Considering a mixed signal composed of various audio sources and recorded with a single microphone, we consider on this paper the blind audio source separation problem which consists in isolating and extracting each of the sources. To perform this task, nonnegative matrix factorization (NMF) based on the Kullback-Leibler and Itakura-Saito $β$-divergences is a standard and state-of-the-art technique that uses the time-frequency representation of the signal. We present a new NMF model better suited for this task. It is based on the minimization of $β$-divergences along with a penalty term that promotes the columns of the dictionary matrix to have a small volume. Under some mild assumptions and in noiseless conditions, we prove that this model is provably able to identify the sources. In order to solve this problem, we propose multiplicative updates whose derivations are based on the standard majorization-minimization framework. We show on several numerical experiments that our new model is able to obtain more interpretable results than standard NMF models. Moreover, we show that it is able to recover the sources even when the number of sources present into the mixed signal is overestimated. In fact, our model automatically sets sources to zero in this situation, hence performs model order selection automatically.
NEC Corporation（日本电气股份有限公司）；Data Science Research Laboratories, NEC Corporation（NEC公司数据科学研究实验室）
This paper proposes a determined blind source separation method using Bayesian non-parametric modelling of sources. Conventionally source signals are separated from a given set of mixture signals by modelling them using non-negative matrix factorization (NMF). However in NMF, a latent variable signifying model complexity must be appropriately specified to avoid over-fitting or under-fitting. As real-world sources can be of varying and unknown complexities, we propose a Bayesian non-parametric framework which is invariant to such latent variables. We show that our proposed method adapts to diff…
CNRS（法国国家科学研究中心）；LTCI（电信与信息处理实验室）；Télécom ParisTech（巴黎高等电信学院）；IRCCyN（南特通信与控制研究院）；École Centrale de Nantes（南特中央理工学院）
This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean distance, the Kullback-Leibler divergence and the Itakura-Saito divergence as special cases (beta = 2,1,0, respectively). The proposed algorithms are based on a surrogate auxiliary function (a local majorization of the criterion function). We first describe a majorization-minimization (MM) algorithm that leads to multiplicative updates, which differ from standard h…
Non-negative blind source separation (non-negative BSS), which is also referred to as non-negative matrix factorization (NMF), is a very active field in domains as different as astrophysics, audio processing or biomedical signal processing. In this context, the efficient retrieval of the sources requires the use of signal priors such as sparsity. If NMF has now been well studied with sparse constraints in the direct domain, only very few algorithms can encompass non-negativity together with sparsity in a transformed domain since simultaneously dealing with two priors in two different domains i…
Non-negative Matrix Factorization (NMF) has already been applied to learn speaker characterizations from single or non-simultaneous speech for speaker recognition applications. It is also known for its good performance in (blind) source separation for simultaneous speech. This paper explains how NMF can be used to jointly solve the two problems in a multichannel speaker recognizer for simultaneous speech. It is shown how state-of-the-art multichannel NMF for blind source separation can be easily extended to incorporate speaker recognition. Experiments on the CHiME corpus show that this method …
Columbia University（哥伦比亚大学）；Adobe Research（Adobe研究院）；Adobe Systems Incorporated（奥多比系统公司）
Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with Poisson likelihood. Unlike the linear Gaussian model, which is well-studied in the nonparametric Bayesian literature, NMF model with beta process prior does not enjoy the conjugacy. We leverage the recently developed stochastic structured mean-field variational inference to relax the conjugacy constraint and restore the dependencies among the latent variables in t…
University of Mons（蒙斯大学）；Univ Rennes（雷恩大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；IRISA（法国雷恩信息与自动化系统研究所）
We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns of the first NMF factor are equal to columns of the input matrix, while sparsity requires that the columns of the second NMF factor are sparse. We call this variant sparse separable NMF (SSNMF), which we prove to be NP-complete, as opposed to separable NMF which can be solved in polynomial time. The main motivation to consider this new model is to handle underdetermined blind source separation problems, such as multispectral image unmixing.…
Non-negative Matrix Factorization (NMF) has proven to be a powerful unsupervised learning method for uncovering hidden features in complex and noisy data sets with applications in data mining, text recognition, dimension reduction, face recognition, anomaly detection, blind source separation, and many other fields. An important input for NMF is the latent dimensionality of the data, that is, the number of hidden features, K, present in the explored data set. Unfortunately, this quantity is rarely known a priori. We utilize a supervised machine learning approach in combination with a recent met…
Center for Artificial Intelligence Technology, Skoltech（斯科尔科沃科学技术研究院人工智能技术中心）；Department of Mathematics and Operational Research, Faculté Polytechnique, Université de Mons（蒙斯大学理工学院数学与运筹学系）；IRIT, Université de Toulouse, CNRS（图卢兹大学计算机科学研究院，法国国家科学研究中心）
Many datasets are obtained as a resolution trade-off between two adversarial dimensions; for example between the frequency and the temporal resolutions for the spectrogram of an audio signal, and between the number of wavelengths and the spatial resolution for a hyper/multi-spectral image. To perform blind source separation using observations with different resolutions, a standard approach is to use coupled nonnegative matrix factorizations (NMF). Most previous works have focused on the least squares error measure, which is the $β$-divergence for $β= 2$. In this paper, we formulate this multi-…
Institut Charles Delaunay (CNRS)（查尔斯·德洛奈研究所（法国国家科学研究中心））；Université de Technologie de Troyes（特鲁瓦技术大学）；LITIS lab（LITIS实验室）；Université de Rouen（鲁昂大学）；Centre de Recherche en Automatique de Nancy (CNRS)（南锡自动化研究中心（法国国家科学研究中心））；Université de Lorraine（洛林大学）
The nonnegative matrix factorization (NMF) is widely used in signal and image processing, including bio-informatics, blind source separation and hyperspectral image analysis in remote sensing. A great challenge arises when dealing with a nonlinear formulation of the NMF. Within the framework of kernel machines, the models suggested in the literature do not allow the representation of the factorization matrices, which is a fallout of the curse of the pre-image. In this paper, we propose a novel kernel-based model for the NMF that does not suffer from the pre-image problem, by investigating the …
Non-negative blind source separation (BSS) has raised interest in various fields of research, as testified by the wide literature on the topic of non-negative matrix factorization (NMF). In this context, it is fundamental that the sources to be estimated present some diversity in order to be efficiently retrieved. Sparsity is known to enhance such contrast between the sources while producing very robust approaches, especially to noise. In this paper we introduce a new algorithm in order to tackle the blind separation of non-negative sparse sources from noisy measurements. We first show that sp…
Werner Reichardt Center for Integrative Neuroscience（维尔纳·赖希哈特综合神经科学中心）；Eberhard Karls Universität Tübingen（图宾根大学）；Bernstein Center for Computational Neuroscience（伯恩斯坦计算神经科学中心）；Institute for Theoretical Physics（理论物理研究所）；Department of Neurophysiology（神经生理学系）；Donders Institute for Brain, Cognition and Behaviour（东德斯脑认知与行为研究所）；Radboud University（拉德堡德大学）；Max Planck Institute for Biological Cybernetics（马克斯·普朗克生物控制论研究所）
An important preprocessing step in most data analysis pipelines aims to extract a small set of sources that explain most of the data. Currently used algorithms for blind source separation (BSS), however, often fail to extract the desired sources and need extensive cross-validation. In contrast, their rarely used probabilistic counterparts can get away with little cross-validation and are more accurate and reliable but no simple and scalable implementations are available. Here we present a novel probabilistic BSS framework (DECOMPOSE) that can be flexibly adjusted to the data, is extensible and…
A New Non-Negative Matrix Factorization Approach for Blind Source Separation of Cardiovascular and Respiratory Sound Based on the Periodicity of Heart and Lung Function
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of New Mexico Comprehensive Cancer Center（新墨西哥大学综合癌症中心）
Factor analysis is broadly used as a powerful unsupervised machine learning tool for reconstruction of hidden features in recorded mixtures of signals. In the case of a linear approximation, the mixtures can be decomposed by a variety of model-free Blind Source Separation (BSS) algorithms. Most of the available BSS algorithms consider an instantaneous mixing of signals, while the case when the mixtures are linear combinations of signals with delays is less explored. Especially difficult is the case when the number of sources of the signals with delays is unknown and has to be determined from t…
The Note-Chord-Voice Framework: Structured Source Separation and Causal Inference for EV Charging Data
Xuteli School, Beijing Institute of Technology（北京理工大学徐特立学院）；School of Integrated Circuits and Electronics, Beijing Institute of Technology（北京理工大学集成电路与电子学院）
Extracting the desired speech from a mixture is a meaningful and challenging task. The end-to-end DNN-based methods, though attractive, face the problem of generalization. In this paper, we explore a sequential approach for target speech extraction by combining blind source separation (BSS) with the x-vector based speaker recognition (SR) module. Two promising BSS methods based on source independence assumption, independent low-rank matrix analysis (ILRMA) and multi-channel variational autoencoder (MVAE), are utilized and compared. ILRMA employs nonnegative matrix factorization (NMF) to captur…
