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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Rissanen, J.: A universal data compression system. IEEE Transactions on Information Theory 29, 656–664 (1983)
Ron, D., Singer, Y., Tishby, N.: The power of amnesia: Learning probabilistic automata with variable memory length. Machine Learning 25, 117–149 (1996)
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)
Zhao, X., Huang, H., Speed, T.P.: Finding short DNA motifs using permuted Markov models. J. Comput. Biol. 12(6), 894–906 (2005)
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)
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)
Bejerano, G., Seldin, Y., Margalit, H., Tishby, N.: Markovian domain fingerprinting: statistical segmentation of protein sequences. Bioinformatics 17(10), 927–934 (2001)
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)
Bejerano, G., Yona, G.: Variations on probabilistic suffix trees: statistical modeling and prediction of protein families. Bioinformatics 17(1), 23–43 (2001)
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)
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)
Bejerano, G.: Algorithms for variable length Markov chain modeling. Bioinformatics 20(5), 788–789 (2004)
Leonardi, F.G.: A generalization of the PST algorithm: modeling the sparse nature of protein sequences. Bioinformatics 22(11), 1302–1307 (2006)
Kurtz, S.: Reducing the space requirement of suffix trees. Software Pract. Exper. 29(13), 1149–1171 (1999)
Giegerich, R., Kurtz, S., Stoye, J.: Efficient implementation of lazy suffix trees. Software Pract. Exper. 33(11), 1035–1049 (2003)
Manber, U., Myers, E.: Suffix arrays: A new method for on-line string searches. SIAM J. Comput. 22(5), 935–948 (1993)
Ferragina, P., Manzini, G., Mäkinen, V., Navarro, G.: Compressed representations of sequences and full-text indexes. ACM Trans. Algorithms 3(2), 20 (2007)
Abouelhoda, M., Kurtz, S., Ohlebusch, E.: Replacing suffix trees with enhanced suffix arrays. Journal of Discrete Algorithms 2, 53–86 (2004)
Bühlmann, P., Wyner, A.J.: Variable length Markov chains. Ann. Statist. 27(2), 480–513 (1999)
Maaß, M.G.: Computing suffix links for suffix trees and arrays. Inf. Process. Lett. 101(6), 250–254 (2007)
Manzini, G., Ferragina, P.: Engineering a lightweight suffix array construction algorithm. Algorithmica 40(1), 33–50 (2004)
Giegerich, R., Kurtz, S.: A comparison of imperative and purely functional suffix tree constructions. Sci. Comput. Program. 25, 187–218 (1995)
Benson, D.A., Karsch-Mizrachi, I., Lipman, D.J., Ostell, J., Wheeler, D.L.: GenBank. Nucleic Acids Res. 36(Database issue), D25–D30 (2008)
Fitzgerald, P.C., Sturgill, D., Shyakhtenko, A., Oliver, B., Vinson, C.: Comparative genomics of drosophila and human core promoters. Genome Biol. 7, R53 (2006)
The UniProt Consortium: The Universal Protein Resource (UniProt). Nucl. Acids Res. 36(suppl.1), D190–195 (2008)
Döring, A., Weese, D., Rausch, T., Reinert, K.: SeqAn an efficient, generic C++ library for sequence analysis. BMC Bioinformatics 9, 11 (2008)
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)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)