Vol.2016-MUS-112 No.7
2016/7/30

৘ใॲཧֶձ‫ڀݚ‬ใࠂ
IPSJ SIG Technical ReportՎ੠ F0 ‫ʹ੻ي‬ର͢ΔԻූਪఆͷͨΊͷϕΠδΞϯ४Ϗʔτಉ‫ ظ‬HMM‫྄ ݟۋ‬1,a)தଜ ӫଠ1,b)ࢳࢁ ࠀण1,c)٢Ҫ ࿨Ղ1,d)֓ཁɿຊߘͰ͸࿈ଓతͳՎ੠ F0 ‫͔੻ي‬Β཭ࢄతͳԻූ‫ྻܥ‬Λਪఆ͢Δ౷‫ܭ‬తख๏Λࣔ͢ɽैདྷɼԻָԻ
‫ڹ‬৴߸͔ΒϑϨʔϜϨϕϧͷՎ੠ F0 Λਪఆ͢ΔͨΊͷ‫͕ڀݚ‬ଟ͘ߦΘΕ͍ͯΔͷͰɼզʑ͸‫߸ه‬తͳָේͷ֫ಘΛ໨తͱͨ͠ F0 ‫͔੻ي‬ΒͷԻූਪఆʹऔΓ૊ΉɽԻූਪఆʹର͢Δૉ๿ͳΞϓϩʔν͸ɼҰఆ࣌ؒ୯Ґʢྫ͑͹ɼ൒Ϗʔτʣ͝ͱʹՎ੠ F0 Λ൒ԻϨϕϧͰ཭ࢄԽ͢Δख๏Ͱ͋Δɽ͔͠͠ͳ͕Βɼ͜ͷΞϓϩʔνͰ͸Վ੠ F0 ‫ָ͕੻ي‬ේʹ‫͞ه‬ΕͨԻߴ͔Βେ͖͘ҳ୤͍ͯ͠Δ৔߹ʹ͏·͍͔͘ͳ͍ɽԻූ
ͷΦϯηοτ͸Ϗʔτ࣌ࠁ͔Β஗ΕͨΓਐΜͩΓ͢ΔʢΦϯηοτมಈʣ͏͑ɼՎ੠ F0 ͸Վএද‫ʹݱ‬ΑΓมಈ͢Δʢप೾਺มಈʣ
ɽ͜ΕΒͷҳ୤Λѻ͏ͨΊʹɼզʑ͸Իූ͕Ϗʔτ࣌ࠁʹΏΔ͘ಉ‫ͯ͠ظ‬มԽ͢Δ
ϕΠδΞϯӅΕϚϧίϑϞσϧΛఏҊ͢ΔɽԻූͷ൒ԻϨϕϧͷԻߴͱΦϯηοτมಈ͸જࡏม਺ͱΈͳ͠ɼप೾਺มಈ͸ग़ྗ෼෍ʹΑͬͯ‫ه‬ड़͢ΔɽԻූɼΦϯηοτมಈɼप೾਺มಈ͸ΪϒεαϯϓϦϯά
Λ༻͍ͯಉ࣌ʹਪఆ͢Δɽ࣮‫݁ݧ‬ՌΑΓϕʔεϥΠϯख๏ʹରͯ͠ఏҊख๏ͷԻූਪఆਫ਼౓͕޲্ͨ͜͠
ͱ͕ࣔͤͨɽ

Վ੠͸௨ৗϙϐϡϥʔԻָͷϝϩσΟϥΠϯΛ‫ܗ‬੒ͯ͠

音高…

੠ղੳ͸Իָ৘ใॲཧͷ෼໺ʹ͓͍ͯॏཁͳςʔϚͷҰͭ音高Ͱ͋ΔɽՎ੠ղੳʹ͓͍ͯɼԻָԻ‫ڹ‬৴߸ʹର͢Δ‫ج‬ຊप

…

レ
ド#
ド

͓Γɼָ‫ۂ‬ͷงғ‫ؾ‬΍ҹ৅ʹେ͖ͳӨ‫ڹ‬Λ༩͑ΔͨΊɼՎ

೾਺ʢF0ʣਪఆ [1–7] ΍Վ੠෼཭ [8, 9] ͸޿͘‫͞ڀݚ‬Εͯૉʹয఺Λ౰ͯͳ͕ΒɼΑΓਂ͘ԻָΛཧղ͢Δ͜ͱΛॿຊ‫Ͱڀݚ‬͸ɼՎ੠ F0 ‫͔੻ي‬ΒԻූ‫ྻܥ‬ΛऔΓग़͢͜ͱΛ໨తͱͨ͠Իූਪఆ໰୊ʹऔΓ૊ΉɽՎ੠ͷ F0 ਪఆʹ+周波数変動

時刻

レ
ド#
ド

音高
レ
ド#
ド

…

͚ΔԻָؑ৆γεςϜ [14] ͳͲʹ༻͍ΒΕ͍ͯΔɽ

時刻…

͘ΧϥΦέγεςϜ [12, 13]ɼϢʔβʔ͕ಛఆͷԻָతཁ+オンセット変動…

͍Δɽ͜ΕΒͷٕज़͸Վखಉఆ [10, 11] ΍Վ੠཈ѹʹ‫ͮج‬

楽譜成分

…

1. ͸͡Ίʹ

ਤ 1: Վ੠ F0 ‫੻ي‬ͷੜ੒աఔɽ

時刻

ؔ͢Δ‫ڀݚ‬͸ଟ͘ߦΘΕ͍ͯΔ͕ɼ࣮༻໘Ͱ͸ָේͷΑ͏ͷΦϯηοτ͕ਖ਼֬ͳϏʔτ࣌ࠁ͔Βେ͖͘ਐΜͩΓ஗Εͳ཭ࢄతʢ‫߸ه‬తʣͳ৘ใΛநग़͢Δ໰୊ʹऔΓ૊ΉඞཁͨΓ͢ΔΑ͏ͳՎ͍ํͰͷ৔߹ʹɼ͜ͷํ๏Ͱ͸͠͹͠͹͕͋Δɽ΋͠ɼϏʔτ৘ใ͕‫ط‬஌Ͱ͋Ε͹ɼ͜ͷ໰୊ʹର͏·͍͔͘ͳ͍ɽ

͢Δૉ๿ͳΞϓϩʔν͸Ұఆ࣌ؒ୯Ґʢྫ͑͹ɼ൒Ϗʔτʣ͜ͷ໰୊Λղܾ͢ΔͨΊʹɼӅΕͨԻූ‫͔ྻܥ‬ΒͲͷΑ͝ͱʹଟ਺ܾʹΑͬͯ൒ԻϨϕϧͷ F0 ʹ཭ࢄԽ͢Δํ๏͏ʹՎ੠ F0 ‫͕੻ي‬ੜ੒͞ΕΔ͔Λද‫͢ݱ‬ΔӅΕϚϧίϑϞ

Ͱ͋Δ [14]ɽ͔͠͠ͳ͕ΒɼՎ੠ͷ F0 ָ͕ේʹ‫͞ه‬ΕͨσϧʢHMMʣʹ‫ͮ͘ج‬౷‫ܭ‬తख๏ΛఏҊ͢Δ (ਤ 1)ɽָේ

ਖ਼֬ͳ൒ԻϨϕϧͷ F0 ͔Βେ͖͘ҳ୤͢Δ৔߹΍ɼԻූʹ‫͞ه‬ΕͨԻූͷ F0 ͸൒Իִؒͷ཭ࢄతͳ஋ͷΈΛऔΓɼϏʔτɼ൒Ϗʔτɼ1/4 ϏʔτͷҐஔͰมΘΓ΍͍͢ɽҰ

1
a)
b)
c)
d)

‫౎ژ‬େֶ
nishikimi@sap.ist.i.kyoto-u.ac.jp
enakamura@sap.ist.i.kyoto-u.ac.jp
itoyama@kuis.kyoto-u.ac.jp
yoshii@kuis.kyoto-u.ac.jpⓒ 2016 Information Processing Society of JapanํͰɼ࣮ࡍͷՎ੠ F0 ‫੻ي‬͸࿈ଓతͳ৴߸Ͱ͋Γɼ࣌ؒͱͱ
΋ʹಈతʹมԽ͢Δɽੜ੒తͳࢹ఺͔Β͜ΕΒ 2 छྨͷ F0Λѻ͏ͨΊʹɼϝϩσΟΛՎͬͨ࿈ଓతͳ F0 ָ͕ේʹॻ͔Εͨ཭ࢄతͳ F0 ͔Β࣌ؒํ޲ͱप೾਺ํ޲ʹҳ୤͢Δ͜

1

Vol.2016-MUS-112 No.7
2016/7/30

৘ใॲཧֶձ‫ڀݚ‬ใࠂ
IPSJ SIG Technical ReportͱΛ‫ͨ͠ڐ‬ɼ४Ϗʔτಉ‫ ظ‬HMMʢSemi-beat-synchronous

音楽音響信号

HMMɼSBS-HMMʣΛఏҊ͢ΔɽఏҊ͢Δ HMM ʹ͓͍ͯɼԻූͷ൒ԻϨϕϧͷ F0 ͱΦϯηοτมಈ͸જࡏม਺ͱͯ͠ද‫͞ݱ‬ΕɼԻූͷप೾਺มಈ͸ग़ྗ֬཰෼෍ʹΑͬ

ビートトラッキング

歌声F0推定ͯϞσϧԽ͞ΕΔɽF0 ‫ͱ੻ي‬Ϗʔτ࣌ࠁ͕༩͑ΒΕΕ͹ɼશͯͷม਺ͱ෼෍͸ΪϒεαϯϓϦϯάΛ༻͍ͯಉ࣌ʹਪ
ఆ͞ΕΔɽ

音符推定

2. ؔ࿈‫ڀݚ‬ຊষͰ͸Վ੠ʹؔ͢Δؔ࿈‫ڀݚ‬Λ঺հ͢Δɽ

2.1 Վ੠Իߴਪఆ
ԻָԻ‫ڹ‬৴߸ʹର͢ΔՎ੠ F0 ‫੻ي‬ͷਪఆʹؔͯ͠͸ଟਤ 2: ఏҊ͢Δ४Ϗʔτಉ‫ ظ‬HMM ʹ‫ͮ͘ج‬Իߴਪఆख๏
ͷશମਤɽ͘ͷ‫͞ͳ͕ڀݚ‬Ε͍ͯΔ [1–7]ɽSubharmonic Summation
ʢSHSʣ[1] ͸‫ج‬ຊप೾਺ͷީิ {f0 , . . . , fM } ͷͦΕͧΕʹϝϩσΟɼϕʔεϥΠϯɼίʔυΛଟ੠Իָ͔Βਪఆ͢Δ

͍ͭͯߴௐ೾੒෼ͷύϫʔͷ૯࿨Λ‫͢ࢉܭ‬Δ͜ͱͰɼ֤࣌

ख๏ΛఏҊ͍ͯ͠ΔɽMauch Β [20] ʹΑͬͯ։ൃ͞Εͨࠁ͝ͱͷ‫ج‬ຊप೾਺Λܾఆ͢Δํ๏Ͱ͋ΔɽPreFEst [3]Tony ͱ͍͏ιϑτ΢ΣΞπʔϧ͸ HMM ͷϏλϏ୳ࡧʹ͸ଟ੠ԻָԻ‫ڹ‬৴߸͔Β࠷΋༏ੑͳௐ೾ߏ଄Λநग़͢Δ͜ΑΓ pYIN ͷग़ྗ͔ΒԻූΛਪఆ͢ΔɽͱʹΑΓϝϩσΟͱϕʔεϥΠϯͷ F0 ‫੻ي‬Λਪఆ͢Δख
๏Ͱ͋Δɽ஑‫ٶ‬Β [2] ͸Վ੠෼཭ͱ F0 ਪఆΛ૬ิతʹߦ͏

2.3 Վ੠ F0 ‫੻ي‬ͷղੳख๏ΛఏҊ͍ͯ͠Δɽ·ͣɼԻָԻ‫ڹ‬৴߸ʹର͢Δ୹࣌ؒՎ੠ F0 ‫͔੻ي‬ΒՎ͍ํͷ‫ݸ‬ੑ΍บΛநग़͢Δ‫ڀݚ‬΋͓ϑʔϦΤม‫׵‬ʢSTFTʣʹΑͬͯಘΒΕͨεϖΫτϩάϥϜ

͜ͳΘΕ͍ͯΔɽେੴΒ [21] ͸࣌ؒมಈͱप೾਺มಈΛߟ͔Βϩόετओ੒෼෼ੳʢRPCAʣ[9] Λ༻͍ͯՎ੠͕෼཭

ྀͨ͠Վ੠ F0 ‫੻ي‬ͷੜ੒աఔΛද‫͢ݱ‬ΔϞσϧΛఏҊ͠͞ΕΔɽͦͯ͠ɼ෼཭ͨ͠Վ੠ʹରͯ͠‫͞ࢉܭ‬ΕΔ SHS Λͨɽ͜ͷϞσϧʹ͓͍ͯɼՎ੠ F0 ‫੻ي‬͸ϊʔτɼද‫ݱ‬ɼඍ༻͍ͯϏλϏ୳ࡧʹΑΓՎ੠ F0 ‫੻ي‬Λ‫ٻ‬ΊΔɽSalamonࡉมಈͷ 3 ͭͷ੒෼͔Β੒Δɽϊʔτ੒෼͸ϊʔτͷཱͪ

Β [4] ͸ϝϩσΟநग़ʹରͯ͠Վ੠ F0 ‫ʹ੻ي‬ಛ௃Λ༻্͍͕Γ΍ΦʔόʔγϡʔτΛ‫ؚ‬Έද‫ݱ‬੒෼͸Ϗϒϥʔτ΍

͍ͯΔɽDurrieu Β [5] ͸ओટ཯͸ιʔεϑΟϧλʔϞσϙϧλϝϯτΛ‫ؚ‬Ήɽϊʔτ੒෼ͱද‫ݱ‬੒෼͸ϊʔτࢦྩϧͰද‫͞ݱ‬Εɼ൐૗Ի͸ඇෛ஋ߦྻҼࢠ෼ղʢNMFʣϕʔͱද‫ʹྩࢦݱ‬Αͬͯ‫ۦ‬ಈ͞ΕΔೋ࣍‫ܥ‬ઢ‫ܗ‬γεςϜͷग़ྗεͷϞσϧͰද‫͞ݱ‬ΕΔϝϩσΟநग़๏ΛఏҊ͍ͯ͠Δɽ

ͱͯ͠ද͞ΕΔɽϊʔτࢦྩͱද‫ྩࢦݱ‬͸ͦΕͧΕԻූ‫ܥ‬de Cheveigné Β [6] ͸‫ج‬ຊप೾਺ਪఆʹରͯ͠‫ޡ‬Γ཰Λ‫ݮ‬ྻͱԻָతද‫ݱ‬ҙਤΛද͠ɼHMM Λ༻͍ͯϞσϧԽ͞Ε

গͤ͞ΔΑ͏֦ுͨࣗ͠‫ݾ‬૬ؔʹ‫ ͮ͘ج‬YIN ͱ‫ݺ‬͹ΕΔΔɽ͜ͷख๏ʹΑΓՎ੠ F0 ‫͔੻ي‬ΒՎএද‫ݱ‬ͷ‫ݸ‬ਓੑΛख๏ΛఏҊ͍ͯ͠ΔɽMauch Β [7] ͸֬཰తख๏Λ༻͍ͯऔΓग़͢͜ͱ͸Մೳ͕ͩɼࣄલʹָේ͕༩͑ΒΔ͜ͱΛԾ

YIN Λ֦ு͢Δ͜ͱͰෳ਺ͷԻߴީิΛग़ྗ͢ΔΑ͏ʹ͠ఆ͓ͯ͠Γɼ௚઀తʹԻූਪఆ໰୊ʹ͸ద༻Ͱ͖ͳ͍ɽ

ͨ pYIN ͱ‫ݺ‬͹ΕΔख๏ΛఏҊ͍ͯ͠Δɽ

3. ఏҊ๏

2.2 Վ੠Իූਪఆ

ຊষͰ͸४Ϗʔτಉ‫ ظ‬HMMʢSBS-HMMʣʹΑΓՎ੠

Վ੠ F0 ‫੻ي‬ͷԻߴΛ཭ࢄԽͯ͠Իූ‫ྻܥ‬Λਪఆ͢Δख๏

F0 ‫੻ي‬ͷੜ੒աఔΛද‫͢ݱ‬Δ͜ͱͰɼF0 ‫੻ي‬ͷഎ‫͋ʹޙ‬΋ఏҊ͞Ε͍ͯΔɽ1 ষͰड़΂ͨଟ਺ܾ๏͸ Songle [14] ʹΔԻූ‫ྻܥ‬Λਪఆ͢ΔͨΊͷख๏ʹ͍ͭͯઆ໌͢Δɽ‫؍‬ଌ࣮૷͞Ε͍ͯΔɽ͜ͷख๏Ͱ͸ɼՎএද‫ݱ‬΍Իߴͷੜ੒աͱͯ͠ಘΒΕΔՎ੠ F0 ‫੻ي‬͸ָේʢԻූ‫ྻܥ‬ʣʹΦϯηο

ఔʹ͍ͭͯߟྀ͍ͯ͠ͳ͍ͷͰ‫ݶ‬ք͕͋ΔɽPaiva Β [15]τมಈͱप೾਺มಈ͕֬཰తʹ෇༩͞ΕΔ͜ͱͰੜ੒͞Ε͸ 5 ͭͷஈ֊Λ‫ͯܦ‬ଟ੠Իָ৴߸͔ΒϝϩσΟͷԻූΛਪ

Δͱͯ͠ఆࣜԽ͢Δɽ

ఆ͢Δख๏ΛఏҊ͍ͯ͠ΔɽRaphael [16] ͸ HMM ʹ‫ͮج‬͍ͯಠএՎ੠Ի‫ڹ‬৴߸͔ΒϦζϜɼςϯϙɼԻූΛಉ࣌ʹਪఆ͢Δख๏ΛఏҊ͍ͯ͠ΔɽPoliner Β [17] ͸Իߴ͸͋
Δ‫ج‬ຊप೾਺ͷߴௐ೾ͷू߹ͱ࣮ͯ͠‫͞ݱ‬ΕΔͱ͍͏Ծఆ
͕ඞཁ͕ͳ͍αϙʔτϕΫλʔϚγϯʢSVMʣʹ‫ͮ͘ج‬ख๏ΛఏҊ͍ͯ͠ΔɽLaaksonen ͸ [18] ίʔυ৘ใΛ༻͍ͯϝϩσΟ࠾ේख๏ΛఏҊ͍ͯ͠ΔɽRyynänen Β [19] ͸ⓒ 2016 Information Processing Society of Japan

3.1 ໰୊ઃఆ
Իූਪఆ໰୊ΛҎԼͷΑ͏ʹఆΊΔʢਤ 2ʣɽ
T

ೖྗ: Վ੠ F0 ‫ ੻ي‬X = {xt }t=1 ͱԻָԻ‫ڹ‬৴߸͔Βࣗಈ
Nਪఆ͞Εͨ 16 ෼Իූ୯ҐͷϏʔτ࣌ࠁ ψ = {ψn }n=1N

ग़ྗ: Իߴ‫ ྻܥ‬Z = {zn }n=1 .

2Vol.2016-MUS-112 No.7
2016/7/30

৘ใॲཧֶձ‫ڀݚ‬ใࠂ
IPSJ SIG Technical Report͜͜Ͱ t ͸࣌ؒϑϨʔϜͷΠϯσοΫεɼT ͸ೖྗͷ F0 ‫ي‬੻ʹʹ͓͚Δ࣌ؒϑϨʔϜͷ਺ɼxt ͸ϑϨʔϜ t Ͱͷର਺Δɽզʑ͸ p(xt |zn ) ʹίʔγʔ෼෍Λ༻͍Δɽίʔγʔ෼෍͸֎Ε஋ʹ‫͋Ͱ݈ؤ‬ΓɼҎԼͷΑ͏ʹप೾਺ʢ୯Ґ͸ηϯτʣɼN ͸Ϗʔτ࣌ࠁͷ਺ɼψn ͸ n ൪

Cauchy(x; µ, λ) =໨ͷϏʔτ࣌ࠁɼzn ∈ {µ1 , . . . , µK } ͸ ψn−1 ͱ ψn ͱͷؒλπ {(x − µ)2 + λ2 }(5)ͷԻߴͰ͋ΓɼK ͸ָේʹ‫ݱ‬ΕΔԻߴͷछྨͷ਺Ͱ͋Δɽ

Ͱఆٛ͞ΕΔɽ͜͜Ͱɼµ ͸ҐஔύϥϝʔλͰ͋Γɼ෼෍‫ۂ‬ͷ࠷ॳͱ࠷‫ޙ‬͸ͦΕͧΕ ψ0 = 1 ͱ ψN = T +1 ͱͰද͞ͷதԝ஋Λܾఆ͢Δɽ·ͨɼλ ͸ई౓ύϥϝʔλͰ͋ΔɽΕΔɽຊߘͰ͸ɼ؆୯ԽͷͨΊ zn (n = 1, . . . , N ) ͸ͦΕͧn ൪໨ͷϏʔτ۠ؒͷԻߴ͕ zn = k Ͱ͋Δ࣌ɼµ ͸஋ µk

Ε 16 ෼ԻූʹରԠ͢Δͱ͢Δɽ16 ෼ԻූΑΓ΋௕͍ԻූΛऔΔɽई౓ύϥϝʔλ͸Իߴ zn ʹґଘ͠ͳ͍஋ΛऔΔɽ

N͸࿈ଓͨ͠ಉ͡ԻߴΛ΋ͭ {zn }n=1 ͷ‫Ͱྻܥ‬ද͞ΕΔɽ

࣮ࡍͷՎ੠ F0 ‫੻ي‬͸ָේʹ‫͞ه‬ΕͨԻߴ͔Βେ͖͘ҳ
୤͢Δ͜ͱ͕͋ΔͷͰɼίʔγʔ෼෍ͷई౓ύϥϝʔλ͸

3.2 ϞσϧͷఆࣜԽԻූͷԻߴભҠɼΦϯηοτมಈɼप೾਺มಈΛಉ࣌ʹද‫͢ݱ‬Δ SBS-HMM ΛఆࣜԽ͢Δɽ

ྡ઀͢Δ F0 ͷࠩ ∆xt ≡ xt − xt−1 ʹԠͯ͡มԽ͢ΔΑ͏ʹ͢Δɽई౓ύϥϝʔλ͸ઈର஋ ∆xt ʹൺྫ͢ΔΑ͏ʹ͠ɼ֤ϑϨʔϜ͝ͱʹҎԼͷΑ͏ʹఆٛ͢Δɽ

3.2.1 ԻߴભҠͷϞσϧԽλt = c|∆xt | + dજࡏԻߴ‫ ྻܥ‬Z ͸ҎԼʹࣔ͢Α͏ʹҰ࣍Ϛϧίϑ࿈࠯
Λͳ͢ɽ

(6)

͜͜Ͱɼc ͸ൺྫ܎਺Ͱ͋Δɽ·ͨɼ∆xt = 0 ͷͱ͖ p(xt |zn )zn |zn−1 , A ∼ Categorical(zn |azn−1 )(1)͜͜ͰɼA = [aT1 , · · · , aTK ] ͸ K × K ͷભҠ֬཰ߦྻͰ͋
!K
Γɼ೚ҙͷ j ∈ {1, . . . , K} ʹ͍ͭͯ k=1 ajk = 1 ͕੒Γཱͭɽ࠷ॳͷજࡏঢ়ଶ z1 ͸

z1 |π ∼ Categorical(z1 |π)(2)͕‫ͳ͘ͳ͖Ͱࢉܭ‬Δ໰୊Λආ͚ΔͨΊʹม਺ d > 0 Λಋೖ
͢Δɽ

3.3 ࣄલ෼෍ͷಋೖզʑ͸Ϟσϧύϥϝʔλ Aɼπ ɼρ ʹରͯ͠ҎԼͷΑ͏ʹσΟϦΫϨ‫ڞ‬໾ࣄલ෼෍Λ͓͘ɽʹΑΓܾఆ͞ΕΔɽ͜͜Ͱɼπ = [π1 , · · · , πK ]T ͸ K ࣍‫ݩ‬!KϕΫτϧͰ͋Γɼ k=1 πk = 1 ͕੒Γཱͭɽ

3.2.2 ΦϯηοτมಈͷϞσϧԽaj ∼ Dirichlet(aj |ξj )(7)

π ∼ Dirichlet(π|ζ)(8)ρ ∼ Dirichlet(ρ|η)(9)ԻූͷΦϯηοτมಈ τ = {τn }Nn=1 ͸ {−G, −G + 1,

͜͜Ͱɼξj = [ξ1 , . . . , ξK ]T ͱ ζ = [ζ1 , . . . , ζK ]T ͸ K ࣍‫ݩ‬Δɽn ൪໨ͷԻූͷ࣮ࡍͷΦϯηοτ࣌ࠁΛ φn = ψn + τnϕΫτϧɼη = [η−G , . . . , ηG ]T ͸ (2G + 1) ࣍‫ݩ‬ϕΫτϧ. . . , G−1, G} ͷ੔਺஋ΛऔΔ཭ࢄજࡏม਺ͱͯ͠ද͞Εͱ͓͘ɽՎ੠ F0 ‫੻ي‬ͷ࠷ॳͱ࠷‫Ͱޙ‬͸ τ0 = 0ɼτN = 0 ͱ͢Δɽτn ͸ҎԼͷΑ͏ʹ֬཰తʹੜ੒͞ΕΔͱ͢Δɽ

τn |ρ ∼ Categorical(τn |ρ)

3.2.3 प೾਺มಈͷϞσϧԽ‫؍‬ଌ F0 xt (φn−1 ≤ t < φn ) ͸֤Ϗʔτ۠ؒʹׂΓ౰ͯΒΕͨ൒Ի୯ҐͷԻߴʹ֬཰తͳप೾਺มಈΛ෇༩͢Δ͜
ͱͰੜ੒͞ΕΔɽxt ͸֤ϑϨʔϜʹ͓͍ͯಠཱʹੜ੒͞ΕΔͱ͠ɼn ൪໨ͷϏʔτ۠ؒͷग़ྗ֬཰͸ɼҎԼͷΑ͏ʹ༩͑ΒΕΔɽ

bzn τn−1 τn ≡⎩t=φn−1p(xt |zn )⎫ φ −φ1⎬ n n−1⎭·ͨɼίʔγʔ෼෍ͷඇෛύϥϝʔλ c ͱ d ʹରͯ͠ҎԼͷΑ͏ʹΨϯϚࣄલ෼෍Λ͓͘ɽ(3)͜͜Ͱɼρ = [ρ−G , . . . , ρG ]T ͸ (2G + 1) ࣍‫ݩ‬ϕΫτϧͰ͋!GΓɼ g=−G ρg = 1 ͕੒Γཱͭɽ

⎧
n −1
⎨ φ%

Ͱ͋Δɽ

c ∼ Gamma(c|c0 , c1 )(10)d ∼ Gamma(d|d0 , d1 )(11)͜͜Ͱɼc0 ɼd0 ͸‫ܗ‬ঢ়ύϥϝʔλɼc1 ɼd1 ͸ϨʔτύϥϝʔλͰ͋Δɽ

3.4 ϕΠζਪఆϕΠζਪఆͷ໨త͸ࣄ‫ޙ‬෼෍ p(Z, τ , A, π, ρ, c, d|X) Λ‫͢ࢉܭ‬Δ͜ͱͰ͋Δɽ͜ͷ‫ࢉܭ‬Λղੳతʹߦ͏ͷ͸೉͍͠ͷͰɼզʑ͸Ϛϧίϑ࿈࠯ϞϯςΧϧϩʢMCMCʣ๏Λ༻͍ͯ͜ΕΒͷม਺ͷ஋ΛαϯϓϦϯά͢Δɽ͜͜ͰɼϞσ(4)ϧύϥϝʔλΛ Θ = {A, π, ρ} ͱ͢ΔɽΘ ͷαϯϓϧʹ

͸ΪϒεαϯϓϦϯάΞϧΰϦζϜΛ༻͍Δɽ·ͨɼજࡏ͜͜Ͱɼp(xt |zn = k) ͸֤ϑϨʔϜͷग़ྗ֬཰Ͱ͋Δɽભม਺‫ ྻܥ‬Z ɼτ ͷαϯϓϧʹ͸ϒϩοΫԽΪϒεαϯϓϦ

Ҡ֬཰ͱग़ྗ֬཰ͷόϥϯεΛऔΔͨΊɼ֤ϑϨʔϜ͝ͱϯάΞϧΰϦζϜͷҰͭͰ͋ΔɼϑΥϫʔυϑΟϧλϦϯ

ͷग़ྗ֬཰ͷੵΛϏʔτ۠ؒ಺ͷϑϨʔϜ਺ͰႈࠜΛͱάɾόοΫϫʔυαϯϓϦϯάΞϧΰϦζϜΛ༻͍Δɽ͜

ⓒ 2016 Information Processing Society of Japan3

Vol.2016-MUS-112 No.7
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IPSJ SIG Technical ReportΕΒͷύϥϝʔλ΍ม਺͸ɼHMM ͷ‫ֶ͠ͳࢣڭ‬शͰ༻͍ಛʹɼજࡏม਺ (zN , τN ) ͸ҎԼͷΑ͏ʹ αzN τN ʹ͕ͨͬ͠ΒΕΔό΢ϜɾϰΣϧνΞϧΰϦζϜͱΑ͹ΕΔ‫ظ‬଴஋࠷ͯαϯϓϧ͞ΕΔɽ

େԽ๏ʢEM ΞϧΰϦζϜʣͱಉ༷ͷํ๏Ͱ൓෮ߋ৽͞ΕβzN τN ∝ αzN τNΔɽc ͱ d ʹؔ͢Δ෼෍͸‫ڞ‬໾ੑ͕ຬͨ͞Εͳ͍ͷͰɼϝτϩϙϦεɾϔΠεςΟϯάεʢMHʣΞϧΰϦζϜΛ༻͍ͯߋ৽͢Δɽ

(16)

3.4.2 Ϟσϧύϥϝʔλ Aɼπ ɼρ ͷֶशຊষͰ͸ Θ ͷ஋ͷֶशʹ͍ͭͯઆ໌͢ΔɽόοΫϫʔ

3.4.1 જࡏม਺ Z ɼτ ͷਪ࿦υαϯϓϦϯάʹ͓͍ͯαϯϓϧ͞Εͨજࡏม਺ͷ‫ྻܥ‬જࡏม਺‫ ྻܥ‬Z ͱ τ Λαϯϓϧ͢Δํ๏Λઆ໌͢Δɽ֤Ϗʔτ۠ؒ͝ͱʹɼҎԼͰ༩͑ΒΕΔ֬཰Λ‫͢ࢉܭ‬Δɽβzn τn = p(zn , τn |zn+1:N , τn+1:N , x1:T )(12)͜͜Ͱɼzn+1:N ɼτn+1:N ɼx1:T ͸ͦΕͧΕ zn+1 , . . . , zN ɼN

{zn , τn }n=1 ʹ͍ͭͯɼzn = j ͔ͭ zn+1 = k Ͱ͋ΔભҠͷ਺Λ sjk ɼτn = g Ͱ͋ΔΦϯηοτมಈͷ਺Λ ug Ͱද͢ɽ·ͨɼz1 = k ͷ࣌ɼvk ͷ஋Λ 1ɼͦΕҎ֎Λ 0 ͱ͢Δɽύϥϝʔλ ajk ɼρg ɼπk ͸ҎԼͰ༩͑ΒΕΔࣄ‫ޙ‬෼෍͔Βαϯϓϧ͞ΕΔ͜ͱͰߋ৽͞ΕΔɽτn+1 , . . . , τN ɼx1 , . . . , xT Λද͢ɽn ൪໨ͷϏʔτ۠ؒͷજࡏม਺ (zn , τn ) ͸ βzn τn ʹै͍αϯϓϧ͞ΕΔɽࣜ (12)p(aj |ξj + sj ) = Dirichlet(aj |ξj + sj )(17)ͷ‫ͱࢉܭ‬જࡏม਺ͷαϯϓϦϯά͸ϑΥϫʔυϑΟϧλϦ

p(ρ|η + u) = Dirichlet(ρ|η + u)(18)ϯάɾόοΫϫʔυαϯϓϦϯάΛ༻͍ͯߦΘΕΔɽ

p(π|ζ + v) = Dirichlet(π|ζ + v)

(19)ϑΥϫʔυϑΟϧλϦϯάͰ͸ҎԼͷ֬཰Λ൓෮‫Ͱࢉܭ‬͜͜Ͱɼsj = [sj1 , . . . , sjK ]T ɼu = [u−G , . . . , uG ]T ɼv =‫ٻ‬ΊΔɽ

[v1 , . . . , vK ]T Ͱ͋Δɽ
αzn τn = p(X0τ1 , . . . , Xτn−2 τn−1 , Xτn−1 τn , zn , τn )3.4.3 ίʔγʔ෼෍ͷύϥϝʔλ cɼd ͷֶश͜͜ͰɼXτn−1 τn ͸ φn−1 = ψn−1 + τn−1 ͔Β φn = ψn + τnύϥϝʔλ c ͱ d ͷਪఆʹ͸ɼMH ΞϧΰϦζϜΛ༻͍·ͰͷϏʔτ۠ؒ಺ͷ‫؍‬ଌ xt Λද͢ɽαzn τn ͸ҎԼͷΑ͏Δɽίʔγʔ෼෍͸‫ڞ‬໾ࣄલ෼෍Λ࣋ͨͳ͍ͷͰ c ͱ d ͷʹ‫͞ࢉܭ‬ΕΔɽࣄ‫ޙ‬෼෍Λղੳతʹ‫͢ࢉܭ‬Δͷ͸ࠔ೉Ͱ͋Δɽc ͱ d ͷ஋͕ͦΕͧΕ ci ͱ di Ͱ͋Δͱ͖ɼఏҊ෼෍ΛҎԼͷΑ͏ʹ

αzn τn = p(X0τ1 , z1 , τ1 )ఆΊΔɽ= p(X0τ1 |z1 , τ1 )p(z1 )p(τ1 )= bz1 0τ1 πz1 ρτ1(13)

αzn τn = p(X0τ1 , . . . , Xτn−1 τn , zn , τn )G)=

τn−1 =−G

·

K
)

(21)

qc (c|ci ) ͔Βαϯϓϧ͞Εͨ c∗ Λ༻͍ͯɼҎԼͷΑ͏ʹ࠾

p(X0τ1 , . . . , Xτn−2 τn−1 , zn−1 , τn−1 )τn−1 =−G

qd (d|di ) = Gamma(d|δdi , δ)୒཰Λ‫͢ࢉܭ‬Δɽ

· p(zn |zn−1 )p(τn )=(20)͜͜Ͱɼγ ͱ δ ͸ఏҊ෼෍ͷϋΠύʔύϥϝʔλͰ͋Δɽp(Xτn−1 τn |zn , τn−1 , τn )zn−1 =1G)

qc (c|ci ) = Gamma(c|γci , γ)bzn τn−1 τn

K
)

*
+
fc (c∗ )qc (ci |c∗ )gc (c∗ , ci ) = min 1,
fc (ci )qc (c∗ |ci )(22)͜͜Ͱɼfc (c) ͸ҎԼͷΑ͏ʹ‫͞ࢉܭ‬ΕΔ໬౓ؔ਺Ͱ͋Δɽ

αzn−1 τn−1 azn−1 zn ρτnzn−1 =1(14)όοΫϫʔυαϯϓϦϯάͰ͸ɼn ൪໨ͷϏʔτ۠ؒʹ͓͍ͯ αzn τn ͷ஋Λ༻͍ͯࣜ (12) ͕‫͞ࢉܭ‬ΕΔɼঢ়ଶ (zn , τn ) ͕࠶‫ؼ‬తʹαϯϓϧ͞ΕΔɽ(n+1) ൪໨ͷঢ়ଶ(zn+1 , τn+1 ) ͕αϯϓϧ͞Εͨ࣌ɼβzn τn ͸ҎԼͷΑ͏ʹ‫ܭ‬ࢉ͞ΕΔɽ

fc (c) ≡ p(c|x1:T , z1:N , τ1:N , Θ, di )
∝
=

N
%

ρτn bzn τn−1 τn

N
%

ρτ n

n=1

n=1

·

βzn τn ∝ p(Xτn τn+1 |zn+1 , τn , τn+1 )t=φn−1

azn−1 zn πz1 q(c)n=2Cauchy(xt |µzn , λct )azn−1 zn πz1 Gamma(c|c0 , c1 )⎫ φ −φ1⎬ n n−1
⎭

(23)

n=2

(24)

ͦͯ͠ɼ΋͠ gc (c∗ , ci ) ͷ஋͕۠ؒ [0, 1] ʹ͓͚ΔҰ༷෼෍· p(X0τ1 , . . . , Xτn−1 τn , zn , τn )ⓒ 2016 Information Processing Society of Japan⎩

λct = ci · ∆xt + di

· p(zn+1 |zn )p(τn+1 )= bzn+1 τn τn+1 azn zn+1 ρτn+1 αzn τn

N
%

⎧
n −1
⎨ φ%

N
%

͔Βαϯϓϧ͞Εͨཚ਺ r ΑΓ΋େ͖͚Ε͹ɼci+1 = c∗ ͱ

(15)͠ɼͦ͏Ͱͳ͚Ε͹ɼci+1 = ci ͱ͢Δɽͨͩ͠ɼc0 ͸ࣄલ

4Vol.2016-MUS-112 No.7
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৘ใॲཧֶձ‫ڀݚ‬ใࠂ
IPSJ SIG Technical Report෼෍ q(c) ͔Βαϯϓϧ͞ΕΔɽd ͷ஋͸ c ͱಉ༷ͷํ๏Ͱߋ৽͞ΕΔɽqd (d|di ) ͔Βαϯϓϧ͞Εͨ d∗ Λ༻͍ͯɼҎԼͷΑ͏ʹ࠾୒཰Λ‫͢ࢉܭ‬Δɽ
*+fd (d∗ )qd (di |d∗ )gd (d∗ , di ) = min 1,(25)
fd (di )qd (d∗ |di )͜͜Ͱɼfd (d) ͸ҎԼͷΑ͏ʹ‫͞ࢉܭ‬ΕΔ໬౓ؔ਺Ͱ͋Δɽද 1: ฏ‫ۉ‬Ұக཰ͱඪ४‫ࠩޡ‬
Ϟσϧ

Ұக཰

SBS-HMM

66.3 ± 1.0ଟ਺ܾ๏ϑϨʔϜϕʔε HMM

56.9 ± 1.1

56.1 ± 1.1
67.0 ± 1.0

BS-HMMfd (d) ≡ p(d|x1:T , z1:N , τ1:N , Θ, ci+1 )
∝
=

N
%

ρτn bzn τn−1 τn

N
%

ρτ n

n=1

n=1

·

N
%

⎧
n −1
⎨ φ%
⎩

N
%

azn−1 zn πz1 q(c)n=2t=φn−1

Cauchy(xt |µzn , λdt )azn−1 zn πz1 Gamma(d|d0 , d1 )⎫ φ −φ1⎬ n n−1⎭(26)ਤ 3: Ұக཰ [%]. ശͻ͛ਤ಺Ͱɼ੺ઢ͸தԝ஋ɼ੨৭ͷn=2

λdt = ci+1 · ∆xt + diശ͸ୈ 1 ࢛෼Ґ͔Βୈ 3 ࢛෼Ґͷൣғɼࠇ৭ͷेࣈ͸ฏ‫ۉ‬(27)஋ɼ੺৭ͷेࣈ͸֎Ε஋Λࣔ͢ɽͦͯ͠ɼ΋͠ gd (d∗ , di ) ͷ஋͕۠ؒ [0, 1] ʹ͓͚ΔҰ༷෼෍͔Βαϯϓϧ͞Εͨཚ਺ r ΑΓ΋େ͖͚Ε͹ɼdi+1 = d∗ʹਪఆ͞ΕΔɽͱ͠ɼͦ͏Ͱͳ͚Ε͹ di+1 = di ͱ͢Δɽͨͩ͠ɼd0 ͸ࣄલ෼෍ q(d) ͔Βαϯϓϧ͞ΕΔɽ

(zN , τN ) = arg max{ωzN τN }(32)

zn = h(n+1)zn+1

(z)

(33)

(τ )
τn = h(n+1)τn+1(34)

zN ,τN3.5 ϏλϏ෮߸ԻූΛද͢જࡏม਺‫ྻܥ‬͸ֶशաఔʹ͓͍ͯҎԼͷࣜ (28) Ͱ༩͑ΒΕΔ໬౓͕࠷େͷ࣌ͷύϥϝʔλΛ༻͍Λิਖ਼͢Δ͜ͱʹΑΓԻූ‫͕ྻܥ‬ಘΒΕΔɽ

ͨϏλϏΞϧΰϦζϜʹΑͬͯਪఆ͞ΕΔɽ

p(x1:T ) =

K
)

G
)

α zN τNN

ਪఆ͞Εͨજࡏม਺ {τn }n=1 ʹΑͬͯද͞ΕΔप೾਺มಈ

4. ධՁ࣮‫ݧ‬(28)ఏҊ๏ͱैདྷ๏Λ༻͍ͯՎ੠ F0 ‫͔੻ي‬Βਪఆ͞ΕͨԻzN =1 τN =−Gਪఆ͍ͨ͠Իූ͸ p(Z, τ |X) Λ࠷େԽ͢Δજࡏม਺ͷ஋Ͱූྻͷਫ਼౓ΛධՁ͢Δ࣮‫ݧ‬ΛߦͬͨɽఆΊΔɽ

4.1 ࣮‫ݧ‬৚݅ωzn τn =100 ‫ۂ‬Λ༻͍ͨɽͦΕͧΕͷ‫ʹۂ‬ରͯ͠ɼϞσϧύϥϝʔmax lnp(X0τ1 , . . . , Xτn−1 τn , z1:n−1 , zn , τ1:n−1 , τn ) (29)λͷֶशɼԻූ‫ྻܥ‬ͷਪఆɼਪఆ͞ΕͨԻූ‫ྻܥ‬ͷਫ਼౓ͷ͋ΔɽϏλϏΞϧΰϦζϜʹ͓͍ͯ ωzn τn ΛҎԼͷΑ͏ʹ࣮‫ʹݧ‬͸ RWC σʔλϕʔε [22] ಺ͷϙϐϡϥʔԻָ

z1:n−1τ1:n−1‫ܭ‬ଌΛߦͬͨɽೖྗͷ F0 ‫੻ي‬͸஑‫ٶ‬Β [2] ͷख๏Λ༻͍ͦͯ͠ɼωzn τn ͸ҎԼͷΑ͏ʹ࠶‫ؼ‬తʹ‫͞ࢉܭ‬ΕΔɽ

ωz1 τ1 = ln ρτ1 + ln bz1 0τ1 + ln πz1
ωzn τn =,zn−1

Durand Β [23] ͷϏʔττϥοΩϯάγεςϜʹΑͬͯಘ(30)-

ln ρτn + max ln bzn τn−1 τn + max ln azn−1 zn +ωzn−1 τn−1
τn−1

ͯϞϊϥϧԻָԻ‫ڹ‬৴߸͔ΒಘΔɽ·ͨɼϏʔτ࣌ࠁ͸

.

(31)

ΒΕͨ΋ͷΛ༻͍Δɽ͜ͷγεςϜ͸શԻූ୯ҐͷϏʔτ/࣌ࠁΛਪఆ͢ΔͷͰɼਪఆ͞ΕͨϏʔτ۠ؒΛ 16 ౳෼͢
Δ͜ͱͰ 16 ෼Իූ୯ҐͷϏʔτ࣌ࠁΛ‫ٻ‬ΊͨɽఏҊ๏ͷϋΠύʔύϥϝʔλ͸ ξ = ɼζ = 1ɼη = 1ɼc0 = d1 = d0 = d1 = 1 ͱͨ͠ɽ͜͜Ͱɼ ͱ 1 ͸ͦΕͧωzn τn ͷ࠶‫͍͓ͯʹࢉܭؼ‬ɼ(zn , τn )=(k, g) ͷ࣌ͷ ωzn τnΕશཁૉ͕ 1 Ͱ͋ΔߦྻͱϕΫτϧͰ͋ΔɽఏҊ෼෍ͷύͷ஋Λ࠷େԽ͢Δঢ়ଶ͕ (zn−1 , τn−1 )=(j, f ) Ͱ͋Δ৔߹ɼϥϝʔλ͸ γ = δ = 1 ͱͨ͠ɽτn ͕औΓ͏Δ࠷େ஋ G ͸

(z)
(τ )
͜ΕΒͷঢ়ଶ͸ hnk = j, hng = f ͱͯ͠‫ه‬࿥͞ΕΔɽ
K,G{ωzN τN }zN =1,τN =−G ͕‫͞ࢉܭ‬Εͨ‫ޙ‬ɼࣜ (30) ͱ (31) ΛN༻͍ͯɼજࡏม਺‫{ ྻܥ‬zn , τn }n=1 ͕ҎԼͷΑ͏ʹ࠶‫ؼ‬త

5ʢͭ·Γ 50 ϛϦඵʣͱͨ͠ɽ

ⓒ 2016 Information Processing Society of JapanϕʔεϥΠϯͱͯ͠ଟ਺ܾ๏Λςετͨ͠ɽ16 ෦Իූʹ
ରԠ͢Δ࣌ؒ۠ؒ͝ͱʹՎ੠ F0 ͷଟ਺ܾΛͱΔ͜ͱͰԻ

5

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2016/7/30

৘ใॲཧֶձ‫ڀݚ‬ใࠂ
IPSJ SIG Technical Reportਤ 4: ֶश͞ΕͨϞσϧύϥϝʔλ ρ ͷྫɽ(a) Φϯηοτมಈਤ 5: Իߴਪఆ‫ޡ‬ΓͷྫɽਪఆԻߴ͕ਖ਼͍͠৔߹͸লུɽߴΛܾఆ͢Δɽൺֱͱͯ͠ɼϑϨʔϜϕʔε HMM ͱϏʔ(b) प೾਺มಈ

τಉ‫ ظ‬HMMʢBS-HMMʣ΋ςετͨ͠ɽϑϨʔϜϕʔਤ 6: Իߴਪఆ݁Ռͷྫɽ౧৭ɼ੨৭ɼ྘৭ɼ੺৭ɼࠇ৭ͷε HMM ͸શͯͷϏʔτ͕۠ؒ 1 ϑϨʔϜͷΈͰ͋Δͱઢ͸ͦΕͧΕ MIDI ϊʔτɼΦϯηοτมಈΛ‫ؚ‬Ή F0 ‫ي‬͢ΔɽBS-HMM ͸ΦϯηοτมಈΛߟྀ͠ͳ͍͜ͱҎ֎੻ɼଟ਺ܾ๏ʹΑͬͯਪఆ͞ΕͨԻߴɼఏҊ๏ʹΑͬͯਪ

SBS-HMM ͱಉ͡Ͱ͋Δɽఆ͞ΕͨԻߴɼࣄલʹਪఆ͞ΕͨϏʔτ࣌ࠁΛද͢ɽਪఆ͞ΕͨԻූྻ͸ָ‫ۂ‬ͷϝϩσΟͱಉ‫ ͨ͠ظ‬MIDIσʔλͱൺֱ͠ɼҰக཰ʢͭ·ΓɼԻߴ͕ਖ਼͘͠ਪఆ͞Ε

͕ଊ͑Δ༷ࢠΛ͍ࣔͯ͠Δɽ্ͷਤʹ͓͍ͯɼ࠷ॳͷϏʔ͍ͯΔϑϨʔϜͷൺ཰ʣΛධՁई౓ͱͯ͠༻͍ͨɽ

τͰͷΦϯηοτ͸Ϗʔτ࣌ࠁΑΓ஗Ε͍ͯΔɽఏҊ๏Ͱ͸Φϯηοτͷ஗ΕΛਖ਼͘͠ଊ͍͑ͯΔͷʹର͠ɼଟ਺ܾ

4.2 ࣮‫݁ݧ‬Ռ๏͸Φϯηοτͱ͢΂͖Ϗʔτ࣌ࠁΛ‫ޡ‬ೝ͍ࣝͯ͠ΔɽԼ

Իූਪఆͷ݁ՌΛද 1 ͱਤ 3 ʹࣔͨ͠ɽఏҊ๏͸ฏ‫ۉ‬Ұͷਤ͸ϏϒϥʔτͷྫͰ͋Δɽଟ਺ܾ๏Ͱ͸ਪఆ݁Ռ͕େ

க཰ʹ͓͍ͯଟ਺ܾ๏ͱϑϨʔϜϕʔε HMM Λେ্͖͖͘ͳप೾਺มಈʹӨ‫͞ڹ‬Ε͍ͯΔɽҰํɼఏҊ๏Ͱ͸ίʔճͬͨɽҰํͰɼఏҊ๏ͱ BS-HMM ͷҰக཰͸΄΅౳͠γʔ෼෍ͷ‫݈ؤ‬ੑʹΑΓϏϒϥʔτʹӨ‫͞ڹ‬ΕΔ͜ͱͳ͘͘ɼͦͷࠩ͸౷‫ܭ‬తʹ༗ҝͳ΋ͷͰ͸ͳ͔ͬͨɽ

ਖ਼͘͠Իߴ͕ਪఆͰ͖͍ͯΔɽ͜ͷ݁Ռ͸ભҠ֬཰ʹΑΔָේϞσϧͱग़ྗ֬཰ʹΑΔप೾਺มಈϞσϧ͕Իූਪఆਫ਼౓ͷ޲্ʹରͯ͠༗ޮͰ͋

5. ͓ΘΓʹ

Δ͜ͱΛ͍ࣔͯ͠ΔɽΦϯηοτมಈͷϞσϧʹΑΓਫ਼౓ຊߘͰ͸ɼϏʔτ࣌ࠁΛ‫ط‬஌ͱͯ͠Վ੠ F0 ‫͔੻ي‬Βָ͕޲্͠ͳ͔ͬͨͷ͸ɼϞσϧύϥϝʔλ ρ ͕ਖ਼ֶ͘͠श

‫ۂ‬ͷԻූਪఆΛߦ͏ख๏ΛఏҊͨ͠ɽՎ੠ F0 ‫੻ي‬ͷੜ੒͞Εͳ͔ͬͨ͜ͱ͕‫ݪ‬Ҽͩͱߟ͑ΒΕΔʢਤ 4ʣɽΦϯηοաఔΛϞσϧԽ͢Δʹࡍ͠ɼָේ੒෼͚ͩͰͳ͘Φϯηοτมಈ͸Φϯηοτͷ྆ଆͷԻߴͷ௕͞΍‫ۂ‬શମͷςϯϙτɾप೾਺มಈΛߟྀͨ͠ɽSBS-HMM ͸ଟ਺ܾ๏΍ϑʹґଘ͢ΔͷͰɼ୯Ұͷ཭ࢄ෼෍ͰΦϯηοτมಈΛଊ͑ϨʔϜϕʔε HMM ΑΓ΋ਖ਼֬ͳԻߴਪఆΛ࣮‫ͨ͠ݱ‬ɽΔͷ͸೉͍͠ɽԻߴ͕ભҠ͍ͯ͠Δؒͷ F0 Λද‫͢ݱ‬ΔͨఏҊ๏Λ༻͍ͯಘΒΕͨΦϯηοτมಈͱप೾਺มಈ͸ΊͷӅΕঢ়ଶΛ༻͍ΔͳͲͯ͠ɼΑΓৄࡉʹΦϯηοτมՎএද‫ݱ‬ͷಛ௃Λଊ͑Δ͏͑ͰॏཁͰ͋Δɽࠓ‫ޙ‬͸ɼ2 ࣍ಈΛϞσϧԽ͢Δ͜ͱ͕ඞཁͩΖ͏ɽ‫఻ܥ‬ୡؔ਺ͳͲΛ༻͍ͯՎ੠ F0 ‫੻ي‬ΛৄࡉʹϞσϧԽ͠ɼ

4.2.1 Իߴਪఆ‫ޡ‬ΓՎএද‫ݱ‬Λछྨ͝ͱʹநग़͢Δख๏ͷ։ൃΛߦ͍͍ͨɽఏ

ओʹೋछྨͷ‫ޡ‬Γ͕‫؍‬ଌ͞Εͨʢਤ 5ʣɽҰͭ໨͸ՎखҊ๏Ͱ͸ɼF0 ਪఆɼϏʔττϥοΩϯάɼԻූਪఆ͸ผʑͷՎএද‫ʹݱ‬ΑΔ΋ͷͰ͋Γɼ1 ൒Ի΍ 2 ൒Իͷ‫ޡ‬Γͱ͠ʹߦΘΕ͕ͨɼ͜ΕΒͷख๏Λ౷߹͢Δ͜ͱ΋ඞཁͰ͋Δɽͯ‫ݱ‬ΕΔɽ͜Ε͸प೾਺มಈ͕Իූਪఆਫ਼౓ʹӨ‫͢ڹ‬Δ͜

·ͨɼ࣮ࡍͷָ‫ʹۂ‬ଘࡏ͢Δແ੠෦෼Λѻ͏͜ͱ͕Ͱ͖ͳ

ͱΛҙຯ͢Δɽೋͭ໨͸ F0 ਪఆ‫ޡ‬ΓʹΑΔ΋ͷͰ͋Γɼ7͔͕ͬͨແ੠෦෼Λద੾ʹѻ͑ΔΑ͏ʹ͍ͨ͠ɽ൒Ի΍ 12 ൒Ի‫ޡ‬Γͱͯ͠‫ݱ‬ΕΔɽ7 ൒Ի΍ 12 ൒Ի͸‫׬‬શँࣙ ຊ‫ڀݚ‬ͷҰ෦͸ JST OngaCREST ϓϩδΣΫτɼ‫౓ޒ‬΍̍ΦΫλʔϒʹରԠ͢Δɽ

JSPS Պ‫ݚ‬අ 24220006ɼ26700020ɼ26280089ɼ15K16054ɼ

4.2.2 Վএද‫ݱ‬நग़ͱ‫݈ؤ‬ੑ

16H01744ɼ16J05486 ͱ‫৿ך‬৘ใՊֶৼ‫ॿஂࡒڵ‬੒ۚʹΑ

ਤ 6 ͷԻූਪఆ݁Ռͷྫ͸ՎखͷՎএද‫ݱ‬ΛఏҊϞσϧⓒ 2016 Information Processing Society of JapanΔࢧԉΛड͚ͯߦΘΕͨɽ

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Vol.2016-MUS-112 No.7
2016/7/30

৘ใॲཧֶձ‫ڀݚ‬ใࠂ
IPSJ SIG Technical Reportࢀߟจ‫ݙ‬
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