Abstract
We consider the problem of discovering the optimal pattern from a set of strings and associated numeric attribute values. The goodness of a pattern is measured by the correlation between the number of occurrences of the pattern in each string, and the numeric attribute value assigned to the string. We present two algorithms based on suffix trees, that can find the optimal substring pattern in O(Nn) and O(N 2) time, respectively, where n is the number of strings and N is their total length. We further present a general branch and bound strategy that can be used when considering more complex pattern classes. We also show that combining the O(N 2) algorithm and the branch and bound heuristic increases the efficiency of the algorithm considerably.
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References
Brazma, A., Jonassen, I., Eidhammer, I., Gilbert, D.: Approaches to the automatic discovery of patterns in biosequences. J. Comput. Biol. 5, 279–305 (1998)
Hirao, M., Hoshino, H., Shinohara, A., Takeda, M., Arikawa, S.: A practical algorithm to find the best subsequence patterns. Theoretical Computer Science 292, 465–479 (2002)
Shinohara, A., Takeda, M., Arikawa, S., Hirao, M., Hoshino, H., Inenaga, S.: Finding best patterns practically. In: Arikawa, S., Shinohara, A. (eds.) Progress in Discovery Science. LNCS (LNAI), vol. 2281, pp. 307–317. Springer, Heidelberg (2002)
Takeda, M., Inenaga, S., Bannai, H., Shinohara, A., Arikawa, S.: Discovering most classificatory patterns for very expressive pattern classes. In: Grieser, G., Tanaka, Y., Yamamoto, A. (eds.) DS 2003. LNCS (LNAI), vol. 2843, pp. 486–493. Springer, Heidelberg (2003)
Hirao, M., Inenaga, S., Shinohara, A., Takeda, M., Arikawa, S.: A practical algorithm to find the best episode patterns. In: Jantke, K.P., Shinohara, A. (eds.) DS 2001. LNCS (LNAI), vol. 2226, pp. 435–440. Springer, Heidelberg (2001)
Inenaga, S., Bannai, H., Shinohara, A., Takeda, M., Arikawa, S.: Discovering best variable-length-don’t-care patterns. In: Lange, S., Satoh, K., Smith, C.H. (eds.) DS 2002. LNCS (LNAI), vol. 2534, pp. 86–97. Springer, Heidelberg (2002)
Bussemaker, H.J., Li, H., Siggia, E.D.: Regulatory element detection using correlation with expression. Nature Genetics 27, 167–171 (2001)
Bannai, H., Inenaga, S., Shinohara, A., Takeda, M., Miyano, S.: A string pattern regression algorithm and its application to pattern discovery in long introns. Genome Informatics 13, 3–11 (2002)
Bannai, H., Inenaga, S., Shinohara, A., Takeda, M., Miyano, S.: Efficiently finding regulatory elements using correlation with gene expression. Journal of Bioinformatics and Computational Biology 2, 273–288 (2004)
Zilberstein, C.B.Z., Eskin, E., Yakhini, Z.: Using expression data to discover RNA and DNA regulatory sequence motifs. In: The First Annual RECOMB Satellite Workshop on Regulatory Genomics (2004)
Bannai, H., Hyyrö, H., Shinohara, A., Takeda, M., Nakai, K., Miyano, S.: An O(N2) algorithm for discovering optimal Boolean pattern pairs. IEEE/ACM Transactions on Computational Biology and Bioinformatics 1, 159–170 (special issue for selected papers of WABI 2004)
Hui, L.: Color set size problem with applications to string matching. In: Apostolico, A., Galil, Z., Manber, U., Crochemore, M. (eds.) CPM 1992. LNCS, vol. 644, pp. 230–243. Springer, Heidelberg (1992)
Miyano, S., Shinohara, A., Shinohara, T.: Which classes of elementary formal systems are polynomial-time learnable? In: Proceedings of the 2nd Workshop on Algorithmic Learning Theory, pp. 139–150 (1991)
Miyano, S., Shinohara, A., Shinohara, T.: Polynomial-time learning of elementary formal systems. New Generation Computing 18, 217–242 (2000)
Gusfield, D.: Algorithms on Strings, Trees, and Sequences. Cambridge University Press, Cambridge (1997)
Knuth, D.E., Morris, J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM Journal on Computing 6, 323–350 (1977)
Kasai, T., Lee, G., Arimura, H., Arikawa, S., Park, K.: Linear-time longest-common-prefix computation in suffix arrays and its applications. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, pp. 181–192. Springer, Heidelberg (2001)
Kasai, T., Arimura, H., Arikawa, S.: Efficient substring traversal with suffix arrays. Technical Report 185, Department of Informatics, Kyushu University (2001)
Spellman, P.T., Sherlock, G., Zhang, M.Q., Iyer, V.R., Anders, K., Eisen, M.B., Brown, P.O., Botstein, D., Futcher, B.: Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Mol. Biol. Cell 9, 3273–3297 (1998)
Shinozaki, D., Akutsu, T., Maruyama, O.: Finding optimal degenerate patterns in DNA sequences. Bioinformatics 19, ii206–ii214 (2003)
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Bannai, H., Hatano, K., Inenaga, S., Takeda, M. (2005). Practical Algorithms for Pattern Based Linear Regression. In: Hoffmann, A., Motoda, H., Scheffer, T. (eds) Discovery Science. DS 2005. Lecture Notes in Computer Science(), vol 3735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11563983_6
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DOI: https://doi.org/10.1007/11563983_6
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