楽譜情報を用いた NMF による音楽音響信号の音源分離 - 奥乃研究室
楽譜情報を用いた NMF による音楽音響信号の音源分離 - 奥乃研究室
楽譜情報を用いた NMF による音楽音響信号の音源分離 - 奥乃研究室
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2N-1<br />
情 報 処 理 学 会 第 69 回 全 国 大 会<br />
<strong>NMF</strong> <br />
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1. <br />
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Hi-Fi <br />
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2 <br />
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Drumix [1] Drumix <br />
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Drumix <br />
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Non-negative Matrix<br />
Factorization (<strong>NMF</strong>) [2] <br />
Drumix <br />
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Drumix <br />
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MIDI <br />
2. <br />
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2.1 Non-negative Matrix Factorization<br />
Non-negative Matrix Factorization (<strong>NMF</strong>) n × m<br />
V V ≃ WH n × r W <br />
r × m H r n, m <br />
W, H V <br />
w l , h l (l =1,...,r) <br />
n, m <br />
W H V WH<br />
Kullback-<br />
Sound source separation for polyphonic musical signal based on <strong>NMF</strong> using<br />
score information: Katsutoshi Itoyama, Kazunori Komatani, Tetsuya<br />
Ogata, and Hiroshi G. Okuno (Kyoto Univ.)<br />
Leiblar Divergence (KLD) W, H <br />
∑<br />
µ<br />
W ia ← W H aµV iµ /(WH) iµ<br />
ia ∑<br />
ν H aν<br />
∑<br />
i<br />
H aµ ← H W iaV iµ /(WH) iµ<br />
aµ ∑<br />
k W ka<br />
V WH KLD <br />
W, H <br />
2.2 Non-negative Tensor Factorization<br />
Non-negative Tensor Factorization (NTF) [3] <br />
<strong>NMF</strong> dn 1 ,n 2 ,...,n d<br />
V 2n 1 ,r W (1) <br />
2n 2 ,r W (2) ... 2n d ,r<br />
W (d) <br />
3 V = (v ijk ) W (1) = (w (1)<br />
ir ),<br />
W (2) =(w (2)<br />
jr ), W (3) =(w (3)<br />
kr ) <strong>NMF</strong><br />
KLD (v ijk ) ( ∑ r w(1) ir w(2) jr w(3) kr ) <br />
W (1) <br />
w (1)<br />
ir<br />
∑j,k ← v ijkw (2)<br />
w(1)<br />
jr w(3) kr /w(1) ir w(2) jr w(3) kr<br />
ir ∑j,k w(2) jr w(3) kr<br />
<strong>NMF</strong> <br />
W (2) ,W (3) <br />
2.3 <strong>NMF</strong>, NTF <br />
t (T 0 ≤ t ≤ T 1 ) f (F 0 ≤ f ≤ F 1 ) <br />
p(f,t) r <br />
<br />
p(f,t) r p 1 (f,t),...,p r (f,t)<br />
<br />
l <br />
<br />
• w l (f)<br />
• h l (t)<br />
f,t <br />
p(f,t) ∑ l w l(f)h l (t) KLD<br />
r (w l (f),h l (t)) <br />
V KLD W, H <br />
<strong>NMF</strong> <br />
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a l (c)<br />
<br />
p(c, f, t) <br />
r (a l (c),w l (f),h l (t)) <br />
<br />
c =1,...,d p(c, f, t) r<br />
(a l (c),w l (f),h l (t)) <br />
NTF <br />
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2-163
1: <br />
2.4 <strong>NMF</strong> <br />
<strong>NMF</strong> NTF <br />
1. W H <br />
2. W <br />
H <br />
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1. <br />
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2. <br />
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MIDI <br />
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<strong>NMF</strong> <br />
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MIDI <br />
1. MIDI MIDI <br />
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2. <br />
<strong>NMF</strong> <br />
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• F0 <br />
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• <br />
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1 <br />
f 0 ,t onset ,t offset F0<br />
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3. <br />
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MIDI <br />
MIDI <br />
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3.1 <br />
“RWC <br />
(RWC-MDB-P-2001)[4]” #001–#010 10 <br />
MIDI MIDI<br />
30 <br />
<br />
2: <br />
3.2 <strong>NMF</strong> <br />
<strong>NMF</strong> <br />
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<strong>NMF</strong> <br />
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2 2 <br />
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#001 10 9 <strong>NMF</strong> <br />
SNR <br />
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SNR <br />
SNR <br />
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<br />
<strong>NMF</strong> <br />
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#001 <br />
SNR <br />
SNR <br />
4. <br />
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<strong>NMF</strong> <br />
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21 COECREST-<br />
Muse <br />
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[1] “Drumix: <br />
” 2006207–208<br />
[2] D. D. Lee et al, “Algorithms for Non-negative Matrix Factorization”,<br />
Advances in Neural Information Porcessing Systems 13: 556–562,<br />
MIT Press, 2001.<br />
[3] D. FitsGerald et al, “Sound Source Separation using Shifted Nonnegative<br />
Tensor Factorization”, ICASSP 2006, 653–656.<br />
[4] “RWC <br />
”Vol. 45No.<br />
3728–7382004
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