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Fast and Adaptive Variable Order Markov Chain Construction

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Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 5251))

Abstract

Variable order Markov chains (VOMCs) are a flexible class of models that extend the well-known Markov chains. They have been applied to a variety of problems in computational biology, e.g. protein family classification. A linear time and space construction algorithm has been published in 2000 by Apostolico and Bejerano. However, neither a report of the actual running time nor an implementation of it have been published since. In this paper we use the lazy suffix tree and the enhanced suffix array to improve upon the algorithm of Apostolico and Bejerano. We introduce a new software which is orders of magnitude faster than current tools for building VOMCs, and is suitable for large scale sequence analysis.

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References

  1. Rissanen, J.: A universal data compression system. IEEE Transactions on Information Theory 29, 656–664 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ron, D., Singer, Y., Tishby, N.: The power of amnesia: Learning probabilistic automata with variable memory length. Machine Learning 25, 117–149 (1996)

    Article  MATH  Google Scholar 

  3. Ben-Gal, I., Shani, A., Gohr, A., Grau, J., Arviv, S., Shmilovici, A., Posch, S., Grosse, I.: Identification of transcription factor binding sites with variable-order Bayesian networks. Bioinformatics 21(11), 2657–2666 (2005)

    Article  Google Scholar 

  4. Zhao, X., Huang, H., Speed, T.P.: Finding short DNA motifs using permuted Markov models. J. Comput. Biol. 12(6), 894–906 (2005)

    Article  Google Scholar 

  5. Ogul, H., Mumcuoglu, E.U.: SVM-based detection of distant protein structural relationships using pairwise probabilistic suffix trees. Comput. Biol. Chem. 30(4), 292–299 (2006)

    Article  MATH  Google Scholar 

  6. Dalevi, D., Dubhashi, D., Hermansson, M.: Bayesian classifiers for detecting HGT using fixed and variable order markov models of genomic signatures. Bioinformatics 22(5), 517–522 (2006)

    Article  Google Scholar 

  7. Bejerano, G., Seldin, Y., Margalit, H., Tishby, N.: Markovian domain fingerprinting: statistical segmentation of protein sequences. Bioinformatics 17(10), 927–934 (2001)

    Article  Google Scholar 

  8. Slonim, N., Bejerano, G., Fine, S., Tishby, N.: Discriminative feature selection via multiclass variable memory Markov model. EURASIP J. Appl. Signal Process 2003(1), 93–102 (2003)

    Article  Google Scholar 

  9. Bejerano, G., Yona, G.: Variations on probabilistic suffix trees: statistical modeling and prediction of protein families. Bioinformatics 17(1), 23–43 (2001)

    Article  Google Scholar 

  10. Posch, S., Grau, J., Gohr, A., Ben-Gal, I., Kel, A.E., Grosse, I.: Recognition of cis-regulatory elements with vombat. J. Bioinform. Comput. Biol. 5(2B), 561–577 (2007)

    Article  Google Scholar 

  11. Apostolico, A., Bejerano, G.: Optimal amnesic probabilistic automata or how to learn and classify proteins in linear time and space. J. Comput. Biol. 7(3-4), 381–393 (2000)

    Article  Google Scholar 

  12. Bejerano, G.: Algorithms for variable length Markov chain modeling. Bioinformatics 20(5), 788–789 (2004)

    Article  Google Scholar 

  13. Leonardi, F.G.: A generalization of the PST algorithm: modeling the sparse nature of protein sequences. Bioinformatics 22(11), 1302–1307 (2006)

    Article  Google Scholar 

  14. Kurtz, S.: Reducing the space requirement of suffix trees. Software Pract. Exper. 29(13), 1149–1171 (1999)

    Article  Google Scholar 

  15. Giegerich, R., Kurtz, S., Stoye, J.: Efficient implementation of lazy suffix trees. Software Pract. Exper. 33(11), 1035–1049 (2003)

    Article  Google Scholar 

  16. Manber, U., Myers, E.: Suffix arrays: A new method for on-line string searches. SIAM J. Comput. 22(5), 935–948 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ferragina, P., Manzini, G., Mäkinen, V., Navarro, G.: Compressed representations of sequences and full-text indexes. ACM Trans. Algorithms 3(2), 20 (2007)

    Article  MathSciNet  Google Scholar 

  18. Abouelhoda, M., Kurtz, S., Ohlebusch, E.: Replacing suffix trees with enhanced suffix arrays. Journal of Discrete Algorithms 2, 53–86 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Bühlmann, P., Wyner, A.J.: Variable length Markov chains. Ann. Statist. 27(2), 480–513 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  20. Maaß, M.G.: Computing suffix links for suffix trees and arrays. Inf. Process. Lett. 101(6), 250–254 (2007)

    Article  Google Scholar 

  21. Manzini, G., Ferragina, P.: Engineering a lightweight suffix array construction algorithm. Algorithmica 40(1), 33–50 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  22. Giegerich, R., Kurtz, S.: A comparison of imperative and purely functional suffix tree constructions. Sci. Comput. Program. 25, 187–218 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  23. Benson, D.A., Karsch-Mizrachi, I., Lipman, D.J., Ostell, J., Wheeler, D.L.: GenBank. Nucleic Acids Res. 36(Database issue), D25–D30 (2008)

    Google Scholar 

  24. Fitzgerald, P.C., Sturgill, D., Shyakhtenko, A., Oliver, B., Vinson, C.: Comparative genomics of drosophila and human core promoters. Genome Biol. 7, R53 (2006)

    Article  Google Scholar 

  25. The UniProt Consortium: The Universal Protein Resource (UniProt). Nucl. Acids Res. 36(suppl.1), D190–195 (2008)

    Google Scholar 

  26. Döring, A., Weese, D., Rausch, T., Reinert, K.: SeqAn an efficient, generic C++ library for sequence analysis. BMC Bioinformatics 9, 11 (2008)

    Article  Google Scholar 

  27. Schulz, M.H., Bauer, S., Robinson, P.N.: The generalised k-Truncated Suffix Tree for time- and space- efficient searches in multiple DNA or protein sequences. Int. J. Bioinform. Res. Appl. 4(1), 81–95 (2008)

    Article  Google Scholar 

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Keith A. Crandall Jens Lagergren

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© 2008 Springer-Verlag Berlin Heidelberg

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Schulz, M.H., Weese, D., Rausch, T., Döring, A., Reinert, K., Vingron, M. (2008). Fast and Adaptive Variable Order Markov Chain Construction. In: Crandall, K.A., Lagergren, J. (eds) Algorithms in Bioinformatics. WABI 2008. Lecture Notes in Computer Science(), vol 5251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87361-7_26

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  • DOI: https://doi.org/10.1007/978-3-540-87361-7_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87360-0

  • Online ISBN: 978-3-540-87361-7

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