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8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
1/72
A Graph
TheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
A Graph Theoretic Model for Music
Information Retrieval
Amna Ilyas
Bates College
April 6, 2013
http://find/http://goback/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
2/72
A Graph
TheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Presentation Outline
1 Representing Musical Themes Using Graphs
2 Similarity Function
3 Further Work
http://find/http://goback/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
3/72
A Graph
TheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
The Graph Model
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
4/72
A Graph
TheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
The Graph Model
Proposed by Alberto Pinto and Goffredo Haus in A NovelXML Music Information Retrieval Method Using GraphInvariants (2007)
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
5/72
A Graph
TheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
The Graph Model
Proposed by Alberto Pinto and Goffredo Haus in A NovelXML Music Information Retrieval Method Using GraphInvariants (2007)Converts a musical theme in a query (audio or scorefragment) into its representative graph.
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
6/72
A Graph
TheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
The Graph Model
Proposed by Alberto Pinto and Goffredo Haus in A NovelXML Music Information Retrieval Method Using GraphInvariants (2007)Converts a musical theme in a query (audio or scorefragment) into its representative graph.
Representative graph is compared with the graphs ofmusical themes in a database.
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
7/72
A Graph
TheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
The Graph Model
Proposed by Alberto Pinto and Goffredo Haus in A NovelXML Music Information Retrieval Method Using GraphInvariants (2007)Converts a musical theme in a query (audio or scorefragment) into its representative graph.
Representative graph is compared with the graphs ofmusical themes in a database.Comparison is done after filtering and then using asimilarity function.
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
8/72
A Graph
TheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
The Graph Model
Proposed by Alberto Pinto and Goffredo Haus in A NovelXML Music Information Retrieval Method Using GraphInvariants (2007)Converts a musical theme in a query (audio or scorefragment) into its representative graph.
Representative graph is compared with the graphs ofmusical themes in a database.Comparison is done after filtering and then using asimilarity function.
The result then is a list of graphs containing the matchingtheme and its variations by the addition of new notes betweenpairs of notes of the query graph.
http://goforward/http://find/http://goback/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A Graph
TheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
A Musical Theme and its Representative Graph
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
A Musical Theme and its Representative Graph
A melodic theme is a musical phrase that is comprised of one
complete recognizable melody.
http://find/http://goback/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
A Musical Theme and its Representative Graph
A melodic theme is a musical phrase that is comprised of one
complete recognizable melody.
Each note becomes a vertex
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
A Musical Theme and its Representative Graph
A melodic theme is a musical phrase that is comprised of one
complete recognizable melody.
Each note becomes a vertexDirected edges between the vertices denote the progressionof the melody from one note (vertex) to another.
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
A Musical Theme and its Representative Graph
A melodic theme is a musical phrase that is comprised of one
complete recognizable melody.
Each note becomes a vertexDirected edges between the vertices denote the progressionof the melody from one note (vertex) to another.The last note is sent back to the first note using a directed
edge.
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Themes and Graphs
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Themes and Graphs
These graphs that are built from musical themes are Eulerian.
http://find/http://goback/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Themes and Graphs
These graphs that are built from musical themes are Eulerian.
A trail in a graph is an alternating sequence of vertices anddirected edges, with no repeated edges (vertices may berepeated).
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Themes and Graphs
These graphs that are built from musical themes are Eulerian.
A trail in a graph is an alternating sequence of vertices anddirected edges, with no repeated edges (vertices may berepeated).
A trail with the same starting and ending vertex is called a
circuit.
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Trails, Circuits and Eulerian Graphs
For instance, one trail in G, that represents a theme from
Tchaikovskys 6th Symphony, Pathetique is
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Trails, Circuits and Eulerian Graphs
For instance, one trail in G, that represents a theme from
Tchaikovskys 6th Symphony, Pathetique is
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
20/72
A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Trails, Circuits and Eulerian Graphs
For instance, one trail in G, that represents a theme from
Tchaikovskys 6th Symphony, Pathetique is
de3c#e2de7b
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A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Trails, Circuits and Eulerian Graphs
For instance, one trail in G, that represents a theme from
Tchaikovskys 6th Symphony, Pathetique is
de3c#e2de7b
One circuit in the graph G is
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
22/72
A Graph
TheoreticModel forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Trails, Circuits and Eulerian Graphs
For instance, one trail in G, that represents a theme from
Tchaikovskys 6th Symphony, Pathetique is
de3c#e2de7b
One circuit in the graph G is
de3c#e2de7be8d
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A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
An Eulerian graph is a graph that contains an Eulerian circuiti.e. a circuit that uses each edge of the graph exactly once.
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
An Eulerian graph is a graph that contains an Eulerian circuiti.e. a circuit that uses each edge of the graph exactly once.
The above graph is Eulerian because it contains the Euleriancircuit
http://find/http://goback/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
An Eulerian graph is a graph that contains an Eulerian circuiti.e. a circuit that uses each edge of the graph exactly once.
The above graph is Eulerian because it contains the Euleriancircuit
be1c#e2de3c#e4be5ee6de7be8de9c#e10b
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
An Eulerian graph is a graph that contains an Eulerian circuiti.e. a circuit that uses each edge of the graph exactly once.
The above graph is Eulerian because it contains the Euleriancircuit
be1c#e2de3c#e4be5ee6de7be8de9c#e10b
All graphs that are constructed from a musical theme areEulerian.
Th h i t ti h
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A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Themes having same representative graphs
It is possible for two different themes to have the same
representative graph.
Th h i t ti h
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A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Themes having same representative graphs
It is possible for two different themes to have the samerepresentative graph. For instance,
This theme has the same representative graph as G.
Th h i t ti h
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Themes having same representative graphs
It is possible for two different themes to have the samerepresentative graph. For instance,
This theme has the same representative graph as G.
This is just a different Eulerian circuit of that same graph.
de7be8de3c#e2de9c#e10be1c#e4be5ee6d
The Eulerian circuit corresponding to the Pathetique theme is
be1c#e2de3c#e4be5ee6de7be8de9c#e10b
Musical Themes and Graphs
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A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Musical Themes and Graphs
However, not every Eulerian circuit of a graph gives a different
musical theme. For instance,
Musical Themes and Graphs
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A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Musical Themes and Graphs
However, not every Eulerian circuit of a graph gives a different
musical theme. For instance,
These two different Eulerian circuits of this graph correspondto this same melodic theme
de7be8de3c#e2de9c#e10be1c#e4be5ee6d
de
7be
8de
9c#e
2de
3c#e
4be
1c#e
10be
5ee
6d
Presentation Outline
http://find/http://goback/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
32/72
A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Presentation Outline
1 Representing Musical Themes Using Graphs
2 Similarity Function
3 Further Work
Transitive Closure
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Transitive Closure
The transitive closure of order i of graph P is the graph Pi
such that V(Pi
) = V(P) and E(Pi
) contains all edges ofPand edges joining any pair of vertices which have a trail of iedges between them.
Transitive Closure
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
Representing
MusicalThemes UsingGraphs
SimilarityFunction
Further Work
Transitive Closure
The transitive closure of order i of graph P is the graph Pi
such that V(Pi
) = V(P) and E(Pi
) contains all edges ofPand edges joining any pair of vertices which have a trail of iedges between them.
We will ignore any trails that include loops because loops onlymean that we are staying on the same note.
Transitive Closure
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusicalThemes UsingGraphs
SimilarityFunction
Further Work
Transitive Closure
The transitive closure of order i of graph P is the graph Pi
such that V(Pi
) = V(P) and E(Pi
) contains all edges ofPand edges joining any pair of vertices which have a trail of iedges between them.
We will ignore any trails that include loops because loops onlymean that we are staying on the same note.
For example, the graph on the right below represents P3 of thegraph P given on the left
Difference Graph
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusicalThemes UsingGraphs
SimilarityFunction
Further Work
Difference Graph
Difference Graph, H\G is obtained by deleting those edges
from H that are in common with G.
Difference Graph
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusicalThemes UsingGraphs
SimilarityFunction
Further Work
Difference Graph
Difference Graph, H\G is obtained by deleting those edges
from H that are in common with G.
Similarity Function
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusicalThemes UsingGraphs
SimilarityFunction
Further Work
Similarity Function
IfV(G) = V(H) and |H\G| = 0 then it means that G and Hare exactly the same.
Similarity Function
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusicalThemes UsingGraphs
SimilarityFunction
Further Work
S a ty u ct o
IfV(G) = V(H) and |H\G| = 0 then it means that G and Hare exactly the same. So such an H should appear at the top of
our list of graphs in the result.
Similarity Function
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusicalThemes UsingGraphs
SimilarityFunction
Further Work
y
IfV(G) = V(H) and |H\G| = 0 then it means that G and Hare exactly the same. So such an H should appear at the top of
our list of graphs in the result.
IfV(G) V(H) then the similarity function is
Similarity Function
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusicalThemes UsingGraphs
SimilarityFunction
Further Work
y
IfV(G) = V(H) and |H\G| = 0 then it means that G and Hare exactly the same. So such an H should appear at the top of
our list of graphs in the result.
IfV(G) V(H) then the similarity function is
(G,H) = |G||G\(H\G)2|
|G| +|G||G\(H\G)3|
|G| +|G||G\(H\G)4|
|G|
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusicalThemes UsingGraphs
SimilarityFunction
Further Work
Consider this theme and its graph A
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusicalThemes UsingGraphs
SimilarityFunction
Further Work
A variation of this theme and its graph B is
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusicalThemes UsingGraphs
SimilarityFunction
Further Work
(B\A) is obtained by deleting those edges from B that are incommon with A
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45/72
A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
(B\A) is obtained by deleting those edges from B that are incommon with A
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
(B\A)2 is the transitive closure of order 2 on the graph (B\A)
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
(B\A)2 is the transitive closure of order 2 on the graph (B\A)
http://find/http://goback/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
(B\A)2 is the transitive closure of order 2 on the graph (B\A)
A\(B\A)2
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
|A\(B\A)2| = 8
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
Similarly, (B\A)3 is the transitive closure of order 3 on thegraph (B\A)
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
Similarly, (B\A)3 is the transitive closure of order 3 on thegraph (B\A)
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A GraphTheoretic
Model forMusic
InformationRetrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
|A\(B\A)3| = 8
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A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
|A\(B\A)4| = 9 because there are no trails of 4 edges betweenany two vertices in (B\A)
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A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
|A\(B\A)4| = 9 because there are no trails of 4 edges betweenany two vertices in (B\A)Then applying the similarity function on B and A, we get
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A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
|A\(B\A)4| = 9 because there are no trails of 4 edges betweenany two vertices in (B\A)Then applying the similarity function on B and A, we get
(A,B) = |A||A\(B\A)2|
|A| +|A||A\(B\A)3|
|A| +|A||A\(B\A)4|
|A|
(A,B) = 989 +98
9 +99
9
(A,B) = 29
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A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
|A\(B\A)4| = 9 because there are no trails of 4 edges betweenany two vertices in (B\A)Then applying the similarity function on B and A, we get
(A,B) = |A||A\(B\A)2|
|A| +|A||A\(B\A)3|
|A| +|A||A\(B\A)4|
|A|
(A,B) = 989 +98
9 +99
9
(A,B) = 29
If we get 0 for a B whereV
(A
) V
(B
), we do not includethat B in the list of results.
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A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
|A\(B\A)4| = 9 because there are no trails of 4 edges betweenany two vertices in (B\A)Then applying the similarity function on B and A, we get
(A,B) = |A||A\(B\A)2|
|A| +|A||A\(B\A)3|
|A| +|A||A\(B\A)4|
|A|
(A,B) = 989 +98
9 +99
9
(A,B) = 29
If we get 0 for a B whereV
(A
) V
(B
), we do not includethat B in the list of results.Greater this fraction for a graph H, the more different it is fromthe query graph. Hence, the results should be given inincreasing order of this fraction.
Presentation Outline
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
58/72
A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
1 Representing Musical Themes Using Graphs
2 Similarity Function
3 Further Work
Short-comings of our approach
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A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
Short-comings of our approach
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A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
It does not consider transformations of the music themesuch as transposition to another key.
Short-comings of our approach
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61/72
A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
It does not consider transformations of the music themesuch as transposition to another key.
It does not involve rhythm.
Short-comings of our approach
http://goforward/http://find/http://goback/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
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A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
It does not consider transformations of the music themesuch as transposition to another key.
It does not involve rhythm.
It only allows for new notes between pairs of notes in thevariation of the theme.
Short-comings of our approach
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
63/72
A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
It does not consider transformations of the music themesuch as transposition to another key.
It does not involve rhythm.
It only allows for new notes between pairs of notes in thevariation of the theme.
The list of results is large because of the possibility of onegraph representing more than one theme. The maximum
number of themes represented by a graph is equal to thetotal number of Eulerian circuits in the graph.
Further Work
http://goforward/http://find/http://goback/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
64/72
A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
This procedure has been implemented and tested on Maple.
Further Work
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
65/72
A GraphTheoretic
Model forMusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
This procedure has been implemented and tested on Maple.
Further work can be done.
Further Work
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
66/72
A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
This procedure has been implemented and tested on Maple.
Further work can be done.
How to allow for variations with notes between pairs of
notes that are already in the original theme?
Further Work
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
67/72
A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
This procedure has been implemented and tested on Maple.
Further work can be done.
How to allow for variations with notes between pairs of
notes that are already in the original theme?Incorporating isometries into the similarity function.
Further Work
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
68/72
A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
This procedure has been implemented and tested on Maple.
Further work can be done.
How to allow for variations with notes between pairs of
notes that are already in the original theme?Incorporating isometries into the similarity function.
Understanding the similarity function proposed by Pintoand Haus.
Further Work
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
69/72
A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
This procedure has been implemented and tested on Maple.
Further work can be done.
How to allow for variations with notes between pairs of
notes that are already in the original theme?Incorporating isometries into the similarity function.
Understanding the similarity function proposed by Pintoand Haus.
Figuring out a way to represent rhythm in a graph.
Further Work
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
70/72
A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
This procedure has been implemented and tested on Maple.
Further work can be done.
How to allow for variations with notes between pairs of
notes that are already in the original theme?Incorporating isometries into the similarity function.
Understanding the similarity function proposed by Pintoand Haus.
Figuring out a way to represent rhythm in a graph.How to make the results more precise?
Further Work
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
71/72
A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
This procedure has been implemented and tested on Maple.
Further work can be done.
How to allow for variations with notes between pairs of
notes that are already in the original theme?Incorporating isometries into the similarity function.
Understanding the similarity function proposed by Pintoand Haus.
Figuring out a way to represent rhythm in a graph.How to make the results more precise?
How to get from the graphs to the musical themes?
http://find/8/22/2019 Ilyas_A Graph Theoretic Model for Music Information Retrieval
72/72
A GraphTheoreticModel for
MusicInformation
Retrieval
Amna Ilyas
RepresentingMusical
Themes UsingGraphs
SimilarityFunction
Further Work
Thank you for your attention today.
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