Learning Overcomplete Representations
Neural Computation
Sparse representations of polyphonic music
Signal Processing - Sparse approximations in signal and image processing
A Generalized Divergence Measure for Nonnegative Matrix Factorization
Neural Computation
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
Csiszár’s divergences for non-negative matrix factorization: family of new algorithms
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Extended SMART algorithms for non-negative matrix factorization
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
IEEE Transactions on Audio, Speech, and Language Processing
Convolutive Speech Bases and Their Application to Supervised Speech Separation
IEEE Transactions on Audio, Speech, and Language Processing
IEEE Transactions on Audio, Speech, and Language Processing
Sided and symmetrized Bregman centroids
IEEE Transactions on Information Theory
Online Learning for Matrix Factorization and Sparse Coding
The Journal of Machine Learning Research
Generative spectrogram factorization models for polyphonic piano transcription
IEEE Transactions on Audio, Speech, and Language Processing
Adaptive harmonic spectral decomposition for multiple pitch estimation
IEEE Transactions on Audio, Speech, and Language Processing
IEEE Transactions on Audio, Speech, and Language Processing
Multichannel nonnegative matrix factorization in convolutive mixtures for audio source separation
IEEE Transactions on Audio, Speech, and Language Processing
Source/filter model for unsupervised main melody extraction from polyphonic audio signals
IEEE Transactions on Audio, Speech, and Language Processing
A general modular framework for audio source separation
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Informed source separation using latent components
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
IEEE Transactions on Neural Networks
Kullback-Leibler divergence for nonnegative matrix factorization
ICANN'11 Proceedings of the 21th international conference on Artificial neural networks - Volume Part I
Single channel music sound separation based on spectrogram decomposition and note classification
CMMR'10 Proceedings of the 7th international conference on Exploring music contents
CMMR'10 Proceedings of the 7th international conference on Exploring music contents
NOLISP'11 Proceedings of the 5th international conference on Advances in nonlinear speech processing
Algorithms for nonnegative matrix factorization with the β-divergence
Neural Computation
Quadratic nonnegative matrix factorization
Pattern Recognition
Sparse nonnegative matrix factorization with ℓ0-constraints
Neurocomputing
Supervised input space scaling for non-negative matrix factorization
Signal Processing
Informed source separation through spectrogram coding and data embedding
Signal Processing
Bayesian non-negative matrix factorization with learned temporal smoothness priors
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Low-Latency instrument separation in polyphonic audio using timbre models
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Fast bregman divergence NMF using taylor expansion and coordinate descent
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Journal of Signal Processing Systems
Correntropy-Based document clustering via nonnegative matrix factorization
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part II
Pairwise clustering with t-PLSI
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part II
Selecting β-divergence for nonnegative matrix factorization by score matching
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part II
Fast reduction of speckle noise in real ultrasound images
Signal Processing
Digital Signal Processing
Adaptive multiplicative updates for projective nonnegative matrix factorization
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Online projective nonnegative matrix factorization for large datasets
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Sparse and unique nonnegative matrix factorization through data preprocessing
The Journal of Machine Learning Research
Journal of Global Optimization
Global convergence of modified multiplicative updates for nonnegative matrix factorization
Computational Optimization and Applications
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This letter presents theoretical, algorithmic, and experimental results about nonnegative matrix factorization (NMF) with the Itakura-Saito (IS) divergence. We describe how IS-NMF is underlaid by a well-defined statistical model of superimposed gaussian components and is equivalent to maximum likelihood estimation of variance parameters. This setting can accommodate regularization constraints on the factors through Bayesian priors. In particular, inverse-gamma and gamma Markov chain priors are considered in this work. Estimation can be carried out using a space-alternating generalized expectation-maximization (SAGE) algorithm; this leads to a novel type of NMF algorithm, whose convergence to a stationary point of the IS cost function is guaranteed. We also discuss the links between the IS divergence and other cost functions used in NMF, in particular, the Euclidean distance and the generalized Kullback-Leibler (KL) divergence. As such, we describe how IS-NMF can also be performed using a gradient multiplicative algorithm (a standard algorithm structure in NMF) whose convergence is observed in practice, though not proven. Finally, we report a furnished experimental comparative study of Euclidean-NMF, KL-NMF, and IS-NMF algorithms applied to the power spectrogram of a short piano sequence recorded in real conditions, with various initializations and model orders. Then we show how IS-NMF can successfully be employed for denoising and upmix (mono to stereo conversion) of an original piece of early jazz music. These experiments indicate that IS-NMF correctly captures the semantics of audio and is better suited to the representation of music signals than NMF with the usual Euclidean and KL costs.