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113 : 1 Copyright c 1 by Kobayashi Keisuke

Desktop Music (DTM) DAW (Digital Audio Workstation) YAMAHA Vocaloid DTM MIDI (Musical Instruments Digital Interface) Lee (Non-negative Matrix Factorization; NMF) NMF K NMF NMF K K 1 NMF (SDR) 3 11 db 3 3

, MIDI 6 8 NMF MIDI NMF MIDI

1 1 1.1................................. 1 1................................... 1 1..1............................ 1 1.............................. 1.3.................................. 1................................... 3.1..................................................................3.............................. 9....................................... 9 3 11 3.1......................... 11 3............................... 11 3..1................................. 1 3.................................... 1 3.3.................................. 1 3.... 1 3................................. 1 3.6...................................... 16 17.1 K................................ 17.1.1................................. 17.1.................................. 17.1.3..................................................................... 3..1................................. 3 i

................................... 31..3............................. 31.3...................................... 39.1....................................... 3.3......................... 6.3.1.................. 6.3.......................... 6.3.3................................................................. 1 6 3 6.1................................. 3 6.................................... 3 8 8 16 ii

.1.................................................................3......................... 6........................ 6............................... 7.6.............. 8.7 B n.................. 1 3.1........................... 11 3.................... 13 3.3 NMF........... 1.1 1......................... 19. 8..........................3 96......................... 1. SDR............................... K = 1 (RWC1)........................6 K = (RWC1)....................... 6.7 K = 3 (RWC1)....................... 7.8 K = (RWC1)....................... 8.9 K = (RWC1)....................... 9.1 NMF....................... 3.11......................... 33.1....................... 33.13 (GP)...................... 3.1 (RWC3).................... 3.1 NMF (UP1)........... 36.16 NMF (UP)........... 37.17 NMF (MAPS)......... 38.1............. 1.......... iii

.3........................................ 7.6....... 8.7......................... 9.8 (UP3)................... 1 1 YAMAHA GRAND C3............................. 6 GP1............................... 6 3 GP............................... 6....................... 63 K = 1 (MIDI)....................... 66 6 K = (MIDI)....................... 67 7 K = 3 (MIDI)....................... 68 8 K = (MIDI)....................... 69 9 K = (MIDI)....................... 7 1 K = 1 (UP1)........................ 71 11 K = (UP1)........................ 7 1 K = 3 (UP1)........................ 73 13 K = (UP1)........................ 7 1 K = (UP1)........................ 7 1 K = 1 (UP)........................ 76 16 K = (UP)........................ 77 17 K = 3 (UP)........................ 78 18 K = (UP)........................ 79 19 K = (UP)........................ 8 K = 1 (UP3)........................ 81 1 K = (UP3)........................ 8 K = 3 (UP3)........................ 83 3 K = (UP3)........................ 8 K = (UP3)........................ 8 K = 1 (UP)........................ 86 6 K = (UP)........................ 87 7 K = 3 (UP)........................ 88 8 K = (UP)........................ 89 9 K = (UP)........................ 9 3 K = 1 (MAPS)....................... 91 31 K = (MAPS)....................... 9 3 K = 3 (MAPS)....................... 93 iv

33 K = (MAPS)....................... 9 3 K = (MAPS)....................... 9 3 K = 1 (GP1)........................ 96 36 K = (GP1)........................ 97 37 K = 3 (GP1)........................ 98 38 K = (GP1)........................ 99 39 K = (GP1)........................ 1 K = 1 (GP)........................ 11 1 K = (GP)........................ 1 K = 3 (GP)........................ 13 3 K = (GP)........................ 1 K = (GP)........................ 1 K = 1 (RWC1)....................... 16 6 K = (RWC1)....................... 17 7 K = 3 (RWC1)....................... 18 8 K = (RWC1)....................... 19 9 K = (RWC1)....................... 11 K = 1 (RWC3)....................... 111 1 K = (RWC3)....................... 11 K = 3 (RWC3)....................... 113 3 K = (RWC3)....................... 11 K = (RWC3)....................... 11 NMF (UP1)........... 117 6 NMF (UP)........... 118 7 NMF (UP3)........... 119 8 NMF (UP)........... 1 9 NMF (MAPS)......... 11 6 NMF (GP1)........... 1 61 NMF (GP)........... 13 6 NMF (RWC1).......... 1 63 NMF (RWC3).......... 1 v

.1 K = 3 K =........... K = 3 K =.......... 3.1........................ 3....................... 3.3........................ 1.................................. 61.................................. 6 3 GP1............................ 6 GP............................ 6.................. 6 vi

1 1.1 Desktop Music (DTM) DAW (Didital Audio Workstation) Vocaloid [1]. DTM MIDI (Musical Instruments Digital Interface) 1. 1..1 1

1.. [ 7]. [8] [9] [1] Lee et al. [11] 1.3 (Non-negative Matrix Factorization; NMF) [1] NMF [9, 13 16] NMF K K R(R < K) R K R K R [17] [18]

1. 6 ( ) 3 NMF 3 6 3

.1.1 7 cm 1 cm. 1.3,. [19]... (1). () (3). () []

.1:.:

.3:.: 6

.: (1) () ( ) []. [] Fletcher [7].6 7

8.6:

.3 3 3 ( ) F n (n ) f n (.1) [7,1] f n = nf 1 + Bn (.1) F (.) (.1) f 1 F = 1 T L µ (.) L T µ ( ) B (.3) B = π3 Ed 6T L (.3) E d, T, L B [1, 1 ] []. B.7 1. (1), () (3) () 9

6 Frequency of n th harmonic component B=1.*1 3 B=.*1 B=1.*1 frequency [Hz] 6 8 1 1 1 16 18 n.7: B n 1

3. 3.1 3.1 NMF NMF 3. NMF Y ( R Ω T ) U( R Ω K ) V ( R K T ) (3.1) Y ω,t Ŷω,t = K U ω,k V k,t (3.1) k Ω T K NMF ω, t NMF ( ) Y U U V U NMF pre-emphasis FFT Log Scaling 3.1: 11

3..1 NMF Y U, V U, V ( (3.)) KL ( (3.3)) ( (3.)) [3, ] D euc (x y) = (x y) (3.) D KL (x y) = (x y) + y log y x (3.3) D IS (x y) = y x log y x 1 (3.) 3. 3.. U, V (3.6) U U. Y V t UV V t (3.) V V. U t Y U t UV (3.6) t. [, 6] D Euc (Y UV ) = Y UV F = ω,t Y ω,t k U ω,k V k,t = ω,t ( Y ω,t Y ω,t k U ω,k V k,t + k U ω,k V k,t ) (3.7) 3 Jensen Jensen f(x i ) f( i λ i x i ) i λ i f(x i ) (3.8) 1

D(y x) : Degree of proximity between x and y 1 9 Euc KL IS 8 7 D( x) 6 3 1 6 8 1 1 1 16 18 x 3.: (3.9) ( i x i ) = ( λ i x i λ i ) i λ i ( x i λ i ) = i x i λ i (3.9) 3 Jensen k U ω,k V k,t k U ω,k V k,t λ k,ω,t (3.1) (3.7) (3.11) D Euc (Y UV ) = ω,t ( Y ω,t Y ω,t k U ω,k V k,t + k U ω,k V k,t λ k,ω,t ) (3.11) 13

(3.11) U ω,k V k,t U ω,k = V ω,k = t Y ω,tv k,t t (3.1) Vk,t λ k,ω,t t Y ω,tu k,t t (3.13) Uk,t λ k,ω,t λ λ i 1 (3.1) λ k,ω,t = U ω,k V k,t k U ω,k V k,t (3.1) (3.13) (3.1) (3.16) t U ω,k = Y ω,tv k,t t V (3.1) k,t k U ω,k V k,t t V ω,k = Y ω,tu k,t t U (3.16) k,t k U ω,k V k,t U, V NMF 3.3 3.3 6.6 db/oct (3.17) H(z) = 1.97z 1 (3.17) 3. NMF Y 1

1 1. x 1 3 1 1. x 1 3 1 1. x 1 3 3.3: NMF NMF X A, B, C,... (3.18) X = A + B + C +... + N (3.18) (3.19) X = log A + log B + log C +... + log N = log(a B C D) (3.19) 3. NMF 1

3.6 NMF 16

.1 K.1.1 NMF NMF K K NMF [7, 8] 1 NMF K 1.1. RWC : ( RWC-DB ) [9], MIDI Aligned Piano Sound ( MAPS-DB ) [3] 1 RWC-DB 3 MAPS-DB RWC-DB RWC1 RWC3 MAPS-DB MAPS GP1 GP, UP1, UP, UP3, UP A3 ( Hz) 16,.1 khz (Short Time Fourie Transform; STFT) 8 ( ms) 18 ( 3 ms) 17

8.1.3 NMF.1 1. 8.3 96 1 8 96 96 8 96 3 8 96 8 STFT 18

6 8 1 x 1 3 6 8 1 x 1 3 Activation Matrix 6 8 1 x 1 3. 1 1...1: 1 19

. 1 1. x 1 3. 1 1. x 1 3 x 1 Activation Matrix 6 x 1 6 x 1 6. 1 1. x 1 3. 1 1...: 8

6 8 1 1 x 1 6 8 1 1 x 1 x 1 1 Activation Matrix 1 x 1 1 1 x 1 1 1 6 8 1 1 x 1. 1 1...3: 96 1

.1: K = 3 K = 1st (K=) nd (K=) 3rd (K=) th (K=) 1st (K=3).89.6 -.66.1 nd (K=3) -...7 -.33 3rd (K=3).3 -.9 -.1.98.1.3..9 ( ) K = 1 (.) K = (.6), 1 khz 1 K = 3 (.7) 3 1 3 K = 1, (1) () (3), () 1 () (Hz) K = (.8) K = 3 K = 1.1 K = 1 K = 3 1 K = (.9) 1 3 1 K = 3 1 3 K = 3 K = 3 3 (. )

.: K = 3 K = 1st(K=) nd (K=) 3rd (K=) th (K=) th (K=) 1st (K=3).78.1.38 -.77.3 nd (K=3) -..8.7. -. 3rd (K=3).6 -.3 -.9.1.96 3 K U V Ŷ Y (Signal to distortionratio;sdr) (.) S SDR = 1 log 1 db (.1) S Ŝ (S, Ŝ ) SDR. SDR K = 3 SDR K = SDR 11 db K 3 K SDR SDR K 3 3

Relationship between number of bases and SDR 1 1 Mean of SDR [db] 8 6 1 3 K : Number of bases.: SDR

x 1 Activation Matrix 9 8. 8 7. 7 6. 6.9 1 1.1 1. 1.3 1. 1. 1.6 1.7 x 1 3. 1 1...: K = 1 (RWC1)

.8 1 1. 1. 1.6 1.8 x 1 3 8 Activation Matrix x 1 6 x 1 8 6.8 1 1. 1. 1.6 1.8 x 1 3. 1 1...6: K = (RWC1) 6

1 3 x 1 3 Activation Matrix x 1 6 x 1 6 x 1 6 1 3 x 1 3 1 3 x 1 3. 1 1...7: K = 3 (RWC1) 7

1 x 1 3 1 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3. 1 1...8: K = (RWC1) 8

x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 3 1 3 x x 3 x 1 x 1 3. 1 1...9: K = (RWC1) 9

.1: NMF...1, 3 3 1 3 K = 3 NMF NMF (.1 U fix ) (.1 V fix ) (.1 U free ) NMF (U fix ) (V free ) NMF 3

.. 3 3 NMF K 6..3.11.1.11 1.1 khz khz.11.1.11 1 khz, khz.1 khz Hz,.13,.1.1,.16,.17,.13,.1 1 3.11..1,.16,.17 1 3.1 ( 6 ) 3 ( 1 3 ) ( 3 khz) (1 khz ) 31

3 6 3 6 3

. 1 1. x 1 3. 1 1. x 1 3. 1 1. x 1 3.11: 1 1 1 1 1 1 x 1 x 1 x 1.1: 33

1 x 1 3 1 x 1 3 1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 x 1 3 1 x 1 3 x 1 3 1. 1 1.. 3.13: (GP) 3

1 x 1 3 1 x 1 3 1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 x 1 3 1 x 1 3 x 1 3 1. 1 1...1: (RWC3) 3

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3 1 1 1 x 1 3 x 1 3 x 1 3. 1 1.. 3.1: NMF (UP1) 36

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 3 1 3 1 3 1x 1 1x 3 1x 3 1 x 1 x 1 3. 1 1.. 3.16: NMF (UP) 37

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 3 1 3 1 3 1x 1 1x 3 1x 3 1 x 1 x 1 3. 1 1...17: NMF (MAPS) 38

6.3 NMF NMF 39

.1.11 khz GP1 (.1) RWC3 (.1(d)) GP (.1) 1,,,, 6, 7 khz khz RWC1 (.1(c)) 1, 3 khz.13. 1. K = 3 3 6 3 6.. 6 6.1 RWC3 (.1) GP (.13)

1. x 1 3 th activation vector 1 Amplitude [deg].8.6.. Frequency [Hz] 1.8 x 1 3 th activation vector 1.6 1. Amplitude [deg] 1. 1.8.6.. Frequency [Hz] 3. x 1 3 th activation vector 3 Amplitude [deg]. 1. 1. Frequency [Hz] (c) 1. x 1 3 th activation vector 1 Amplitude [deg].8.6.. Frequency [Hz] (d).1: 1

7 x 1 3rd activation vector 6 Amplitude [deg] 3 1. 1 1.. Time [sec] 8 x 1 6th activation vector 7 Amplitude [deg] 6 3 1. 1 1.. Time [sec].:

.1: GP1 GP RWC1 RWC3 (deg/sec).3 1 1.1 1 1.97 1 3.6 1.: UP1 UP UP3 UP MAPS (deg/sec) 1.1 1 1.9 1 1.19 1 1.31 1 1.3 1..3.3 UP1.3 UP,.3(c) MAPS UP1 UP. khz MAPS khz 1. khz.. sec 3 6 6.. ( ).,(c),(e) UP1, UP,MAPS.(d)(f) UP1, UP,MAPS MAPS 6 UP1 (.) UP(.(c)) MAPS(.(e)) Hz 3

1.8 x 1 3 th activation vector 1.6 1. Amplitude [deg] 1. 1.8.6.. Frequency [Hz] 1. x 1 3 th activation vector Amplitude [deg] 1. Frequency [Hz] 1.8 x 1 3 th activation vector 1.6 1. Amplitude [deg] 1. 1.8.6.. Frequency [Hz] (c).3:

th basis vector. x 1 th activation vector Frequency [Hz] Amplitude [deg] 3. 3. 1. 1...6.8 1 1. 1. 1.6 Amplitude [deg] x 1 3. 1 1.. 3 Time[sec] th basis vector 3. x 1 th activation vector 3 Frequency [Hz] Amplitude [deg]. 1. 1....6.8 1 1. 1. 1.6 1.8 Amplitude [deg] (c) x 1 3. 1 1.. 3 Time[sec] (d) th basis vector x 1 th activation vector. Frequency [Hz] Amplitude [deg] 3. 3. 1. 1..6.7.8.9 1 1.1 1. 1.3 1. 1. 1.6 Amplitude [deg] (e) x 1 3. 1 1.. Time[sec] (f).:

.3 MIDI.3.1. (c) MIDI.(c) MIDI. sec MIDI.8 sec MIDI.6 (b ). sec.6 sec.3..7 (c) MIDI 1. 1.6 MIDI 1.3 6

8 x 1 3rd activation vector 7 Amplitude [deg] 6 3 1. 1 1.. Time [sec] 9 x 1 3rd activation vector 8 7 Amplitude [deg] 6 3 1. 1 1.. 3 Time[sec] 7 x 1 3rd activation vector 6 Amplitude [deg] 3 1. 1 1.. 3 Time [sec] (c).: 7

7 x 1 3rd activation vector 6 Amplitude [deg] 3 1. 1 1.. Time[sec] x 1 3rd activation vector 3. Amplitude [deg] 3. 1. 1.. 1 1.. 3 Time[sec].6: 8

3 x 1 3 1st basis vectors. Amplitude [deg] 1. 1. Frequency [Hz] 3 x 1 3 1st basis vectors. Amplitude [deg] 1. 1. Frequency [Hz]. x 1 3 1st basis vectors. Amplitude [deg] 1.8 1.6 1. 1. 1.8.6. Frequency [Hz] (c).7: 9

.3: GRAND UPRIGHT MIDI GRAND.77.63.73 UPRIGHT.78.67 MIDI 1. 7 1 8 1 [] 7, 8 8 8 1 6 6 1 MIDI,, 7 MIDI.3.77.63 MIDI MIDI MIDI MIDI.3.3 khz khz.8

1 1.. x 1 3 1 1.. x 1 3 1 1.. x 1 3.8: (UP3) khz. khz MIDI 1

MIDI khz

6 6.1 NMF NMF 3 + NMF MIDI MIDI khz 6. ( ) NMF MIDI NMF 3

MIDI

Mr. Elbarougy, Mr.Chau, Mr.Ngo

[1]. : ( )., Vol. 67, No. 1, pp. 6, 1. [],.., Vol. 9, No. 3, pp. 178 183, 1993. [3].., Vol., No. 1-, pp. 1 1, 7. [],. :.. SP,, Vol. 99, No. 66, pp. 1 6,. [],... [ ], Vol., No. 1, pp. 7 1,. [6],,.., 13. [7] N.H. Fletcher and T.D.Rossing. The Physics of Musical Instruments second edition, chapter 1, pp. 3 398. springer, 1998. [8],. :.. D-II,, II-, Vol. 81, No. 7, pp. 11 117, 1998. [9],,,,,. gmm midi (,,, )., Vol. 7, No., pp. 183 18, 1. [1],,,.., Vol. 3, No. 1, pp. 83 8, mar 3. [11] C.T.Lee, Y.H.Yang, and H.H.Chen. Multipitch estimation of piano music by exemplar-based sparse representation. Multimedia,IEEE transactions on, Vol. 1, No. 3, pp. 68 618, 1. 6

[1] D. D. Lee and H. S. Seung. Learning the parts of objects by non-negative matrix factorization. Nature, Vol. 1, pp. 788 791, 1999. [13] P.Smaragdis and J.C.Brown. Non-negative matrix factorization for polyphonic music. IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, pp. 19, 3. [1],,,,. nmf., No., pp. 163 16, 7. [1] F.Rigaud, A.Falaize, B.David, and L.Daudet. Does inharmonicity improve an nmfbased piano transcription model? Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 11 1, 13. [16],,,,,,. gmm nmf., Vol., No. 1, pp. 3839 38, 11. [17],,. :., Vol. 3, No.,. [18],. ( ( ), 13)., Vol. 37, No. 17, pp. 6 68, 13. [19].. http://jp.yamaha.com/ products/musical-instruments/keyboards/about/gp/#upgp. [] W.Goebl, R.Bresin, and A.Galembo. Once again: The perception of piano touch and tone: Can touch audibly change piano sound independently of intensity? Proceedings of the International Symposium on Musical Acoustics,, pp. 33 33,. [1] F.Rigaud, B.David, and L.Daudet. A parametric model of piano tuning. Proc. of the 1th International Conference on Difital Audio Effects, pp. 393 399, 11. [] F.Rigaud, A.Falaize, B.David, and L.Daudet. Does inharmonicity improve an nmfbased piano transcription model? ICASSP, 13. [3] A.Lefévre, F. Bach, and C.Févotte. Online algorithms for nonnegative matrix factorization with the itakura-saito divergence. In Proc. IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), Mohonk, NY, Oct. 11. 7

[] C.Févotte. Majorization-minimization algorithm for smooth itakura-saito nonnegative matrix factorization. In Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, May 11. []. nmf /., Vol. 9, No. 9, pp. 89 833, 1. [6]. :.. [ ], Vol. 11, No., p. 1, 11. [7],,,,,... [ ], Vol. 11, No. 6, pp. 1 8, jul 11. [8],.. MUS, Vol. 1-MUS-96, No. 8, pp. 1 8, 1. [9],,,. Rwc :., Vol. 3, No. 1, pp. 83 8, mar 3. [3] V.Emiya, R.Badeau, and B.David. Multipitch estimation of piano sounds using a new probabilistic spectral smoothness principle. IEEE Transactions on Audio, Speech and Language Processing, No. 18, pp. 163 16, 1. 8

1,7 1 3 1 1.m 1 PC ( I/F) 6 RWC-DB GP1 GP1 YAMAHA GRAND C3( 1) 1cm, 18cm 3 9

図 1: YAMAHA GRAND C3 (c) (d) 図 : GP1 のマイク設置 6

1: PC OS CPU DELL precision M6 windows 7 (3-bit) intel core i7 MATLAB13a Roland OCTA-CAPTURE Audio-Technica AT8Ra (1,,, ch) RAMSA WM-C7 (3 ch) SENNHEISER HDA GP GP YAMAHA GRAND S6A 11cm, 1cm 3 MAPS-DB UP1,UP,UP UP1,, YAMAHA YU3SZ 1 cm, 19cm, 6 cm UP3 UP3 KAWAI K8 YAMAHA 61

: [sec] 1 A3( Hz) m 3 P1 A3 f 3 P1 3 A3 p 3 P1 A3 m 3 P1 A( Hz) m 3 P1 6 A3 m 3 P 7 A f 3 P1 8 A p 3 P1 9 A3 m 3 P 1 A3 m 3 P 11 A3 m 3 P3 1 A3 m 3 P3 1 A3 p 3 P 1 A3 p 3 P3 3: GP1 Ch [cm] 1 7 cm 9 cm 8 18 cm 9 cm 3 7 cm 1 cm 8 1 cm MIDI 9 UP1 1 1 UP 1 19 UP3 UP 9 MAPS 3 3 GP1 3 39 GP1 RWC1 9 RWC3 K = 1 6

: GP Ch 1 7. cm 1 cm 8 cm 113 cm 1 cm cm 3 7. cm 11 cm 8 cm 1 cm : Ch 1 7 cm 1 cm 19 cm 7 cm 1 cm 179 cm 3 8 cm 1 cm 19 cm 1cm 1 cm 6

x 1 Activation Matrix 7.6 7. 7. 7 6.8 6.6 6. 6. 6.8.9 1 1.1 1. 1.3 1. 1. 1.6 1.7 1.8 1.9 x 1 3. 1 1.. 3 : K = 1 (MIDI) 66

1 1. x 1 3 7 Activation Matrix x 1 6 3 1 x 1 7 6 3 1 1 1. x 1 3. 1 1.. 3 6: K = (MIDI) 67

. 1 1. x 1 3 Activation Matrix x 1 6 x 1 6 x 1 6. 1 1.. 1 1. x 1 3 x 1 3. 1 1.. 3 7: K = 3 (MIDI) 68

1 1.. x 1 3 1 1.. x 1 3 Activation Matrix x 1 x 1 x 1 x 1 1 1.. x 1 3 x 1 3 1 1... 1 1.. 3 8: K = (MIDI) 69

1 x 1 3 1 x 1 3 1 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 x 1 3 1 x 1 3. 1 1.. 3 9: K = (MIDI) 7

x 1 Activation Matrix 8. 8 7. 7 6..9 1 1.1 1. 1.3 1. 1. 1.6 x 1 3. 1 1.. 3 1: K = 1 (UP1) 71

1 1. x 1 3 8 x 1 Activation Matrix 6 8 x 1 6 1 1. x 1 3. 1 1.. 3 11: K = (UP1) 7

. 1 1.. x 1 3 6 Activation Matrix x 1 x 1 6 x 1 6. 1 1.. x 1 3. 1 1.. x 1 3. 1 1.. 3 1: K = 3 (UP1) 73

1 x 1 3 1 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3. 1 1.. 3 13: K = (UP1) 7

1 x 1 3 1 1 x 1 3 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3. 1 1.. 3 1: K = (UP1) 7

x 1 Activation Matrix 7. 7 6.8 6.6 6. 6. 6.8.6.9 1 1.1 1. 1.3 1. 1. 1.6 x 1 3. 1 1.. 3 1: K = 1 (UP) 76

1 1. x 1 3 Activation Matrix x 1 6 3 1 x 1 6 3 1 1 1. x 1 3. 1 1.. 3 16: K = (UP) 77

1 1. x 1 3 Activation Matrix x 1 x 1 x 1 1 1. 1 1. x 1 3 x 1 3. 1 1.. 3 17: K = 3 (UP) 78

. 1 1. x 1 3. 1 1. x 1 3 Activation Matrix x 1 x 1 x 1 x 1. 1 1.. 1 1. x 1 3 x 1 3. 1 1.. 3 18: K = (UP) 79

. 1 1.. x 1 3. 1 1.. x 1 3. 1 1.. x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1. 1 1.. x 1 3. 1 1.. x 1 3. 1 1.. 3 19: K = (UP) 8

x 1 Activation Matrix 9. 9 8. 8 7..9 1 1.1 1. 1.3 1. 1. x 1 3. 1 1.. 3 : K = 1 (UP3) 81

.8 1 1. 1. 1.6 1.8 x 1 3 Activation Matrix x 1 8 6 x 1 8 6.8 1 1. 1. 1.6 1.8 x 1 3. 1 1.. 3 1: K = (UP3) 8

1 1.. x 1 3 8 x 1 Activation Matrix 6 8 x 1 6 8 x 1 6 1 1.. x 1 3 1 1.. x 1 3. 1 1.. 3 : K = 3 (UP3) 83

1 x 1 3 1 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3. 1 1.. 3 3: K = (UP3) 8

x 1 3 x 1 3 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1 x 1 3 x 1 3. 1 1.. 3 : K = (UP3) 8

x 1 Activation Matrix 9 8. 8 7. 7.9 1 1.1 1. 1.3 1. 1. x 1 3. 1 1.. 3 : K = 1 (UP) 86

.8 1 1. 1. 1.6 1.8 x 1 3 8 Activation Matrix x 1 6 x 1 8 6.8 1 1. 1. 1.6 1.8 x 1 3. 1 1.. 3 6: K = (UP) 87

1 x 1 3 6 Activation Matrix x 1 x 1 6 x 1 6 1 1 x 1 3 x 1 3. 1 1.. 3 7: K = 3 (UP) 88

1 x 1 3 1 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 1 3 1 x 1 x 1 3. 1 1.. 3 8: K = (UP) 89

. 1 1.. x 1 3. 1 1... 1 1.. x 1 3 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1. 1 1... 1 1.. x 1 3 x 1 3. 1 1.. 3 9: K = (UP) 9

x 1 Activation Matrix 7. 7 6.8 6.6 6. 6. 6.8.6.9 1 1.1 1. 1.3 1. 1. 1.6 1.7 x 1 3. 1 1.. 3: K = 1 (MAPS) 91

1 1. x 1 3 6 Activation Matrix x 1 3 1 x 1 6 3 1 1 1. x 1 3. 1 1.. 31: K = (MAPS) 9

1 1. x 1 3 Activation Matrix x 1 x 1 x 1 1 1. 1 1. x 1 3 x 1 3. 1 1.. 3: K = 3 (MAPS) 93

1 x 1 3 1 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3. 1 1.. 33: K = (MAPS) 9

1 3 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 3 1 3 1 3 x 1 3 x 1 3 x 1 3 1 3 x 1 3. 1 1.. 3: K = (MAPS) 9

x 1 Activation Matrix 7. 7. 7 6.8 6.6 6. 6. 6.9 1 1.1 1. 1.3 1. 1. 1.6 1.7 x 1 3. 1 1.. 3 3: K = 1 (GP1) 96

1 1. x 1 3 7 Activation Matrix x 1 6 3 1 x 1 7 6 3 1 1 1. x 1 3. 1 1.. 3 36: K = (GP1) 97

1 1. x 1 3 6 Activation Matrix x 1 x 1 6 x 1 6 1 1. 1 1. x 1 3 x 1 3. 1 1.. 3 37: K = 3 (GP1) 98

1 1. x 1 3 1 1. x 1 3 Activation Matrix x 1 x 1 x 1 x 1 1 1. 1 1. x 1 3 x 1 3. 1 1.. 3 38: K = (GP1) 99

1 x 1 3 1 x 1 3 1 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3. 1 1.. 3 39: K = (GP1) 1

x 1 1. Activation Matrix 1 9. 9 8..9 1 1.1 1. 1.3 1. 1. x 1 3. 1 1.. 3 : K = 1 (GP) 11

.8 1 1. 1. 1.6 1.8 x 1 3 Activation Matrix x 1 8 6 x 1 8 6.8 1 1. 1. 1.6 1.8 x 1 3. 1 1.. 3 1: K = (GP) 1

. 1 1. x 1 3 8 Activation Matrix x 1 6 x 1 8 6 x 1 8 6. 1 1.. 1 1. x 1 3 x 1 3. 1 1.. 3 : K = 3 (GP) 13

1 x 1 3 1 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3. 1 1.. 3 3: K = (GP) 1

. 1 1. x 1 3. 1 1.. 1 1. x 1 3 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1. 1 1.. 1 1. x 1 3 x 1 3. 1 1.. 3 : K = (GP) 1

x 1 Activation Matrix 9 8. 8 7. 7 6. 6.9 1 1.1 1. 1.3 1. 1. 1.6 1.7 x 1 3. 1 1.. : K = 1 (RWC1) 16

.8 1 1. 1. 1.6 1.8 x 1 3 8 Activation Matrix x 1 6 x 1 8 6.8 1 1. 1. 1.6 1.8 x 1 3. 1 1.. 6: K = (RWC1) 17

1 3 x 1 3 Activation Matrix x 1 6 x 1 6 x 1 6 1 3 x 1 3 1 3 x 1 3. 1 1.. 7: K = 3 (RWC1) 18

1 x 1 3 1 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3. 1 1.. 8: K = (RWC1) 19

x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 3 1 3 x x 3 x 1 x 1 3. 1 1.. 9: K = (RWC1) 11

8.6 x 1 Activation Matrix 8. 8. 8 7.8 7.6 7. 7. 7 6.8.9 1 1.1 1. 1.3 1. 1. 1.6 x 1 3. 1 1.. : K = 1 (RWC3) 111

.8 1 1. 1. 1.6 1.8 x 1 3 8 Activation Matrix x 1 6 x 1 8 6.8 1 1. 1. 1.6 1.8 x 1 3. 1 1.. 1: K = (RWC3) 11

1 1.. x 1 3 Activation Matrix x 1 6 x 1 6 x 1 6 1 1.. 1 1.. x 1 3 x 1 3. 1 1.. : K = 3 (RWC3) 113

. 1 1.. x 1 3. 1 1.. x 1 3 Activation Matrix x 1 x 1 x 1 x 1. 1 1... 1 1.. x 1 3 x 1 3. 1 1.. 3: K = (RWC3) 11

1 x 1 3 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 1 1 1 x 1 3 x 1 3 x 1 3 x 1 3. 1 1.. : K = (RWC3) 11

UP1 UP 6 UP3 7 UP 8 MAPS 9 GP1 6 GP 61 RWC1 6 RWC3 63 116

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3 1 1 1 x 1 3 x 1 3 x 1 3. 1 1.. 3 : NMF (UP1) 117

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 3 1 3 1 3 1x 1 1x 3 1x 3 1 x 1 x 1 3. 1 1.. 3 6: NMF (UP) 118

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3 1 x 1 3 1 x 1 3 1 x 1 3. 1 1.. 3 7: NMF (UP3) 119

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 1 x 1 3 x 1 3 1 1 1 x 1 3 x 1 3 x 1 3. 1 1.. 3 8: NMF (UP) 1

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 3 1 3 1 3 1x 1 1x 3 1x 3 1 x 1 x 1 3. 1 1.. 9: NMF (MAPS) 11

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 x 1 3 1 x 1 3 1 x 1 3 1 x 1 3 x 1 3 1. 1 1.. 3 6: NMF (GP1) 1

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 x 1 3 1 x 1 3 1 x 1 3 1 x 1 3 x 1 3 1. 1 1.. 3 61: NMF (GP) 13

x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 x 1 3 x 1 3 x 1 3 x 1 3 x 1 3. 1 1.. 6: NMF (RWC1) 1

1 x 1 3 x 1 Activation Matrix x 1 x 1 x 1 x 1 x 1 1 x 1 3 1 x 1 3 1 x 1 3 1 x 1 3 x 1 3 1. 1 1.. 63: NMF (RWC3) 1

Kobayashi,K.,Morikawa,D.,Akagi,M., Study on Analyzing Individuality of Piano Sounds Using Non-negative Matrix Factorization, The 6th seminar of A3 foresight program, February 1. Kobayashi,K.,Morikawa,D.,Akagi,M., Study on Analyzing Individuality of Instrurment Sounds Using Non-negative Matrix Factorization, Proc. 1 RISP International Workshop on Nonliner Circuits, Communications and Signal Processing, 33 36, March 1., in, December13., 1,March 1. 16

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