Simple Violet

Generative model in nonnegative matrix factorization and its application to multichannel sound source separationDaichi KitamuraPh.D. StudentDepartment of InformaticsSchool of Multidisciplinary SciencesThe Graduate University for Advanced Studies (SOKENDAI)

20151124

1

2

3

: Daichi Kitamura: 2519903112:

:

4

16 ~ 22, 22 ~ 24, 24 ~ 27

4

5

Kagawa

5

6

Nara

NAIST

6

7

Tokyo

14F

7

NAIST

nonnegative matrix factorization: NMF8

8

9

-

TimeFrequency

22

10

10

NMF2001NMF11

11

[Lee, et al., 1999]

Amplitude

Amplitude()()()Time

TimeFrequency

Frequency

12

(nonnegative matrix factorization: NMF)

12

13 etc. ()

13

14

(, convex cone)

(, convex cone):

NMF

332 [D. Donoho, et al., 2003]

14

15

NMF16

[Lee, et al., 2001]

16

NMF

KL

IS

NMF: KLIS: IS-divergence=0IS=1KL=2EUC17

17

18

18

NMFEUC: =2

19

19

: KL=1 [A. T. Cemgil, 2009]

NMFKL20

20

: =0

NMFIS21

21

NMFBregmanNMF [I. S. Dhillon, et al., 2005] NMFIS-NMF22

22

NMF [C. Fvotte, et al., 2009]NMF111

NMF

23

23

STFT

NMF [C. Fvotte, et al., 2009]24

0

ImaginaryReal

24

NMF [C. Fvotte, et al., 2009]25

Frequency binTime frame

: 0

25

ISNMFNMFNMF [C. Fvotte, et al., 2009]26

NMF

26

ISNMFKLNMFEx. [D. FitzGerald, et al., 2009], [D. Kitamura, et al., 2014]ISNMFNMF201510WASPAA2015Cauchy NMF [A. Liutkus, et al., 2015]NMF27

27

Cauchy NMF [A. Liutkus, et al., 2015] [A. Liutkus, et al., 2015] NMF

28

0

28

NMFCauchy NMF [A. Liutkus, et al., 2015]29

29

ISNMFKL

heavy-taildenoisingCauchy NMF [A. Liutkus, et al., 2015]30

30

NMFNMF ISNMFNMFNMF31

32

blind source separation: BSS

BSSICA[Comon, 1994]IVA[Hiroe, 2006], [Kim, 2006]BSS33

State-of-the-art

BSS

33

IVA [Hiroe, 2006], [Kim, 2006]

NMF34

12

1

1FrequencyTime

34

NMF [Ozerov, 2010], [Sawada, 2013]

35/21

TimeFrequency

TimeFrequency

TimeFrequency

TimeFrequency

TimeFrequency

35

NMF [Ozerov, 2010], [Sawada, 2013]NMF

log-det div.

36

36

1NMFNMFNMFNMFNMF

37

IVA

NMF

NMF

11

1NMF

37

111

1

38

2x211

2

38

1111

39

: :

39

NMF1

40

1. 1 2. 3.

NMFIVA

NMFIVA

40

41

IVA

NMFNMF

41

42 SiSECRWCP 22 IVA, NMF1NMFFFT 512 ms 128 ms (1/4) 130 SDR

2 m

1

5.66 cm50

50

2E2A: 300 ms

42

: ultimate nz tour, guitar and synth.43

Proposed methodMultichannel NMFIVA

Source 1

Source 210

IVA

7.8 s3011.8 s30598.5 s250

: 19.7 s (16kHz)

43

44

NMFNMFISNMFNMFISNMFNMF 1NMF

45

45

1/3NMFD. D. Lee, H. S. Seung, Learning the parts of objects by nonnegative matrix factorization, Nature, vol.401, pp.788791, 1999.D. D. Lee, H. S. Seung, Algorithms for non-negative matrix factorization, Proc. Advances in Neural Information Processing Systems, vol.13, pp.556562, 2001.NMFD. Donoho, V. Stodden, When does non-negative matrix factorization give correct decomposition into parts?, MIT Press, 2003.-divergence NMFS. Eguchi, K. Yano, Robustifying maximum likelihood estimation, Technical Report of Institute of Statistical Mathematics, 2001.M. Nakano, H. Kameoka, J. Le Roux, Y. Kitano, N. Ono, S. Sagayama, Convergence-guaranteed multiplicative algorithms for non-negative matrix factorization with beta-divergence, Proc. International Workshop on Machine Learning for Signal Processing, pp.283-288, 2010.KLNMFNMFA. T. Cemgil, Bayesian inference for nonnegative matrix factorization models, Comput. Intell. Neurosci., vol.2009, pp.117, 2009.Bregman-divergence-based NMFI. S. Dhillon, S. Sara, Generalized nonnegative matrix approximations with Bregman divergences, Proc. NIPS 2005, pp. 283-290, 2005.46

46

2/3ISNMFC. Fvotte, N. Bertin, J.-L. Durrieu, Nonnegative matrixfactorization with the Itakura-Saito divergence. With applicationto music analysis, Neural Computation, vol.21, no.3, 2009.KLNMFD. Fitzgerald, M. Cranitch, E. Coyle, On the use of the beta divergence for musical source separation, Proc. Irish Signals Syst. Conf., 2009.D. Kitamura, H. Saruwatari, K. Yagi, K. Shikano, Y. Takahashi, K. Kondo, Music signal separation based on supervised nonnegative matrix factorization with orthogonality and maximum-divergence penalties, IEICE Trans. Fundam. Electron., Commun. Comput. Sci., vol.E97-A, no.5, pp.11131118, 2014.Cauchy NMFA. Liutkus, R. Badeau, Generalized Wiener filtering with fractional power spectrograms, Proc. ICASSP, pp.266270, 2015.A. Liutkus, D. Fitzgerald, Cauchy nonnegative matrix factorization, Proc. WASPAA, 2015.ICAP. Comon, Independent component analysis, a new concept?, Signal Processing, vol.36, no.3, pp.287314, 1994.47

47

3/3IVAT. Kim, T. Eltoft T.-W. Lee, Independent vector analysis: an extension of ICA to multivariate components, Proc. International Conference on Independent Component Analysis and Blind Source Separation, pp.165172, 2006.A. Hiroe, Solution of permutation problem in frequency domain ICA using multivariate probability density functions, Proc. International Conference on Independent Component Analysis and Blind Source Separation, pp.601608, 2006.T. Kim, H. T. Attias, S.-Y. Lee T.-W. Lee, Blind source separation exploiting higher-order frequency dependencies, IEEE Trans. ASLP, vol.15, no.1, pp.7079, 2007.NMFA. Ozerov, C. Fvotte, Multichannel nonnegative matrix factorization in convolutive mixtures for audio source separation, IEEE Trans. ASLP, vol.18, no.3, pp.550563, 2010.H. Sawada, H. Kameoka, S. Araki, N. Ueda, Multichannel extensions of non-negative matrix factorization with complex-valued data, IEEE Trans. ASLP, vol.21, no.5, pp.971982, 2013.1NMFD. Kitamura, N. Ono, H. Sawada, H. Kameoka, H. Saruwatari, Efficient multichannel nonnegative matrix factorization exploiting rank-1 spatial model, Proc. ICASSP, pp.276280, 2015.HP: http://d-kitamura.sakura.ne.jp/index.html-divergence NMFCauchy NMF48

48

IVAresult52null, track 3014159.346MNMFresult52null, track 8515408.488result52null, track 11514787.781mix5null, track 5515451.809IVAresult51null, track 2915593.904MNMFresult51null, track 8415747.32result51null, track 11416583.781