparison of phylogenetic trees. Math. Biosci. 53(1-2), 131–147 (1981)
Saitou, N., Nei, M.: The neighbor-joining method: a new method for reconstructing phylogenetic trees. The Mol. Biol. Evol. 4(4), 406–425 (1987)
Shasha, D., Wang, J.T.L., Zhang, S.: Unordered Tree Mining with Applications to Phylogeny. In: Proc. IEEE International Conference on Data Engineering (ICDE 2004) (2004)
Sneath, P.H.A., Sokal, R.R.: Numerical Taxonomy, pp. 230–234. WH Freeman and Company, New York (1973)
Touzet, H.: Tree edit distance with gaps. Information Processing Letters 85(3), 123–129 (2003)
Wang, J.T., Zhang, K., Jeong, K., Shasha, D.: A system for approximate tree matching. IEEE Transactions on Knowledge and Data Engineering 6(4), 559–571 (1994)
Eastabrook, G.F., McMorris, F.R., Meacham, C.A.: TreeRank: A similarity measure for nearest neighbor searching in phylogenetic databases. In: Proc. of the 15th International Conference on Scientific and Statistical Database Management (1985)
Waterman, M.S., Smith, T.F.: On the similarity of dendrograms. Journal of Theoretical Biology 73, 789–800 (1978)
Zhang, K., Shasha, D.: Simple fast algorithms for the editing distance between trees and related problems. SIAM Journal of Computing (1989)
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Zhang, Q., Liu, E.Y., Sarkar, A., Wang, W. (2009). Split-Order Distance for Clustering and Classification Hierarchies. In: Winslett, M. (eds) Scientific and Statistical Database Management. SSDBM 2009. Lecture Notes in Computer Science, vol 5566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02279-1_37
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DOI: https://doi.org/10.1007/978-3-642-02279-1_37
Publisher Name: Springer, Berlin, Heidelberg
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