Algorithms for Computing Geometric Measures of Melodic Similarity

@article{Aloupis2006AlgorithmsFC,
  title={Algorithms for Computing Geometric Measures of Melodic Similarity},
  author={Greg Aloupis and T. Fevens and Stefan Langerman and Tomomi Matsui and Antonio Mesa and Yurai N{\'u}{\~n}ez Rodr{\'i}guez and David Rappaport and Godfried T. Toussaint},
  journal={Computer Music Journal},
  year={2006},
  volume={30},
  pages={67-76}
}
Greg Aloupis, Thomas Fevens, Stefan Langerman, Tomomi Matsui, Antonio Mesa, Yurai Nunez, David Rappaport, and Godfried Toussaint *School of Computer Science, McGill University 3480 University Street Montreal, Quebec, Canada H3A 2A7 {athens,godfried}@cs.mcgill.ca †Department of Computer Science and Software Engineering, Concordia University 1455 de Maisonneuve Boulevard West Montreal, Quebec, Canada H3G 1M8 fevens@cs.concordia.ca ‡ Chercheur Qualifie du FNRS, Departement d’Informatique… 
Melodic Identification Using Probabilistic Tree Automata
TLDR
Stochastic k-testable tree-models are applied for computing the similarity between two melodies as a probability, and the results are compared to those achieved by tree edit distances, showing that k- testabletree-models outperform other reference methods in both recognition rate and efficiency.
Date of acceptance Grade Instructor Using Mathematical Morphology for Geometric Music Retrieval
TLDR
This thesis investigates geometric approaches to MIR, and develops and implements four algorithms for geometric music retrieval that are basically extensions to classic image correlation and hit-or-miss transformation techniques used widely in template matching applications.
A geometrical distance measure for determining the similarity of musical harmony
TLDR
A new geometric distance function that quantifies the harmonic distance between two pieces of music is presented and it is shown that it can be efficiently used for retrieving similar chord sequences, and that it significantly outperforms a baseline string matching approach.
A Fuzzy-Clustering Based Approach for Measuring Similarity Between Melodies
TLDR
This work proposes the use of fuzzy c-means clustering as a tool for the measurement of the similarity between two melodies with a different number of notes and presents an algorithm, FOCM, able to read two melodies from files with MusicXML format and to perform the clustering to calculate the dissimilarity between any two melodies.
Tree language automata for melody recognition
TLDR
The application of stochastic k-testable treemodels for computing the similarity between two melodies as a probability, compared to the classical edit distance has been addressed and the results show that k- testable tree-models seem to be adequate for the task, since they outperform other reference methods in both recognition rate and efficiency.
BIRITS: A Music Information Retrieval System Using Query-by-Playing Techniques
  • Lucas MartinianoC. Silla
  • Computer Science
    2017 IEEE 29th International Conference on Tools with Artificial Intelligence (ICTAI)
  • 2017
TLDR
A two-stage query-by-playing (QBP) system using symbolic representations where from a melody snippet of a song it is performed the retrieval of a set of similar songs, improving the performance of queries regardless of the noise.
Music information retrieval based on tonal harmony
TLDR
This doctoral dissertation investigates two approaches towards automatic harmony analysis and evaluates harmonic annotations, which explain the role of a chord in its tonal context, both qualitatively as well as quantitatively, and shows how they can aid in harmonic similarity estimation and automatic chord transcription.
Necklaces , Convolutions , and X + Y Citation
TLDR
Subquadratic algorithms that, given two necklace each with n beads at arbitrary positions, compute the optimal rotation of the necklaces to best align the beads in the best perfect matching are given.
Visualization of Composer Relationships Using Implicit Data Graphs
TLDR
An approach to visually hint possible relationships among a large number of composers is developed, based on the composer works as well as their lifetimes in order to guess directions of influence.
Partial Matching of Planar Polygons Under Translation and Rotation
TLDR
This paper proposes an approach that uses a turning function representation of the shape and also uses a L2 measure for comparing matches and finds the best match along some fixed length portions of two polygons where the polygons may be arbitrarily translated and rotated.
...
...

References

SHOWING 1-10 OF 42 REFERENCES
ON GENERALIZATIONS OF CONICS AND ON A GENERALIZATION OF THE FERMAT-TORRICELLI PROBLEM
Depending on the choice of the coefficients a to e, respectively, or the coordinates b1, b2 and weights ai one gets ellipses, parabolas, and hyperbolas and it is possible to convert the curve
Using transportation distances for measuring melodic similarity
TLDR
By using weighted point sets and the EMD/PTD instead of Howard’s method (1998) using the DARMS encoding for determining melodic similarity, it is possible to group together about twice as many known occurrences of a melody within the RISM A/II collection.
Measuring melodic similarity: Human vs. algorithmic Judgments
Background in second subdiscipline (mathematical music theory): The topology of the space of mathematical melodies, an abstraction from musical melodies, reducing them to pairs of onsets and pitches
Melodic Similarity : concepts, procedures, and applications
Part 1 Concepts and procedures: conceptual and representational issues in melodic comparison - concepts of melody, searchable representations of pitch, searchable representations of duration and
A Comparison of Rhythmic Similarity Measures
TLDR
Comparison measures of rhythm similarity are compared on the basis of how much insight they provide about the structural inter-relationships that exist within families of rhythms, when phylogenetic trees and graphs are computed from the distance matrices determined by these similarity measures.
An efficiently computable metric for comparing polygonal shapes
TLDR
A method for comparing polygons that has these properties and works for both convex and nonconvex polygons and runs in time O(mn log mn) where m is the number of vertices in one polygon and n is the size of the polygons in the other.
Distance metrics and indexing strategies for a digital library of popular music
  • Cristian FrancuC. Nevill-Manning
  • Computer Science
    2000 IEEE International Conference on Multimedia and Expo. ICME2000. Proceedings. Latest Advances in the Fast Changing World of Multimedia (Cat. No.00TH8532)
  • 2000
TLDR
The experiments with MIDI files are described, a new, more accurate distance metric between queries and songs is proposed, and possibilities for efficient indexing are discussed.
Pattern Matching in Polyphonic Music as a Weighted Geometric Translation Problem
TLDR
It is shown that the music pattern matching problem is at least as hard as a basic problem called 3-SUM that is conjectured to have no subquadratic algorithm, and an algorithm is given with running time O(nm log m), where n is the size of the score and m is thesize of the pattern.
African Rhythm
Opening Paragraph Most people are vaguely aware that the characteristic feature of African music is its rhythms. Some would say with the late Professor Hornbostel of Berlin that ‘it is syncopated
Introduction to Algorithms
TLDR
The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
...
...