similarity measures for rhythmic sequences
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July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
joao.martins@plymouth.ac.uk
Joao MartinsMarcelo GimenesJônatas Manzolli Adolfo Maia Jr.
Future Music Lab – University of PlymouthNICS – UNICAMP
Similarity Measures for
Rhythmic Sequences
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
INTRODUCTION SCV EXAMPLES APPLICATIONS CONCLUSIONS
INTRODUCTIONSCVEXAMPLESAPPLICATIONSCONCLUSIONS
Outline ¦ Scope ¦ Other Measures
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
Similarity measures are fundamental in music information retrieval and play one of the most important roles in Artificial Intelligence towards the establishment of fitness functions.
The aim is to create a similarity measure for rhythmic sequences that can capture patterns in several hierarchical levels, spanning from a small rhythmic phrase to longer structures.
INTRODUCTIONSCVEXAMPLESAPPLICATIONSCONCLUSIONS
Outline ¦ Scope ¦ Other Measures
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
Euclidean distance Levenshtein distance Mongeau and Sankoff (1990)
INTRODUCTIONSCVEXAMPLESAPPLICATIONSCONCLUSIONS
Outline ¦ Scope ¦ Other Measures
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
INTRODUCTION
SCVEXAMPLESAPPLICATIONSCONCLUSIONS
Representation ¦ Similarity Coefficient Vector ¦ Model
Representation of rhythmic sequences previously quantized discarding expressive timing info
Shmulevich, I. and Povel, D. (2000)
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
INTRODUCTION
SCVEXAMPLESAPPLICATIONSCONCLUSIONS
Representation ¦ Similarity Coefficient Vector ¦ Model
Similarity Coefficient Vector (SCV) This vector is a measure of similarity between all the
subsequences It is built counting the sparsity of a distances matrix
for a given k-level
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
INTRODUCTION
SCVEXAMPLESAPPLICATIONSCONCLUSIONS
Representation ¦ Similarity Coefficient Vector ¦ Model
Diagram
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
INTRODUCTIONMODEL
ExamplesAPPLICATIONSCONCLUSIONS
Building the Matrix ¦ ≠ Length ¦ Finding the most similar
Example on how the algorithm builds the 3rd level matrix for two sequences of different lengths.
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
This is an example of the comparison between the sequences
V = 1 0 1 1 W = 1 0 1 1 0 1
The first sequence is completely included in the second, therefore we can find a positive value in the last level of the SCV
The sum of all coefficients of the SCV is 1.625 which can be seen as a single value expressing similarity between the sequences
INTRODUCTIONMODEL
ExamplesAPPLICATIONSCONCLUSIONS
Building the Matrix ¦ ≠ Length ¦ Finding the most similar
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
INTRODUCTIONMODEL
ExamplesAPPLICATIONSCONCLUSIONS
= Length ¦ ≠ Length ¦ Finding the most similar
Gray code0 0 0
0 1 0
1 1 0
1 0 0
1 0 1
1 1 1
0 1 1
0 0 1
Matlab application to explore the similarities in the rhythmic space
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
INTRODUCTIONMODELEXAMPLES
APPLICATIONSCONCLUSIONS
Musicology ¦ NetRhythms ¦ RGem ¦ Others
Computational musicology is broadly defined as the study of Music by means of computer modelling and simulation.
Complimentary approach to traditional musicology
What theories of music evolutionary origins make sense?
How do learning and evolved components interact to shape the musical culture that develops over time?
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
INTRODUCTIONMODELEXAMPLES
APPLICATIONSCONCLUSIONS
Musicology ¦ NetRhythms ¦ RGem ¦ Others
The input sequence Each element of V is a vector in
which the correspond to small rhythmic group with sampled events and amplitude
The network weights The weight vectors W correspond
to the internal representation of the agents
SARDNET (Sequential Activation Retention and Decay Network) is an extended Kohonen self-organising feature map. This network was developed to study sequences and organization of phonemes in the context of language (James and Miikkulainen (1995)
Comparison using the SCV determines the winning node of the network
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
INTRODUCTIONMODELEXAMPLES
APPLICATIONSCONCLUSIONS
Musicology ¦ NetRhythms ¦ RGeme ¦ Others
# Meme dFL dLL nL W1 01011101 1 1 6 1.042 11011101 1 1 31 1.043 10001000 1 1 1 1.024 10010101 1 1 1 1.025 11011010 1 1 1 1.026 10011010 1 1 4 1.017 10011001 1 1 4 1.018 11111111 1 1 1 1.009 10000000 1 1 1 1.00
# Meme dFL dLL nL W1 01011101 1 2 7 1.072 11011101 1 2 37 1.083 10001000 1 1 1 1.024 10010101 1 2 21 1.065 11011010 1 2 2 1.046 10011010 1 1 4 1.027 10011001 1 2 10 1.048 11111111 1 1 1 1.019 10000000 1 2 2 1.0310 00010101 2 2 1 1.0411 10100101 2 2 1 1.0212 11011111 2 2 2 1.0213 10010111 2 2 4 1.0214 10011111 2 2 2 1.0215 11011000 2 2 1 1.0116 10000101 2 2 2 1.0117 11010101 2 2 1 1.01
Sty
le M
atrix
1
Sty
le M
atrix
2
time = 1
Simulation
time = 2
dFL: date of first listening
dLL: date of last listening
nL: number of listenings
W: weight
Every time a new music is listened to, new memes are included in the Style Matrix and the weights of all the memes are updated according to the similarity measure .
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
INTRODUCTIONMODELEXAMPLES
APPLICATIONSCONCLUSIONS
Musicology ¦ NetRhythms ¦ RGem ¦ Others
Composition
Pedagogy
July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)
adolfo@nics.unicamp.br
Contributions This work contributes with a measure of similarity between sequences,
exploring all hierarchical levels and keeping the information about the lower levels.
Future Work Future developments involve the comparison between the SCV and other
similarity measurements and how can we relate this measurement with human perception
Acknowledgements The authors would like to acknowledge the financial support of the
Lerverhulme Trust, São Paulo State Research Foundation (FAPESP) and CAPES (Brazil)
INTRODUCTIONMODELEXAMPLESAPPLICATIONS
CONCLUSIONS Contributions ¦ Future work ¦ Acknowledgements
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