A Pattern Extraction Algorithm for Abstract Melodic Representations that Allow Partial Overlapping of Intervallic Categories

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special "don't care" symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established "step-leap " representation is examined. In the step-leap representation, each melodic diatonic interval is classified as a step (±s), a leap (±l) or a unison (u). Binary don't care symbols are introduced to represent categories e.g. ∗ = s, ∗ = l and # = -s, # = -l. For such a sequence, we are interested in finding maximal repeating pairs and repetitions with a hole (two matching subsequences separated with an intervening non-matching symbol). We propose an O(n+d(n-d)+z)-time algorithm for computing all such repetitions in a given sequence x = x[1..n] with d binary don't care symbols, where z is the output size.

[1]  Dan Gusfield,et al.  Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology , 1997 .

[2]  Kjell Lemström,et al.  Musical Information Retrieval Using Musical Parameters , 1998, ICMC.

[3]  Brian Christopher Smith,et al.  Query by humming: musical information retrieval in an audio database , 1995, MULTIMEDIA '95.

[4]  Wojciech Rytter,et al.  Jewels of stringology , 2002 .

[5]  Emilios Cambouropoulos,et al.  Musical Parallelism and Melodic Segmentation: : A Computational Approach , 2006 .

[6]  Franco P. Preparata,et al.  Optimal Off-Line Detection of Repetitions in a String , 1983, Theor. Comput. Sci..

[7]  Costas S. Iliopoulos,et al.  Computing Approximate Repetitions in Musical Sequences , 2000, Stringology.

[8]  Costas S. Iliopoulos,et al.  Approximate string matching for music analysis , 2004, Soft Comput..

[9]  Costas S. Iliopoulos,et al.  String Regularities with Don't Cares , 2003, Nord. J. Comput..

[10]  Moshe Lewenstein,et al.  Approximate subset matching with Don't Cares , 2001, SODA '01.

[11]  Maxime Crochemore,et al.  Algorithms For Computing Approximate Repetitions In Musical Sequences , 2002, Int. J. Comput. Math..

[12]  M. Fischer,et al.  STRING-MATCHING AND OTHER PRODUCTS , 1974 .

[13]  Rajeev Raman,et al.  String-Matching techniques for musical similarity and melodic recognition , 1998 .

[14]  Uzi Vishkin,et al.  On Finding Lowest Common Ancestors: Simplification and Parallelization , 1988, AWOC.