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34
C.: Multichannel nonnegative matrix factorization in convolutive mixtures for audio source separation
 IEEE Trans. Audio, Speech, Language Process
, 2010
"... We consider inference in a general datadriven objectbased model of multichannel audio data, assumed generated as a possibly underdetermined convolutive mixture of source signals. Each source is given a model inspired from nonnegative matrix factorization (NMF) with the ItakuraSaito divergence, wh ..."
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Cited by 79 (17 self)
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We consider inference in a general datadriven objectbased model of multichannel audio data, assumed generated as a possibly underdetermined convolutive mixture of source signals. Each source is given a model inspired from nonnegative matrix factorization (NMF) with the ItakuraSaito divergence, which underlies a statistical model of superimposed Gaussian components. We address estimation of the mixing and source parameters using two methods. The first one consists of maximizing the exact joint likelihood of the multichannel data using an expectationmaximization algorithm. The second method consists of maximizing the sum of individual likelihoods of all channels using a multiplicative update algorithm inspired from NMF methodology. Our decomposition algorithms were applied to stereo music and assessed in terms of blind source separation performance. Index Terms — Multichannel audio, nonnegative matrix factorization, nonnegative tensor factorization, underdetermined convolutive blind source separation. 1.
Sparse Bayesian methods for lowrank matrix estimation. arXiv:1102.5288v1 [stat.ML
, 2011
"... Abstract—Recovery of lowrank matrices has recently seen significant ..."
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Cited by 28 (11 self)
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Abstract—Recovery of lowrank matrices has recently seen significant
IDENTIFYING REPEATED PATTERNS IN MUSIC USING SPARSE CONVOLUTIVE NONNEGATIVE MATRIX FACTORIZATION
"... We describe an unsupervised, datadriven, method for automatically identifying repeated patterns in music by analyzing a feature matrix using a variant of sparse convolutive nonnegative matrix factorization. We utilize sparsity constraints to automatically identify the number of patterns and their ..."
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Cited by 17 (3 self)
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We describe an unsupervised, datadriven, method for automatically identifying repeated patterns in music by analyzing a feature matrix using a variant of sparse convolutive nonnegative matrix factorization. We utilize sparsity constraints to automatically identify the number of patterns and their lengths, parameters that would normally need to be fixed in advance. The proposed analysis is applied to beatsynchronous chromagrams in order to concurrently extract repeated harmonic motifs and their locations within a song. Finally, we show how this analysis can be used for longterm structure segmentation, resulting in an algorithm that is competitive with other stateoftheart segmentation algorithms based on hidden Markov models and self similarity matrices. 1.
Transcribing Multiinstrument Polyphonic Music with Hierarchical Eigeninstruments
 in Sig. Process
, 2011
"... Abstract—This paper presents a general probabilistic model for transcribing singlechannel music recordings containing multiple polyphonic instrument sources. The system requires no prior knowledge of the instruments present in the mixture (other than the number), although it can benefit from inform ..."
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Cited by 16 (2 self)
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Abstract—This paper presents a general probabilistic model for transcribing singlechannel music recordings containing multiple polyphonic instrument sources. The system requires no prior knowledge of the instruments present in the mixture (other than the number), although it can benefit from information about instrument type if available. In contrast to many existing polyphonic transcription systems, our approach explicitly models the individual instruments and is thereby able to assign detected notes to their respective sources. We use training instruments to learn a set of linear manifolds in model parameter space which are then used during transcription to constrain the properties of models fit to the target mixture. This leads to a hierarchical mixtureofsubspaces design which makes it possible to supply the system with prior knowledge at different levels of abstraction. The proposed technique is evaluated on both recorded and synthesized mixtures containing two, three, four, and five instruments each. We compare our approach in terms of transcription with (i.e. detected pitches must be associated with the correct instrument) and without sourceassignment to another multiinstrument transcription system as well as a baseline NMF algorithm. For twoinstrument mixtures evaluated with sourceassignment, we obtain average framelevel Fmeasures of up to 0.52 in the completely blind transcription setting (i.e. no prior knowledge of the instruments in the mixture) and up to 0.67 if we assume knowledge of the basic instrument types. For transcription without source assignment, these numbers rise to 0.76 and 0.83, respectively. Index Terms—Music, polyphonic transcription, NMF, subspace, eigeninstruments
The signal separation evaluation campaign (2007–2010): Achievements and remaining challenges
 Signal Processing
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 12 (7 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Topic Discovery through Data Dependent and Random Projections
"... We present algorithms for topic modeling based on the geometry of crossdocument wordfrequency patterns. This perspective gains significance under the so called separability condition. This is a condition on existence of novelwords that are unique to each topic. We present a suite of highly effici ..."
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Cited by 12 (6 self)
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We present algorithms for topic modeling based on the geometry of crossdocument wordfrequency patterns. This perspective gains significance under the so called separability condition. This is a condition on existence of novelwords that are unique to each topic. We present a suite of highly efficient algorithms with provable guarantees based on datadependent and random projections to identify novel words and associated topics. Our key insight here is that the maximum and minimum values of crossdocument frequency patterns projected along any direction are associated with novel words. While our sample complexity bounds for topic recovery are similar to the stateofart, the computational complexity of our random projection scheme scales linearly with the number of documents and the number of words per document. We present several experiments on synthetic and realworld datasets to demonstrate qualitative and quantitative merits of our scheme. 1.
The why and how of nonnegative matrix factorization
 REGULARIZATION, OPTIMIZATION, KERNELS, AND SUPPORT VECTOR MACHINES. CHAPMAN & HALL/CRC
, 2014
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Soft Partitioning in Networks via Bayesian Nonnegative Matrix Factorization
"... Identifying overlapping communities in networks is a challenging task. In this work we present a novel approach to community detection that utilizes the Bayesian nonnegative matrix factorization (NMF) model to extract overlapping modules from a network. The scheme has the advantage of computational ..."
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Cited by 5 (0 self)
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Identifying overlapping communities in networks is a challenging task. In this work we present a novel approach to community detection that utilizes the Bayesian nonnegative matrix factorization (NMF) model to extract overlapping modules from a network. The scheme has the advantage of computational efficiency, soft community membership and an intuitive foundation. We present the performance of the method against a variety of benchmark problems and compare and contrast it to several other algorithms for community detection. 1
TUNING PRUNING IN SPARSE NONNEGATIVE MATRIX FACTORIZATION
"... Nonnegative matrix factorization (NMF) has become a popular tool for exploratory analysis due to its part based easy interpretable representation. Sparseness is commonly invoked in NMF (SNMF) by regularizing by the l1 − norm both to alleviate the nonuniqueness of the NMF representation as well as ..."
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Cited by 4 (0 self)
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Nonnegative matrix factorization (NMF) has become a popular tool for exploratory analysis due to its part based easy interpretable representation. Sparseness is commonly invoked in NMF (SNMF) by regularizing by the l1 − norm both to alleviate the nonuniqueness of the NMF representation as well as promote sparse (i.e. part based) representations. While sparseness can prune excess components thereby potentially also establish the number of components it is an open problem what constitutes the adequate degree of sparseness, i.e. how to tune the pruning. In a hierarchical Bayesian framework SNMF corresponds to imposing an exponential prior while the regularization strength can be expressed in terms of the hyperparameters of these priors. Thus, within the Bayesian modelling framework Automatic Relevance Determination (ARD) can learn these pruning strengths from data. We demonstrate on three benchmark NMF data how the proposed ARD framework can be used to tune the pruning thereby also estimate the NMF model order. 1.
Efficient Bayesian Community Detection using Nonnegative Matrix
, 2010
"... Identifying overlapping communities in networks is a challenging task. In this work we present a novel approach to community detection that utilises the Bayesian nonnegative matrix factorisation (NMF) model to produce a probabilistic output for node memberships. The scheme has the advantage of comp ..."
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Cited by 4 (0 self)
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Identifying overlapping communities in networks is a challenging task. In this work we present a novel approach to community detection that utilises the Bayesian nonnegative matrix factorisation (NMF) model to produce a probabilistic output for node memberships. The scheme has the advantage of computational efficiency, soft community membership and an intuitive foundation. We present the performance of the method against a variety of benchmark problems and compare and contrast it to several other algorithms for community detection. Our approach performs favourably compared to other methods at a fraction of the computational costs.