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distributed under the terms of the Creative Commons Attribution License
3.0 Unported, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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YLVXDOL]DWLRQ XQLW DQG QRWH LQSXW XQLW 7KH YLVXDOL]DWLRQXQLWLQFOXGHVDFRQWUROSDQHODQGVFDWWHUSORWIRUFKHFNLQJFRQVLVWHQF\ DQG W\SLFDOLW\ YDOXHV :H GHVLJQHG WKH QRWHLQSXW XQLW LQ WKH µSLDQR UROO¶ VW\OH EHFDXVH &7FRPSRVHUVXSSRUWVPHORG\FRPSRVLWLRQ7KLVXQLWLVDOVRXVHGDVD
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WKH LQWHUIDFH VHH )LJ  \HOORZ UHFWDQJOH  7KH ;D[LV
UHSUHVHQWVWKHFRQVLVWHQF\YDOXHRIHDFKVRQJDQGWKH<
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PRGHOVDQGWRSLFGLVWULEXWLRQ

Page 503

① Probabilistic modelof each song

② Probabilistic modelof song set

Piece 1probabilistic modelof song set

probabilistic modelof piece 1(composed by user)

Probabilistic model
andTopic distributionof song set

T0 T1 T2 T3 T4

generative probabilityon the basis of the conditional probability distribution

Piece 2

Song setby users
Song setby several composers

Ɖ;ǆͮŚͿ ǆ͗ ŶŽƚĞŶƵŵďĞƌŚ͗ ĐŽŶƚĞǆƚ ŚсǆƚͲь͙ǆƚͲϮ ͕ǆƚͲϭ

Composer Aʼ s generative probability

Notenumber
58
57
59
70
69
72
71
・・・

Song setby usersmodel of piece 2

Piece 3

Song setby several composers

model of piece 3

probabilistic modelof song set(composed byseveral composers)

Piece Nmodel of piece N③ Calculation of consistency and typicalityEliminate
the top candidate)LJXUH0HWKRGRIFDOFXODWLQJFRQVLVWHQF\DQGW\SLFDOLW\EDVHGRQGLIIHUHQWGDWDVHWV

Note
number
58
57
59
70
69
72
71
・・・

3.3.1 Computing the consistency and typicality:H FDOFXODWH FRQVLVWHQF\ DQG W\SLFDOLW\ E\ FRPSDULQJPRGHOV RI RQH VRQJ LQFOXGLQJ WKH XVHU¶V ZRUN LQ SURJUHVV ZLWKDPRGHORIVRQJVHW$VLQRXUSUHYLRXVPHWK
RG>@ZHFRPSXWHWKHFRQVLVWHQF\DQGW\SLFDOLW\RID
VRQJDVFRPSDUHGWRDVHWRIRWKHUVRQJV:HXVHWKHXV
HU¶V VRQJ VHW IRU FDOFXODWLQJ FRQVLVWHQF\ DQG XVH D VHWFRQWDLQLQJ WKH VRQJV RI PDQ\ FRPSRVHUV IRU FDOFXODWLQJW\SLFDOLW\+HUHZHXVH+3<70WRFDOFXODWHDWRSLFGLVWULEXWLRQRIHDFK VRQJ >@ DQG WUDLQ D SUREDELOLVWLF PRGHO WKDW FDQFRPSXWHWKHFRQVLVWHQF\DQGWKHW\SLFDOLW\>@$IWHUZH
JHW SUREDELOLVWLF PRGHOV IRU WKH VRQJ DQG VRQJ VHWV ZH
FDOFXODWHWKHGLVWDQFHIURPWKHVRQJ¶VPRGHODQGWKHVRQJ
VHW¶VPRGHO>@ )LJXUH :HXVHDVDPHORGLFIHDWXUHDVHTXHQFH RI 0,', QRWH QXPEHUV 6LQFH WKH PRGHO LV
WUDLQHG ZLWKRXW XVLQJ QRWH GXUDWLRQV RU RQVHW LQWHUYDOVVXFKLQIRUPDWLRQLVQRWLQFOXGHG
3.3.2 The suggestion of musical notes by HPYTM$V GHVFULEHG HDUOLHU LQ WKLV SDSHU &7FRPSRVHU VXJJHVWVPXVLFDOQRWHVIRUVXSSRUWLQJDXVHU¶VFRPSRVLWLRQ7KHVH
QRWHVDUHJHQHUDWHGE\DSUREDELOLVWLFPRGHOFRQVLGHULQJWRSLFGLVWULEXWLRQZH FDOFXODWHG XVLQJ VRQJVHW:HJHQ
HUDWH WKHVH PXVLFDO QRWHV RQ WKH EDVLV RI WKH FRQGLWLRQDO
SUREDELOLW\GLVWULEXWLRQp x_h  xQRWHQXPEHUhFRQWH[W
h xW … xt-2 xt-1  EHFDXVH WKLV GLVWULEXWLRQ FDQ FRQVLGHU
SUHYLRXVQRWHVWKURXJKWKHJHQHUDWLYHSURFHVV )LJXUH &7FRPSRVHUJHQHUDWHVILYHVXJJHVWLRQVIRUJHWWLQJYDULDWLRQV RIXSGDWHG FRQVLVWHQF\ DQG W\SLFDOLW\ WRUHDFK WKHXVHU¶V JRDO FRQVLVWHQF\W\SLFDOLW\ 8VXDOO\ JHQHUDWHG
PHORGLHV WHQG WR LQFOXGH PRUH KLJKSUREDELOLW\ FDQGLGDWHVWKDQORZSUREDELOLW\FDQGLGDWHV7KLVLQIOXHQFHVWKH
FRQVLVWHQF\ YDOXH RI WKH VRQJ EHLQJ FRPSRVHG +HQFH
ZHVHWSDWWHUQVRIVXJJHVWLRQVRIPXVLFDOQRWHVE\XVLQJDJHQHUDWLYHSUREDELOLW\PRGHOIURPZKLFKWKHWRSFDQGLGDWHVZHUHHOLPLQDWHGRQHE\RQH

Eliminate
the top 2 candidates

Generative
probability
0.220494
0.0946835
0.0909367
0.049605
0.0481931
0.0454947
0.0365473
・・・

Sampling

Generative
probability
0.220494
0.0946835
0.0909367
0.049605
0.0481931
0.0454947
0.0365473
・・・

Note
number
58
57
59
70
69
72
71
・・・

Generative
probability
0.220494
0.0946835
0.0909367
0.049605
0.0481931
0.0454947
0.0365473
・・・

Eliminate
the top 3 candidates

Notenumber
58
57
59
70
69
72
71
・・・

Sampling

Generative
probability
0.220494
0.0946835
0.0909367
0.049605
0.0481931
0.0454947
0.0365473
・・・

Sampling)LJXUH*HQHUDWLQJPHORGLHVEDVHGRQWKHGDWDVHW2XUV\VWHPYDULHVXSGDWHGFRQVLVWHQF\DQGW\SLFDOLW\E\FKDQJLQJWKHQXPEHURIKLJKSUREDELOLW\FDQGLGDWHVHOLPLQDWHG
7KLVKHOSVXVHUVGHFLGHVZKLFKVXJJHVWLRQVWRVHOHFWEH
FDXVHWKH\FDQFRQVLGHUKRZWKH\GHVLJQZKROHVRQJVDQG
SKUDVHV,IWKH\ZDQWWRFRPSRVHKLJKFRQVLVWHQF\SLHFH
WKH\ VHOHFW VXJJHVWHG PHORGLHV WKDW JHQHUDWHG DOO RI WKHUDQNLQJV DQG WKH\ DOVR FKRRVH PHORGLHV JHQHUDWHG E\
ORZSUREDELOLW\VHWVLQVRPHSDUWVIRULQFUHDVLQJDQGGH
FUHDVLQJWKHFRQVLVWHQF\DQGW\SLFDOLW\YDOXHVLQVSHFLILF
SDUWVRIWKHSLHFHVWKH\FRPSRVH

(;3(5,0(17&7FRPSRVHU SURYLGHV VXJJHVWLRQV EDVHG RQ SUREDELOLV
WLF PRGHOV IRU VXSSRUWLQJ WKH XVHU¶V FRPSRVLWLRQ :H
JHQHUDWHGVRPHNLQGVRIVXJJHVWLRQVE\HOLPLQDWLQJKLJKSUREDELOLW\ FDQGLGDWHV )LJXUH   ,Q WKLVVHFWLRQ ZH H[DPLQH ZKHWKHU ZH SURYLGH YDULRXV XSGDWHG FRQVLVWHQF\YDOXHVE\JHQHUDWLQJPXVLFDOQRWHVEDVHGRQRXUPHWKRG
,Q WKLV H[SHULPHQW ZKLFK ZDV GRQH DV D VLPXODWLRQ LQZKLFK WKH XVHUV VXEPLWWHG WKHLU SDVW SLHFHV ZH LQSXWWHG
DVDVRQJVHWH[LVWLQJVRQJVRIFODVVLFDOFRPSRVHUV$OORI
WKH GDWDVHWV ZHUHYRFDOVRQJV LQ WKH FODVVLFDO JHQUH DQGLQWKHH[SHULPHQWZHXVHGVRQJVWKDWZHUHFRPSRVHG
E\ %UDKPV VRQJV WRWDO PXVLFDO QRWHV  0R]DUW VRQJV  WRWDO PXVLFDO QRWHV  DQG 6FKXEHUW 
VRQJV  WRWDO PXVLFDO QRWHV  :H H[WUDFWHG PHORG\PXVLFDOQRWHVIURPWKHVHVRQJV¶VWDQGDUG0,',ILOHV:H
FDOFXODWHG FRQVLVWHQFLHV LQ DVXSSRVHG FDVH LQ ZKLFK WKHXVHUDFFHSWHGHDFKJHQHUDWHGPXVLFDOQRWHDQGSORWWHGDVWUDQVLWLRQV RI FRQVLVWHQFLHV YDOXHV $Q H[SHULPHQWDO DS
SURDFK XVLQJ WKLV NLQG RI XVHU EHKDYLRU VLPXODWLRQ KDV
EHHQXVHGLQSUHYLRXVVWXGLHV>@

Page 504

Piece 1
Piece 2

Calculateconsistency

0.33420.3598 0.3390 0.3342 0.3217

Sort songs into
descending order

15 6 10 14

0.3112 0.3098 0.3050 0.3024

0.3019Piece 3

anddevide these
into 4 groups…

…

Piece 171 7 2 50.35980.1171

3 13 4 120.3019 0.2989 0.2975 0.2968

T0 T1 T2 T3 T4

Song-setmodel
estimation[3]

T0 T1 T2 T3 T4

T0 T1 T2 T3 T4

8 16 9 11 170.2328 0.1946 0.1631 0.1588 0.1171

T0 T1 T2 T3 T4)LJXUH([SHULPHQWDOSURFHGXUHRI
 'DWDVHWVDQGH[SHULPHQWDOSURFHGXUH
:HXVHG%UDKPVVRQJVDVDGDWDVHWDQGWUDLQHGDJHQ
HUDWLYHSUREDELOLVWLFPRGHOJHQHUDWHGVXJJHVWLRQVRIPXVLFDO QRWHV DQG FDOFXODWHG XSGDWHG FRQVLVWHQF\ E\ XVLQJWKH+3<707KHQXPEHURIWRSLFVZDVVHWWRDQGWKH
PRGHO SDUDPHWHUV RI WKH +3<70 ZHUH WUDLQHG E\ XVLQJ
WKHWRNHQEDVHG*LEEVVDPSOHU>@ZLWKLWHUDWLRQV
:H JHQHUDWHG  PXVLFDO QRWHV DQG FDOFXODWHG FRQVLVWHQF\HDFKWLPHPXVLFDOQRWHVZHUHDGGHG



VLVWHQF\ DQG XVLQJ  0R]DUW VRQJV DV WKH GDWDVHW IRUJHQHUDWLQJWKHVXJJHVWHGPXVLFDOQRWHV 5HVXOWV)LJXUHDQGDUHOLQHJUDSKVUHSUHVHQWLQJWUDQVLWLRQVRIFRQVLVWHQF\YDOXHVZKHQWKHXVHUFRQWLQXHVDFFHSWLQJWKH
V\VWHP¶VVXJJHVWLRQRIPXVLFDOQRWHV7KHKRUL]RQWDOD[LV
UHSUHVHQWVWKHQXPEHURIPXVLFDOQRWHVDGGHGDQGYHUWLFDOD[LVUHSUHVHQWVWKHFRQVLVWHQF\RIWKHSLHFH%HORZZH
GHVFULEHWKHUHVXOWVRIWKUHHH[SHULPHQWV

4.1.1 Experiment 1: Comparing updated consistency withthe changing number of candidates eliminated from ranking$VGHVFULEHGHDUOLHULQWKLVSDSHU&7FRPSRVHUSURSRVHVVHYHUDO VXJJHVWLRQV ZKLFK KDYH GLIIHUHQW XSGDWHG FRQVLVWHQF\ YDOXHV E\ HOLPLQDWLQJ KLJKSUREDELOLW\ FDQGLGDWHV )LJXUH   ,Q WKH VXJJHVWLRQV RI PXVLFDO QRWHVEDVHGRQWKHFRQGLWLRQDOSUREDELOLW\GLVWULEXWLRQZHVHW
SDWWHUQVRIVXJJHVWLRQVRIPXVLFDOQRWHVE\XVLQJDJHQ
HUDWLYH SUREDELOLW\ PRGHO IURP ZKLFK WKH WRS FDQGLGDWHV
ZHUHHOLPLQDWHGRQHE\RQH

4.2.1 Result 1: Comparing updated consistency with thechanging number of candidates eliminated from ranking
7KH WRS RI )LJXUH  VKRZV WKH WUDQVLWLRQ RI FRQVLVWHQF\YDOXH ZKHQ WKH VLPXODWHG XVHU NHHSV FKRRVLQJ RXU VXJJHVWLRQRIPXVLFDOQRWHV:HIRXQGWKDWZHFDQJHWYDULDWLRQV RI FRQVLVWHQF\ YDOXH DIWHU DERXW  PXVLFDO QRWHV
DGGHG E\ DGMXVWLQJ HOLPLQDWLRQ VWUDWHJ\ VHH WKH WRS RI
)LJ  JUD\ OLQH  ,Q DGGLWLRQ WKH FRQVLVWHQF\ YDOXHV RI
VRPH PHORGLHV JHQHUDWHG E\ HOLPLQDWLQJ WKH VW WR WKKLJKHVWSUREDELOLW\FDQGLGDWHVZHUHORZHUWKDQWKHYDOXH
JHQHUDWHGIURPWKHWRSFDQGLGDWHV

4.1.2 Experiment 2: Comparing updated consistency withthe changing topic distribution:HDOVRSUHVXPHGWKDWFRQVLVWHQF\RIJHQHUDWHGPXVLFDOQRWHV ZLOO EHFRPH GLIIHUHQW ZKHQ ZH XVH WRSLF GLVWULEXWLRQVRIVSHFLILFVRQJVIRUH[DPSOHWKHWRSLFGLVWULEXWLRQRI JURXSV FRQWDLQLQJ KLJKFRQVLVWHQF\ VRQJV JHQHUDWHV
PRUHKLJKFRQVLVWHQF\VXJJHVWLRQVRIPXVLFDOQRWHVWKDQ
GRHV WKH WRSLF GLVWULEXWLRQ RI JURXSV FRQWDLQLQJ ORZFRQVLVWHQF\ VRQJV +HQFH ZH JHQHUDWHG  SDWWHUQV RI
VXJJHVWLRQV RI PXVLFDO QRWHV E\ HDFK  GLIIHUHQW WRSLFGLVWULEXWLRQV :H JRW  GLIIHUHQW WRSLF GLVWULEXWLRQV E\GLYLGLQJ%UDKPVVRQJVLQWRJURXSVLQDFFRUGDQFHZLWKWKHUDQNLQJRIFRQVLVWHQF\YDOXHRIWKHVHVRQJV )LJXUH 

4.2.2 Result 2. Comparing updated consistency withchanging the topic distribution
7KHJUDSKLQWKHPLGGOHRI)LJXUHVKRZVWKHFRQVLVWHQF\YDOXHVZKHQZHVLPXODWHGDXVHUZKRRQDFFHSWLQJRXU
VXJJHVWLRQV PHWKRG 7KH VXJJHVWLRQV RI PXVLFDO QRWHV
ZHUH JHQHUDWHG XVLQJ WKH WRSLF GLVWULEXWLRQ ZKLFK FDOFXODWHG  %UDKPV VRQJV WKDW KDG KLJK FRQVLVWHQF\ YDOXHV
7KH UHVXOW VKRZV WKDW WKH FRQVLVWHQF\ YDOXHV WKDW ZHUH
JHQHUDWHG IURP WKH WRSLF GLVWULEXWLRQ RI KLJKHVWFRQVLVWHQF\ VRQJ VHW DQG XVHG DOO VHWV RI QRWHV LQ WKHKLJKSUREDELOLW\ UDQNLQJ KDG KLJKHU FRQVLVWHQF\ YDOXHVWKDQ WKRVH JHQHUDWHG XVLQJ WRSLF GLVWULEXWLRQ FDOFXODWHG
E\DOOVRQJVDQG2QWKHRWKHUKDQGDVVHHQLQWKHERWWRP
RI )LJXUH  WKH FRQVLVWHQF\ YDOXHV JHQHUDWHG XVLQJ WKHWRSLFGLVWULEXWLRQZKLFKFDOFXODWHGORZFRQVLVWHQF\VRQJ
VHW KDG QDUURZHU UDQJHV RI YDOXHV WKRVH JHQHUDWHG XVLQJ
DOOWKHVRQJV

4.1.3 Experiment 3: Calculating updated consistency byusing suggestions of musical notes generated from another composer’s probabilistic models and topic distribution$VIROORZLQJRXUK\SRWKHVLV LIRXUPHWKRGZRUNVZHOO 
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the suggestion of musical notes generated from anothercomposer’s models and topic distribution)LJXUH  VKRZV WKH WUDQVLWLRQ RI FRQVLVWHQF\ YDOXHZKHQWKHVLPXODWHGXVHUNHHSVFKRRVLQJRXUVXJJHVWHGPXVLFDOQRWHVZKHQWKHVXJJHVWLRQVZKLFKZHUHJHQHUDWHGE\XV
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Page 505

Use all candidates

Eliminate the top 4 candidates

Use all candidates

Eliminate the top 4 candidates

Eliminate the top candidate

Eliminate the top 5 candidates

Eliminate the top candidate

Eliminate the top 5 candidates

Eliminate the top 2 candidates

Eliminate the top 6 candidates

Eliminate the top 2 candidates

Eliminate the top 6 candidates

Eliminate the top 3 candidates

Eliminate the top 3 candidates

0.40

0.35

0.30

Consistency

Consistency

0.35

0.25

0.20

0

200

400

600

Number of added notes

800

0.10

1000

Consistency

0.25

0.20

0.15

0

200

400

600

Number of added notes

800

1000

Consistency transition

Datasets (Probabilistic model): 17 Brahms songs
Datasets (Topic distribution): 4 Brahms songs ( Worst 4 high-consistency songs )
0.40

0.35

Consistency

200

400

600

Number of added notes

800

1000



 'LVFXVVLRQ

0.30

0.30

0.25

0.20

0.15

0.10

0

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G

Datasets (Probabilistic model): 17 Brahms songs
Datasets (Topic distribution): 4 Brahms songs ( Top 4 high-consistency songs )

0.35

0.10

0.25

0.15

Consistency transition

0.40

0.30

0.20

0.15

0.10

Consistency transition
Datasets for calculating consistency: 17 Brahms songs
Datasets for generating notes: 16 Mozart songs

Consistency transition
Datasets: 17 Brahms songs

0.40

0

200

400

600

Number of added notes

800

1000

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