Abstract
Recent research in music retrieval has shown that a combinatorial approach to the problem could be fruitful. Three distinguishing requirements of this particular problem are (a) approximate searching permitting missing, extra, and distorted notes, (b) transposition invariance, to allow matching a sequence that appears in a different scale, and (c) handling polyphonic music. These combined requirements make up a complex combinatorial problem that is currently under research. On the other hand, bit-parallelism has proved a powerful practical tool for combinatorial pattern matching, both flexible and efficient. In this paper we use bit-parallelism to search for several transpositions at the same time, and obtain speedups of O(w/logk) over the classical algorithms, where the computer word has w bits and k is the error threshold allowed in the match. Although not the best solution for the easier approximation measures, we show that our technique can be adapted to complex cases where no competing method exists, and that are the most interesting in terms of music retrieval.
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
Cambouropoulos, E.: A general pitch interval representation: Theory and applications. Journal of New Music Research 25, 231–251 (1996)
Crochemore, M., Iliopoulos, C.S., Pinzon, Y.J., Rytter, W.: Finding motifs with gaps. In: First International Symposium on Music Information Retrieval (ISMIR 2000), Plymouth, MA (2000)
Crochemore, M., Iliopoulos, C.S., Navarro, G., Pinzon, Y.: A bit-parallel suffix automaton approach for (δ, γ)-matching in music retrieval. In: Nascimento, M.A., de Moura, E.S., Oliveira, A.L. (eds.) SPIRE 2003. LNCS, vol. 2857, pp. 211–223. Springer, Heidelberg (2003)
Crochemore, M., Iliopoulos, C.S., Pinzon, Y.J., Reid, J.F.: A fast and practical bit-vector algorithm for the longest common subsequence problem. Information Processing Letters 80(6), 279–285 (2001)
Crochemore, M., Rytter, W.: Text Algorithms. Oxford University Press, Oxford (1994)
Dovey, M.J.: A technique for “regular expression” style searching in polyphonic music. In: the 2nd Annual International Symposium on Music Information Retrieval (ISMIR 2001), Bloomington, IND, October 2001, pp. 179–185 (2001)
Holub, J., Iliopoulos, C.S., Mouchard, L.: Distributed string matching using finite automata. Journal of Automata, Languages and Combinatorics 6(2), 191–204 (2001)
Hyyrö, H., Navarro, G.: Faster bit-parallel approximate string matching. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 203–224. Springer, Heidelberg (2002)
Lemström, K., Laine, P.: Musical information retrieval using musical parameters. In: Proceedings of the 1998 International Computer Music Conference, Ann Arbor, MI, pp. 341–348 (1998)
Lemström, K., Tarhio, J.: Transposition invariant pattern matching for multitrack strings. Nordic Journal of Computing (2003) (to appear)
Lemström, K., Ukkonen, E.: Including interval encoding into edit distance based music comparison and retrieval. In: Proceedings of the AISB 2000 Symposium on Creative & Cultural Aspects and Applications of AI & Cognitive Science, Birmingham, April 2000, pp. 53–60 (2000)
Meredith, D., Lemström, K., Wiggins, G.A.: Algorithms for discovering repeated patterns in multidimensional representations of polyphonic music. Journal of New Music Research 31(4), 321–345 (2002)
MIDI Manufacturers Association, Los Angeles, California. The Complete Detailed MIDI 1.0 Specification (1996)
Myers, G.: A fast bit-vector algorithm for approximate string matching based on dynamic programming. Journal of the ACM 46(3), 395–415 (1999). In Farach-Colton, M. (ed.) CPM 1998. LNCS, vol. 1448, Springer, Heidelberg (1998)
Paul, W., Simon, J.: Decision trees and random access machines. In: Proc. Int’l. Symp. on Logic and Algorithmic, Zurich, pp. 331–340 (1980)
Wiggins, G.A., Lemström, K., Meredith, D.: Sia(M): A family of efficient algorithms for translation-invariant pattern matching in multidimensional datasets (submitted)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lemström, K., Navarro, G. (2003). Flexible and Efficient Bit-Parallel Techniques for Transposition Invariant Approximate Matching in Music Retrieval. In: Nascimento, M.A., de Moura, E.S., Oliveira, A.L. (eds) String Processing and Information Retrieval. SPIRE 2003. Lecture Notes in Computer Science, vol 2857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39984-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-39984-1_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20177-9
Online ISBN: 978-3-540-39984-1
eBook Packages: Springer Book Archive