. Berry, Algorithms and applications for approximate nonnegative matrix factorization, Speech and Language Processing, pp.155-17350, 2006.
DOI : 10.1016/j.csda.2006.11.006

]. A. Bregman and ]. J. Brown, Auditory Scene Analysis. The perceptual organization of sounds Calculation of a constant q spectral transform, J. Acoust. Soc. Am, vol.89, issue.1, pp.425-434, 1991.

]. J. Brown, Musical fundamental frequency tracking using a pattern recognition method, The Journal of the Acoustical Society of America, vol.92, issue.3, pp.1394-1402, 1992.
DOI : 10.1121/1.403933

]. J. Cardoso and A. T. , Blind signal separation : statistical principles Special issue on blind source separation Bayesian Music Transcription, Proc. IEEE Thèse de doctorat, pp.2009-2025, 1998.

. Cemgil, A generative model for music transcription, IEEE Transactions on Audio, Speech and Language Processing, vol.14, issue.2, pp.679-694, 2006.
DOI : 10.1109/TSA.2005.852985

C. Et-kergomard, ]. A. Chaigne, and J. Kergomard, Acoustique des instruments de musique, Echelles. Belin, 2008.

C. Et-challan, ]. J. Chailley, H. Challan-]-f, and G. Champagne, Théorie de la musique Application de la distance d'édition à la correction de dictées musicales Disponible à l'adresse www Constrained nonnegative matrix factorization method for EEG analysis in early detection of Alzheimer's disease, Proc. of International Conference on Acoustics, Speech and Signal Processing, pp.893-896, 1951.

J. Chien, S. K. Chien, and . Jeng, An automatic transcription system with octave detection, IEEE International Conference on Acoustics Speech and Signal Processing, pp.1865-1868, 2002.
DOI : 10.1109/ICASSP.2002.5744990

]. Choi, Algorithms for orthogonal nonnegative matrix factorization, Proc. of the International Joint Conference on Neural Networks, IJCNN 2008, part of the IEEE World Congress on Computational Intelligence, WCCI 2008, pp.1828-1832, 2008.

. Cichocki, Csisz??r???s Divergences for Non-negative Matrix Factorization: Family of New Algorithms, 6th International Conference on Independent Component Analysis and Blind Signal Separation (ICA'06), pp.32-39, 2006.
DOI : 10.1007/11679363_5

. Cichocki, Nonnegative matrix and tensor factorization, IEEE Signal Processing Magazine, pp.142-145, 2008.
DOI : 10.1002/9780470747278

. Ding, On the equivalence between Non-negative Matrix Factorization and Probabilistic Latent Semantic Indexing, Computational Statistics & Data Analysis, vol.52, issue.8, pp.523913-3927, 2008.
DOI : 10.1016/j.csda.2008.01.011

]. S. Dixon, On the computer recognition of solo piano music, Proc. Australasian Computer Music Conference, pp.31-37, 2000.

D. Et-stodden, ]. D. Donoho, and V. Stodden, When does non-negative matrix factorization give a correct decomposition into parts, Advances in Neural Information Processing Systems, 2003.

R. Doval, X. Doval, and . Rodet, Estimation of fundamental frequency of musical sound signals, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing, pp.3657-3660, 1991.
DOI : 10.1109/ICASSP.1991.151067

. Drakakis, Analysis of financial data using non-negative matrix factorization, International Mathematical Forum, vol.3, pp.37-401853, 2008.

. Duan, Unsupervised Single-Channel Music Source Separation by Average Harmonic Structure Modeling, IEEE Transactions on Audio, Speech, and Language Processing, vol.16, issue.4, pp.766-778, 2008.
DOI : 10.1109/TASL.2008.919073

. Durrieu, Singer melody extraction in polyphonic signals using source separation methods, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.169-172, 2008.
DOI : 10.1109/ICASSP.2008.4517573

E. Et-körner, ]. J. Eggert, and E. Körner, Sparse coding and NMF, IEEE International Joint Conference on Neural Networks, pp.2529-2533, 2004.

. Eguchi, ]. S. Kano, Y. Eguchi, and . Kano, Robustifying maximum likelihood estimation. Rapport Technique, Tokyo Institute of Statistical Mathematics, 2001.

]. V. Emiya, Transcription automatique de la musique de piano, Thèse de doctorat, 2008.
URL : https://hal.archives-ouvertes.fr/pastel-00004867

. Emiya, Multipitch estimation of inharmonic sounds in colored noise, Proc. 10th International Conference on Digital Audio Effects (DAFx), pp.10-15, 2007.

. Emiya, Automatic transcription of piano music based on HMM tracking of jointly-estimated pitches, Proc. Eur. Conf. Sig. Proces. (EUSIPCO), pp.25-29, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00545769

]. M. Feder-et-weinstein, E. Feder, and . Weinstein, Parameter estimation of superimposed signals using the EM algorithm, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.36, issue.4, pp.477-489, 1988.
DOI : 10.1109/29.1552

F. Et-hero, ]. J. Fessler, and A. O. Hero, Space-alternating generalized expectation maximization algorithm, IEEE Transactions on Signal Processing, vol.42, issue.10, pp.2664-2677, 1994.

F. Et-spreij, ]. L. Finesso, and P. Spreij, Approximate nonnegative matrix factorization via alternating minimization, Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems, pp.5-9, 2004.

F. Et-rossing, ]. N. Fletcher, and T. D. Rossing, The Physics of Musical Instruments, 1998.

]. W. Hess, Pitch Determination of Speech Signals, 1983.
DOI : 10.1007/978-3-642-81926-1

]. T. Hofmann, Probabilistic latent semantic analysis, Proc. Uncertainty in Artificial Intelligence, UAI, pp.289-296, 1999.

]. J. Hopke, A guide to positive matrix factorization. Rapport Technique, 2000.

]. P. Hoyer, Non-negative sparse coding, Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing, pp.557-565, 2002.
DOI : 10.1109/NNSP.2002.1030067

]. P. Hoyer, Non-negative matrix factorization with sparseness constraints, Journal of Machine Learning Research, vol.5, pp.1457-1469, 2004.

. Itakura, ]. F. Saito, S. Itakura, and . Saito, Analysis synthesis telephony based on the maximum likelihood method, Proc. 6th International Congress on Acoustics, pp.17-20, 1968.

]. M. Jeter-et-pye, W. C. Jeter, and . Pye, Some nonnegative matrices without nonnegative rank factorizations, Industrial Mathematics, vol.32, pp.37-41, 1982.

J. Et-paatero, ]. S. Junnto, and P. Paatero, Analysis of daily precipitation data by positive matrix factorization, Environmetrics, vol.5, issue.2, pp.127-144, 1994.

]. H. Kameoka, Statistical Approach to Multipitch Analysis, Thèse de doctorat, 2007.

. Kameoka, Harmonic temporal-structured clustering via deterministic annealing em algorithm for audio feature extraction, Proc. International Symposium on Music Information Retrieval (ISMIR), pp.11-15, 2005.

. Kameoka, A Multipitch Analyzer Based on Harmonic Temporal Structured Clustering, Proc. 6 th European Conference on Speech Communication and Technology (EUROSPEECH), pp.982-994, 1999.
DOI : 10.1109/TASL.2006.885248

. Kashino, Application of the Bayesian probability network to music scene analysis. Dans Computational Auditory Scene Analysis, pp.115-137, 1998.

K. Et-choi, ]. M. Kim, and S. Choi, Monaural music source separation : Nonnegativity, sparseness, and shift-invariance, Proc. 6 th International Conference on Independent Component Analysis and Blind Source Separation, pp.617-624, 2006.

. Kim, Determining Patterns in Neural Activity for Reaching Movements Using Nonnegative Matrix Factorization, EURASIP Journal on Advances in Signal Processing, vol.2005, issue.19, pp.20053113-3121, 2005.
DOI : 10.1155/ASP.2005.3113

K. , C. Kim, and S. Choi, A method of initialization for nonnegative matrix factorization, Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, pp.537-540, 2007.

. A. Klapuri and . Klapuri, Means of integrating audio content analysis algorithms, Proc. 110th convention of the audio engineering society (AES), pp.12-15, 2001.

. A. Klapuri and . Klapuri, Multipitch estimation and sound separation by the spectral smoothness principle, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221), pp.3381-3384, 2001.
DOI : 10.1109/ICASSP.2001.940384

]. A. Klapuri, Automatic Music Transcription, Proceedings of the Stockholm Music Acoustics Conference (SMAC), volume II, pp.587-590, 2003.
DOI : 10.1007/978-0-387-30441-0_20

]. A. Klapuri, A perceptually motivated multiple-F0 estimation method, IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 2005., pp.16-19, 2005.
DOI : 10.1109/ASPAA.2005.1540227

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.74.1152

]. A. Klapuri, Multipitch Analysis of Polyphonic Music and Speech Signals Using an Auditory Model, IEEE Transactions on Audio, Speech, and Language Processing, vol.16, issue.2, pp.255-266, 2008.
DOI : 10.1109/TASL.2007.908129

. Klapuri, ]. A. Davy, M. Klapuri, and . Davyklingenberg, Signal Processing Methods for Music Transcription Non-negative matrix factorization : Ill-posedness and a geometric algorithmstar, Pattern Recognition, issue.5, pp.42918-928, 2006.

]. R. Kompass, A Generalized Divergence Measure for Nonnegative Matrix Factorization, Neural Computation, vol.39, issue.3, pp.780-791, 2007.
DOI : 10.1162/089976602320264033

T. W. Kuhn, A. W. Kuhn, and . Tucker, Nonlinear programming, Proc. 2nd Berkeley Symposium, pp.481-492, 1951.

. Laurberg, Theorems on Positive Data: On the Uniqueness of NMF, Computational Intelligence and Neuroscience, vol.5, 2008.
DOI : 10.1109/LSP.2002.800502

L. Et-seung, ]. D. Lee, H. S. Seung-]-d, H. S. Lee, ]. V. Seung et al., Learning the parts of objects by non-negative matrix factorization Algorithms for non-negative matrix factorization IPUS : an architecture for integrated signal processing and signal interpretation in complex environments, Proc. AAAI, pp.788-791556, 1993.

]. P. Leveauleveau, Instrument-Specific Harmonic Atoms for Mid-Level Music Representation, Thèse de doctorat, pp.116-128, 2007.
DOI : 10.1109/TASL.2007.910786

. Li, Learning spatially localized, parts-based representation, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, pp.207-212, 2001.
DOI : 10.1109/CVPR.2001.990477

]. Lin, On the convergence of multiplicative update algorithms for non-negative matrix factorization, IEEE Transactions on Neural Networks, vol.18, issue.6, pp.1589-1596, 2007.

]. Lin, Projected Gradient Methods for Nonnegative Matrix Factorization, Neural Computation, vol.5, issue.10, pp.2756-2779, 2007.
DOI : 10.1007/BF01584660

]. Lin, Nonnegative matrix factorization based on alternating nonnegativity-constrained least squares and the active set method, Lissandre, 1990] M. Lissandre. Maîtriser SADT. Armand Colin, pp.713-730, 1990.

Y. Liu, K. Liu, and . Yuan, Sparse p-norm Nonnegative Matrix Factorization for clustering gene expression data, International Journal of Data Mining and Bioinformatics, vol.2, issue.3, pp.236-249, 2008.
DOI : 10.1504/IJDMB.2008.020524

Z. Liu, Non-negative matrix factorization based methods for object recognition, Pattern Recognition Letters, vol.25, issue.8, pp.893-897, 2004.
DOI : 10.1016/j.patrec.2004.02.002

. Liu, Nonnegative Matrix Factorization for EEG Signal Classification, International Symposium on Neural Networks, volume II, pp.470-475, 2004.
DOI : 10.1007/978-3-540-28648-6_75

]. J. Macqueen, Some methods for classification and analysis of multivariate observations, Proc. of 5th Berkeley Symposium on Mathematical Statistics and Probability, pp.281-297, 1967.

. Mallat, ]. S. Zhang, Z. Mallat, and . Zhang, Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3397-3415, 1993.
DOI : 10.1109/78.258082

]. M. Marolt, Non-negative matrix factorization with selective sparsity constraints for transcription of bell chiming recordings, Proc. of the 6th Sound and Music Computing Conference (SMC), pp.23-25, 2009.

]. K. Martin-martin, Automatic transcription of simple polyphonic music, 3rd Joint Meeting of the Acoustical Societies of America and Japan, pp.23-28, 1996.
DOI : 10.1121/1.416589

]. K. Martin-martin, A blackboard system for automatic transcription of simple polyphonic music, 1996.

H. Meddis, M. J. Meddis, and . Hewitt, Virtual pitch and phase sensitivity of a computer model of the auditory periphery. I: Pitch identification, The Journal of the Acoustical Society of America, vol.89, issue.6, pp.2866-2882, 1991.
DOI : 10.1121/1.400725

]. H. Minc, Nonnegative matrices, 1988.

. Mongeau, ]. M. Sankoff, D. Mongeau, and . Sankoff, Comparison of musical sequences, Computers and the Humanities, vol.15, issue.3, pp.161-175, 1990.
DOI : 10.1007/BF00117340

URL : https://hal.archives-ouvertes.fr/hal-01098807

. Monti, ]. G. Sandler, M. Monti, and . Sandler, Automatic polyphonic piano note extraction using fuzzy logic in a blackboard system, Proc. 5th International Conference on Digital Audio Effects (DAFx), pp.39-44, 2002.

]. J. Moorer, On the segmentation and analysis of continuous musical sound by digital computer, Thèse de doctorat, 1975.

M. , K. F. Murray, and K. Kreutz-delgado, Sparse image coding using learned overcomplete dictionaries, Proc. 14th IEEE Workshop on Machine Learning for Signal Processing, pp.579-588, 2004.

]. G. Peeterspielemeier, Music pitch representation by periodicity measures based on combined temporal and spectral representations Time-frequency analysis of musical signals, Proc. International Conference on Acoustics, Speech and Signal Processing Proc. of the IEEE, pp.14-191216, 1996.

]. M. Piszczalski, A computational model of music transcription, Thèse de doctorat, 1986.

. Piszczalski, ]. M. Galler, B. Piszczalski, and . Galler, Predicting musical pitch from component frequency ratios, The Journal of the Acoustical Society of America, vol.66, issue.3, pp.710-720, 1979.
DOI : 10.1121/1.383221

]. M. Plumbley, Conditions for nonnegative independent component analysis, IEEE Signal Processing Letters, vol.9, issue.6, pp.177-180, 2002.
DOI : 10.1109/LSP.2002.800502

]. M. Plumbley, Algorithms for nonnegative independent component analysis, IEEE Transactions on Neural Networks, vol.14, issue.3, pp.534-543, 2003.
DOI : 10.1109/TNN.2003.810616

]. M. Plumbley, A "nonnegative PCA" algorithm for independent component analysis, IEEE Transactions on Neural Networks, vol.15, issue.1, pp.66-76, 2004.
DOI : 10.1109/TNN.2003.820672

. Plumbley, Automatic Music Transcription and Audio Source Separation, Cybernetics and Systems, vol.84, issue.6, pp.603-627, 2002.
DOI : 10.1162/neco.1995.7.1.51

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.6930

. Plumbley, Sparse representations of polyphonic music, Signal Processing, vol.86, issue.3, pp.417-431, 2006.
DOI : 10.1016/j.sigpro.2005.06.007

E. Poliner, D. P. Poliner, and . Ellis, A Discriminative Model for Polyphonic Piano Transcription, EURASIP Journal on Advances in Signal Processing, vol.2007, issue.1, pp.154-162, 2007.
DOI : 10.1162/089976601750264965

. Polissar, Atmospheric aerosol over Alaska: 2. Elemental composition and sources, Journal of Geophysical Research: Atmospheres, vol.25, issue.D15, pp.19045-19057, 1998.
DOI : 10.1029/98JD01212

]. L. Rabiner, On the use of autocorrelation analysis for pitch detection, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.25, issue.1, pp.24-33, 1977.
DOI : 10.1109/TASSP.1977.1162905

. Rabiner, A comparative performance study of several pitch detection algorithms, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.24, issue.5, pp.399-418, 1976.
DOI : 10.1109/TASSP.1976.1162846

. Raczy?ski, Multipitch analysis with harmonic nonnegative matrix approximation, Proc. of the 8th International Conference on Music Information Retrieval (ISMIR'07), pp.23-27, 2007.

]. C. Raphael, Automatic transcription of piano music, Proc. Internationam Conference on Music Information Retrieval (ISMIR), pp.13-17, 2002.

]. L. Rigouste, Méthodes probabilistes pour l'analyse exploratoire de données textuelles, Thèse de doctorat, 2006.

P. Christian and . Robert, The Bayesian Choice : From Decision-Theoretic Foundations to Computational Implementation (Springer Texts in Statistics), 2007.

]. T. Virtanen, Sound Source Separation in Monaural Music Signals, Thèse de doctorat, 2006.

]. T. Virtanen, Monaural Sound Source Separation by Nonnegative Matrix Factorization With Temporal Continuity and Sparseness Criteria, IEEE Transactions on Audio, Speech and Language Processing, vol.15, issue.3, pp.1066-1074, 2007.
DOI : 10.1109/TASL.2006.885253

. Virtanen, Bayesian extensions to nonnegative matrix factorisation for audio signal modelling, Proc. of the International Conference on Acoustics, Speech and Signal Processing, pp.1825-1828, 2008.

]. T. Virtanen-et-klapuri, A. Virtanen, . Klapuri-]-r, A. Zdunek, and . Cichocki, Separation of harmonic sounds using linear models for the overtone series Fast nonnegative matrix factorization algorithms using projected gradient approaches for large-scale problems, Proc. IEEE International Conference on Acoustics, [Zdunek et Cichocki, 2002.

F. Zhang, Ye Zhang et Yong Fang A NMF algorithm for blind separation of uncorrelated signals, Proc. of the 2007 International Conference on Wavelet Analysis and Pattern Recognition, pp.999-1003, 2007.

. Zheng, Initialization enhancer for non-negative matrix factorization, Engineering Applications of Artificial Intelligence, vol.20, issue.1, pp.101-110, 2007.
DOI : 10.1016/j.engappai.2006.03.001

. Zwicker, ]. E. Fastl, H. Zwicker, and . Fastl, Psychoacoustics : Facts and Models, 1999.
DOI : 10.1007/978-3-662-09562-1

A. P. Klapuri, Automatic Music Transcription, Proceedings of the Stockholm Music Acoustics Conference (SMAC), pp.587-590, 2003.
DOI : 10.1007/978-0-387-30441-0_20

J. Bello, G. Monti, and M. Sandler, Techniques for automatic music transcription, Proceedings of International Conference on Music Information Retrieval (ISMIR'00), 2000.

M. D. Plumbley, S. A. Abdallah, J. P. Bello, M. E. Davies, G. Monti et al., Automatic Music Transcription and Audio Source Separation, Cybernetics and Systems, vol.84, issue.6, pp.603-627, 2002.
DOI : 10.1162/neco.1995.7.1.51

S. A. Abdallah and M. D. Plumbley, Unsupervised Analysis of Polyphonic Music by Sparse Coding, IEEE Transactions on Neural Networks, vol.17, issue.1, pp.179-196, 2006.
DOI : 10.1109/TNN.2005.861031

D. D. Lee and H. S. Seung, Learning the parts of objects by non-negative matrix factorization, Nature, vol.401, pp.788-791, 1999.

J. F. Cardoso, Blind signal separation: statistical principles, Proc. IEEE. Special issue on blind source separation, pp.2009-2025, 1998.
DOI : 10.1109/5.720250

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.7237

M. D. Plumbley, Algorithms for nonnegative independent component analysis, IEEE Transactions on Neural Networks, vol.14, issue.3, pp.534-543, 2003.
DOI : 10.1109/TNN.2003.810616

P. Smaragdis and J. C. Brown, Non-negative matrix factorization for polyphonic music transcription, 2003 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (IEEE Cat. No.03TH8684), pp.177-180, 2003.
DOI : 10.1109/ASPAA.2003.1285860

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.475.7518

M. Aharon, M. Elad, and A. Bruckstein, K-SVD and its nonnegative variant for dictionary design, Proceedings of the SPIE conference wavelets, p.591411, 2005.

D. D. Lee and H. S. Seung, Algorithms for non-negative matrix factorization, Advances in Neural Information Processing Systems, pp.556-562, 2001.

J. P. Bello, L. Daudet, and M. B. Sandler, Automatic Piano Transcription Using Frequency and Time-Domain Information, IEEE Transactions on Audio, Speech and Language Processing, vol.14, issue.6, 2006.
DOI : 10.1109/TASL.2006.872609

M. Goto, H. Hashiguchi, T. Nishimura, and R. Oka, RWC music database: Popular, classical, and jazz music databases, Proc. of the 3rd International Conference on Music Information Retrieval, pp.287-288, 2002.

G. Poliner and D. P. Ellis, A Discriminative Model for Polyphonic Piano Transcription, EURASIP Journal on Advances in Signal Processing, vol.2007, issue.1, 2006.
DOI : 10.1162/089976601750264965

. Vincent, it is observed that using a nonlinear frequency scale resulted in a representation of smaller size, with better temporal resolution in the higher frequency range, than usual Short-Time Fourier Transform (STFT), while preserving the subsequent transcription performance, 2007.