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

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

Abstract

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.

Keywords

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

Notes

Acknowledgements

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

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Aalborg UniversityAalborgDenmark

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