RecurSIA-RRT: Recursive Translatable Point-Set Pattern Discovery with Removal of Redundant Translators

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1168)


We introduce two algorithms, RecurSIA and RRT, designed to increase the compression factor achievable using point-set cover algorithms based on the SIA and SIATEC pattern discovery algorithms. SIA computes the maximal translatable patterns (MTPs) in a point set, while SIATEC computes the translational equivalence class (TEC) of every MTP in a point set, where the TEC of an MTP is the set of translationally invariant occurrences of that MTP in the point set. In its output, SIATEC encodes each MTP TEC as a pair, \(\langle P,{V}\rangle \), where \(P\) is the first occurrence of the MTP and \({V}\) is the set of non-zero vectors that map \(P\) onto its other occurrences. RecurSIA recursively applies a TEC cover algorithm to the pattern \(P\), in each TEC, \(\langle P,{V}\rangle \), that it discovers. RRT attempts to remove translators from \({V}\) in each TEC without reducing the total set of points covered by the TEC. When evaluated with COSIATEC, SIATECCompress and Forth’s algorithm on the JKU Patterns Development Database, using RecurSIA with or without RRT increased compression factor and recall but reduced precision. Using RRT alone increased compression factor and reduced recall and precision, but had a smaller effect than RecurSIA.


Pattern discovery Point sets Music analysis Data compression SIATEC COSIATEC SIATECCompress Forth’s algorithm Geometric pattern discovery in music 



The author would like to thank Geraint A. Wiggins for suggesting the idea of applying the COSIATEC algorithm recursively to the patterns in TECs.


  1. 1.
    Collins, T.: Improved methods for pattern discovery in music, with applications in automated stylistic composition. Ph.D. thesis, Faculty of Mathematics, Computing and Technology, The Open University, Milton Keynes (2011)Google Scholar
  2. 2.
    Collins, T.: JKU Patterns Development Database (2013).
  3. 3.
    Collins, T., Thurlow, J., Laney, R., Willis, A., Garthwaite, P.H.: A comparative evaluation of algorithms for discovering translational patterns in baroque keyboard works. In: 11th International Society for Music Information Retrieval Conference (ISMIR 2010), Utrecht, The Netherlands, 9–13 August 2010, pp. 3–8 (2010)Google Scholar
  4. 4.
    Forth, J.C.: Cognitively-motivated geometric methods of pattern discovery and models of similarity in music. Ph.D. thesis, Department of Computing, Goldsmiths, University of London (2012)Google Scholar
  5. 5.
    Forth, J., Wiggins, G.A.: An approach for identifying salient repetition in multidimensional representations of polyphonic music. In: Chan, J., Daykin, J.W., Rahman, M.S. (eds.) London Algorithmics 2008: Theory and Practice, pp. 44–58. College Publications, London (2009)Google Scholar
  6. 6.
    Giraud, M., Groult, R., Levé, F.: Subject and counter-subject detection for analysis of the Well-Tempered Clavier fugues. In: Aramaki, M., Barthet, M., Kronland-Martinet, R., Ystad, S. (eds.) CMMR 2012. LNCS, vol. 7900, pp. 422–438. Springer, Heidelberg (2013). Scholar
  7. 7.
    Giraud, M., Groult, R., Levé, F.: Truth file for the analysis of Bach and Shostakovich fugues (2013/12/27 version) (2013).
  8. 8.
    Louboutin, C., Meredith, D.: Using general-purpose compression algorithms for music analysis. J. New Music. Res. 45(1), 1–16 (2016)CrossRefGoogle Scholar
  9. 9.
  10. 10.
    Meredith, D.: Point-set algorithms for pattern discovery and pattern matching in music. In: Dagstuhl Seminar on Content-based Retrieval (No. 06171, 23–28 April 2006). Schloss Dagstuhl, Germany (2006).
  11. 11.
    Meredith, D.: COSIATEC and SIATECCompress: pattern discovery by geometric compression. In: MIREX 2013 (Competition on Discovery of Repeated Themes & Sections) (2013).
  12. 12.
    Meredith, D.: Using point-set compression to classify folk songs. In: Fourth International Workshop on Folk Music Analysis (FMA 2014), 12–13 June 2014. Bogazici University, Istanbul (2014)Google Scholar
  13. 13.
    Meredith, D.: Music analysis and point-set compression. J. New Music. Res. 44(3), 245–270 (2015)CrossRefGoogle Scholar
  14. 14.
    Meredith, D.: Analysing music with point-set compression algorithms. In: Meredith, D. (ed.) Computational Music Analysis, pp. 335–366. Springer, Cham (2016). Scholar
  15. 15.
    Meredith, D., Lemström, K., Wiggins, G.A.: Algorithms for discovering repeated patterns in multidimensional representations of polyphonic music. J. New Music. Res. 31(4), 321–345 (2002)CrossRefGoogle Scholar
  16. 16.
    Meredith, D., Lemström, K., Wiggins, G.A.: Algorithms for discovering repeated patterns in multidimensional representations of polyphonic music. In: Cambridge Music Processing Colloquium (2003).
  17. 17.
    Rissanen, J.: Modeling by shortest data description. Automatica 14(5), 465–471 (1978)CrossRefGoogle Scholar
  18. 18.
    Vereshchagin, N.K., Vitányi, P.M.B.: Kolmogorov’s structure functions and model selection. IEEE Trans. Inf. Theory 50(12), 3265–3290 (2004)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Vitányi, P.M.B., Li, M.: Minimum description length induction, Bayesianism and Kolmogorov complexity. IEEE Trans. Inf. Theory 46(2), 446–464 (2000)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Wiggins, G.A., Lemström, K., Meredith, D.: SIA(M)ESE: an algorithm for transposition invariant, polyphonic content-based music retrieval. In: Proceedings of the Third International Conference on Music Information Retrieval (ISMIR 2002), Paris, France, 13–17 October 2002, pp. 283–284 (2002)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Aalborg UniversityAalborgDenmark

Personalised recommendations