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3D"Collapse3D"Expand
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Search-Effectiveness Measures for Symbolic Music Queries in Very Large Databases<= /p>

Musical Features

Example Feature Sea= rches

Anchored vs. Unanch= ored Searches

Raw Data Extraction=

Individual Match Co= unt Profile

Time To Uniqueness<= /a>

Time To Sufficiency=

Composite Match-Cou= nt Profiles

Anchored/Unanchored Profile Slopes

Average Profiles For Pitch Features

Feature-Class Search Characteristics

Entropy

Probability Distrib= utions

Entropy Rate (Avera= ge Entropy)

Entropy and Entropy= Rates

Entropy-Rate Estima= tion from TTS

Expectation Functio= n

Expectation Functio= n (2)

Match-Count and Derivative Profile Comparison

Comparison of Expec= tation Function Plots

Derivative Plots fo= r 12i features

Application 1: Joint Feature Analysis

Mutual Information<= /a>

Combining Pitch and Rhythm Searches

Joint Feature Searc= hes: pgc/rgc vs. 12i

Joint Feature Search Effectiveness

Application 2: Synt= hetic Database Analysis

Effects of Duplicate Entries on Profiles

Effect of Incipit L= ength on Profiles

Summary

Search-Effectiveness Measures for Symbolic Music Queries in Very Large Databases<= /p>

Extra Slides:

Proof for Derivative Plots

Themefinder Website=

Themefinder Collect= ions

Matches on First Se= ven Notes

Search Failure Rate= s

Joint Pitch/Rhythm Effects on TTS

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Search-Effectiveness Measures for Symbolic Music Queries in Very Large Databases<= /p>

Musical Features

Example Feature Sea= rches

Anchored vs. Unanch= ored Searches

Raw Data Extraction=

Individual Match Co= unt Profile

Time To Uniqueness<= /a>

Time To Sufficiency=

Composite Match-Cou= nt Profiles

Anchored/Unanchored Profile Slopes

Average Profiles For Pitch Features

Feature-Class Search Characteristics

Entropy

Probability Distrib= utions

Entropy Rate (Avera= ge Entropy)

Entropy and Entropy= Rates

Entropy-Rate Estima= tion from TTS

Expectation Functio= n

Expectation Functio= n (2)

Match-Count and Derivative Profile Comparison

Comparison of Expec= tation Function Plots

Derivative Plots fo= r 12i features

Application 1: Joint Feature Analysis

Mutual Information<= /a>

Combining Pitch and Rhythm Searches

Joint Feature Searc= hes: pgc/rgc vs. 12i

Joint Feature Search Effectiveness

Application 2: Synt= hetic Database Analysis

Effects of Duplicate Entries on Profiles

Effect of Incipit L= ength on Profiles

Summary

Search-Effectiveness Measures for Symbolic Music Queries in Very Large Databases<= /p>

Extra Slides:

Proof for Derivative Plots

Themefinder Website=

Themefinder Collect= ions

Matches on First Se= ven Notes

Search Failure Rate= s

Joint Pitch/Rhythm Effects on TTS

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ISMIR Barcelona 2004
‹footer›
Sapp, Liu, Selfridge-Field
<= /div>
‹#›
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<= /td> =
Search-Effectiveness Measures for Symboli= c
Music Queries in Very Large Databases=
=
Cra= ig Stuart Sapp
craig@ccrma.stanford.edu
<= /td>
Yi-W= en Liu
jacobliu@stanford.edu
=
Eleanor Selfridge-Field
esf= ield@stanford.edu
ISMIR 2004
Universitat Pompeu Fabra
Barcelona, Spain
12 October 2004
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=
•  Features can be extracted from a sco= re on many levels of quantization from highly
specific to very generic:
+=
<= /td>
7 Pitch features
(lis= ted above)
<= /td> <= /td> <= /td>
   4. beat level
   5. metric level
   6. metric gross contour
   7. metric refined contour
• How do all of these different features affect searching in= a database?
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Example Feature Searches
F= eature
Q= uery
<= /td>
Anchored
<= /td> <= /td>
Unanchored
p= ch
F A = C
464
1,710
1= 2p
5 9 = 0
464
1,710
m= i
+M3 = +m3
1,924
6,882
1= 2i
+4 += 3
1,925
6,894
s= d
1 3 = 5
2,009
7,024
p= rc
U U<= /font>
4,677
17,712
p= gc
U U<= /font>
19,787
76,865
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image/gif R0lGODlhtgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQCt AAkAgAAAAAAAAALIhI95EerbHnsUzIqzje5Sr4UIJ36lJZ3ompGJO7avAqtLeUUTszf+6/sZeJsg L1gEEYWs4XGTVBqdQORSl+PkZrvok0Ucrrpgpg56PovVP+a4Db5R1WIUycM2C7FxrR3eZ0dVJEhn uFaXdsNWGDNGOKhI9+jn1yiJiARJqNjXswh6GCf4WIdISZp4ypVpirqKidm4atpZWQXhFHakidaz C7Fr9BXlm8v5FOarhXeV/KnbPPLMiwxlg92Uvc3d7f39DQI+Tl4eUgAAOw== ------=_NextPart_01C51A99.636BBA10 Content-Location: file:///C:/1939C634/Sapp_etal_ismir2004_files/v3_slide0004_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhvwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgC3 AAkAgAAAAAAAAALXhI95Eeq/oJwUtlivY5PXn2igJYnhiJjop67pCbtK+3gXx+DNHub77wMEbzmD TqMTCoFLz3LhCz5xKWr113xmtVoTFhg1QpHKqdjIO5fN6++tukab3+d0WvnO37PkspVN1Cb45SfG E8iHp0bXZVjoiCdy+GIHWagHWcnYWKeYdxmJhmRVGYllOSkYp+i56KeS6sgomRmhWQvl2vrJaxvz CXqV22QzhFgUFoUsJVrUfCrpVExszEeU1EzNJM3sRK1d7S0zPoPh4kWerr7O3i4s4+3sPk8vUQAA Ow== ------=_NextPart_01C51A99.636BBA10 Content-Location: file:///C:/1939C634/Sapp_etal_ismir2004_files/v3_master03_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBAAIAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAC AAUAgAAAAAAAAAIERG4YBQA7 ------=_NextPart_01C51A99.636BBA10 Content-Location: file:///C:/1939C634/Sapp_etal_ismir2004_files/v3_slide0034.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Search-Effectiveness Measures for Symbolic Music Queries in Very Lar= ge Databases
Raw Data Extraction
1
10,= 585 matches
2
  1,351 matches
3
     464 matches
4
     161 matches
5
      83 matches
6
      21 matches
7
      12 matches
=
•  Now plot the number of database matc= hes for a known
search target with an increasingly larger symbol count.
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Individual Match Count Profile
Quer= y length
=
•  Anchored and Unanchored searches equivalent
when the search length reached 8 symbols
=
•  Unique match found when the search l= ength
reached 10 symbols.
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file:///C:/1939C634/Sapp_etal_ismir2004_files/v3_master03_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBAAIAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAC AAUAgAAAAAAAAAIERAJmVwA7 ------=_NextPart_01C51A99.636BBA10 Content-Location: file:///C:/1939C634/Sapp_etal_ismir2004_files/v3_slide0009.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Search-Effectiveness Measures for Symbolic Music Queries in Very Lar= ge Databases
Time To Uniqueness
Quer= y length
=
TTU =3D the number of query symbols needed to find the
exa= ct match in the database.  Turns out to not= be very
useful since it is more susceptible to noise in the data.
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R0lGODlhBAAIAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAC AAUAgAAAAAAAAAIETHCGUAA7 ------=_NextPart_01C51A99.636BBA10 Content-Location: file:///C:/1939C634/Sapp_etal_ismir2004_files/v3_slide0010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Search-Effectiveness Measures for Symbolic Music Queries in Very Lar= ge Databases
Time To Sufficiency
Quer= y length
= <= /td>
TTS =3D the number of query symbols needed to find the
sufficient match in the database (in our case set to no more
tha= n 10 matches and constant w.r.t. database size).
•  More informative than TTU for entrop= y rate estimations (covered later).
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Composite Match-Count Profiles
• Average all individual profiles over entire database:
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------=_NextPart_01C51A99.636BBA10 Content-Location: file:///C:/1939C634/Sapp_etal_ismir2004_files/v3_slide0029.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Search-Effectiveness Measures for Symbolic Music Queries in Very Lar= ge Databases
Anchored/Unanchored Profile Slopes
Syn= thetic Database
Real= Database
Anc= hored Searching: O(log N)
Una= nchored Searching: O(N2)
<= /td> =
• Slopes of curves for anchored/unanchored profiles not significantly different.=
• Anchored searching is much faster.
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Average Profiles For Pitch Features
Quer= y length
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Feature-Class Search Characteristics
=
•  Rhythm features TTS values are about= twice that of pitch features (except blv and
mgc which are 5 times larger than pitch feature TTS)
• Rhythm cannot be modeled by Markov processes as well as Pitch = (wavy lines)
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=
•  Entropy measurements can be used to<= /font>
characterize match-count profiles.
<= /td>
e= ntropy
     definition:
= H =3D Entropy: number of bits needed to encode each symbol Xi<= /sub>.
=
P =3D Normalized probability distribution for random
       variable X, where
=
•  H is a measure of the maximum randomness the random
variable X can possess.
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Probability Distributions
3D"Text
=
3.4 bits/note is the lower symbol storage size limit needed to
sto= re sequences of 12-tone intervals (Folksong data set).
=
•  Entropy can be used as a basic estim= ate for how many notes are
necessary to find a unique/sufficient match in the database, but ...
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Entropy Rate (Average Entropy)
<= /td>
e= ntropy-rate
     definition:
= G =3D entropy rate (bits/symbol)
= N =3D count of elements in sequence: {X1, X2, X3, ..., XN}
=
The entropy rate is the average number of bits required to
rep= resent an N length sequence of random variables X.
is = the “first-order” entropy
is = the “nth-order” entropy
=
Difference between entropy and entropy rate quantifies the
con= text dependent nature of the random variable X.
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Entropy and Entropy Rates
for= various repertories in the Themefinder database
<= /td> <= /td> <= /td> <= /td>
• Classical set has most diverse pitch
content and utilizes it the most.
• Polish set has the most context-
dependent pitch sequences – next note
is easiest to predict in this set.
• Renaissance entropy rate is very
close to it entropy (less context
dependency).
• Folksongs slightly “simpler” than
classical music.
• Music of 17th and 18th centuries has
same entropy rate as that of the 16th
century, but entropy of 16th century is
lower. (More notes added but rarely
used).
3D"Text
(12p= features)
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Entropy-Rate Estimation from TTS
M=
•  Entropy characterizes the minimum po= ssible average TTS.
•  Entropy-rate characterizes the actual average TTS.
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Search-Effectiveness Measures for Symbolic Music Queries in Very Lar= ge Databases
Expectation Function
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Expectation Function (2)
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Match-Count and Derivative Profile Comparison
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Measures for Symbolic Music Queries in Very Lar= ge Databases
Derivative Plots for 12i features
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Application 1: Joint Feature Analysis
What to do with all of these techniques?
Pit= ch + Rhythm
•  How independent/dependent are pitch = and rhythm features?
<= /td>
•  What is the effect of searching pitc= h and rhythm features
in parallel?
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Mutual Information
join= t entropy
H= (a)
H= (b)
H= (a,b)
e= .g., pitch
e= .g., rhythm
mut= ual information
= I(a;b) =3D H(a) + H(b) – H(a,b)
con= ditional entropy
con= ditional entropy
= H(a|b) =3D H(a,b) – H(b)
= H(b|a) =3D H(a,b) – H(a)
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Combining Pitch and Rhythm Searches
= H(rgc) =3D 1.4643
= H(pgc) =3D 1.5325
= H(pgc, rgc) =3D 2.9900
= I(pgc; rgc) =3D H(pgc) + H(rgc) – H(pgc,rgc) =3D 0.0068
•  Pitch and Rhythm are very independent features (for pgc+rgc).
•  Combining independent search features should be effective.
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Joint Feature Searches: pgc/rgc vs. 12i
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(All= dataset)
Quer= y length
• =  pgc and rgc are generic features less prone to query errors.
=
•  These 3*3 states performs searches as efficiently as the
88 states of twelve tone intervals. I.e., two highly quantized independent=
features works as well as a single non-quantized feature.
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Effects of Duplicate Entries on Profiles
= =
Duplicate entries in the database do not have a significant ef= fect on
entropy-rate measurements:
=
Tail of curve can be used to estimate the
number of duplicate entries in database.
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Search-Effectiveness Measures for Symbolic Music Queries in Very Lar= ge Databases
Summary
<= /td> <= /td> = <= /td> <= /td> <= /td>
• Match-Count Profiles: Examines match
characteristics of a musical feature for longer and
longer queries.
• Entropy Rate: Characterizes match count profiles
well with a single number.  Useful f= or predicting the
expected average number of matches for a given length
query.
• TTS: The number of symbols in query necessary to
generate a sufficiently small number of matches
(average).  TTU not as useful due to noise.
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<= /td> =
Search-Effectiveness Measures for Symboli= c
Music Queries in Very Large Databases=
=
Cra= ig Stuart Sapp
craig@ccrma.stanford.edu
<= /td>
Yi-W= en Liu
jacobliu@stanford.edu
=
Eleanor Selfridge-Field
esf= ield@stanford.edu
ISMIR 2004
Universitat Pompeu Fabra
Barcelona, Spain
12 October 2004
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Extra Slides:
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Proof for Derivative Plots
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Themefinder Collections
D= ata set
<= span style=3D'mso-spacerun:yes'>  Count
=    Web Interface
Clas= sical
10,718
  themefinder.org
Folk= song
8,473
  themefinder.org
Rena= issance
18,946
  latinmotet.themefinder.org
US = RISM A/II
55,490
Poli= sh
6,060
  lux.themefinder.org
Lux= embourg
612
100,= 299
t= otal:
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Matches on First Seven Notes
A.
B.
C.
D.
E.
F.
x2
G.
H.
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Search Failure Rates
Dat= abase size: 100,299
Ave= rage note count/incipit: 16
=
• Plo= t measures how often a search produces too many
matches for query sequences as long as the database entry.
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