Non-negative mixtures

This is the author's accepted pre-print of the article, first published as M. D. Plumbley, A. Cichocki and R. Bro. Non-negative mixtures. In P. Comon and C. Jutten (Ed), Handbook of Blind Source Separation: Independent Component Analysis and Applications. Chapter 13, pp. 515-547. Academic Press, Feb 2010. ISBN 978-0-12-374726-6 DOI: 10.1016/B978-0-12-374726-6.00018-7file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.2

Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs

Statistical single channel source separation

PhD ThesisSingle channel source separation (SCSS) principally is one of the challenging fields in signal processing and has various significant applications. Unlike conventional SCSS methods which were based on linear instantaneous model, this research sets out to investigate the separation of single channel in two types of mixture which is nonlinear instantaneous mixture and linear convolutive mixture. For the nonlinear SCSS in instantaneous mixture, this research proposes a novel solution based on a two-stage process that consists of a Gaussianization transform which efficiently compensates for the nonlinear distortion follow by a maximum likelihood estimator to perform source separation. For linear SCSS in convolutive mixture, this research proposes new methods based on nonnegative matrix factorization which decomposes a mixture into two-dimensional convolution factor matrices that represent the spectral basis and temporal code. The proposed factorization considers the convolutive mixing in the decomposition by introducing frequency constrained parameters in the model. The method aims to separate the mixture into its constituent spectral-temporal source components while alleviating the effect of convolutive mixing. In addition, family of Itakura-Saito divergence has been developed as a cost function which brings the beneficial property of scale-invariant. Two new statistical techniques are proposed, namely, Expectation-Maximisation (EM) based algorithm framework which maximizes the log-likelihood of a mixed signals, and the maximum a posteriori approach which maximises the joint probability of a mixed signal using multiplicative update rules. To further improve this research work, a novel method that incorporates adaptive sparseness into the solution has been proposed to resolve the ambiguity and hence, improve the algorithm performance. The theoretical foundation of the proposed solutions has been rigorously developed and discussed in details. Results have concretely shown the effectiveness of all the proposed algorithms presented in this thesis in separating the mixed signals in single channel and have outperformed others available methods.Universiti Teknikal Malaysia Melaka(UTeM), Ministry of Higher Education of Malaysi

Incorporating prior information in nonnegative matrix factorization for audio source separation

In this work, we propose solutions to the problem of audio source separation from a single recording. The audio source signals can be speech, music or any other audio signals. We assume training data for the individual source signals that are present in the mixed signal are available. The training data are used to build a representative model for each source. In most cases, these models are sets of basis vectors in magnitude or power spectral domain. The proposed algorithms basically depend on decomposing the spectrogram of the mixed signal with the trained basis models for all observed sources in the mixed signal. Nonnegative matrix factorization (NMF) is used to train the basis models for the source signals. NMF is then used to decompose the mixed signal spectrogram as a weighted linear combination of the trained basis vectors for each observed source in the mixed signal. After decomposing the mixed signal, spectral masks are built and used to reconstruct the source signals. In this thesis, we improve the performance of NMF for source separation by incorporating more constraints and prior information related to the source signals to the NMF decomposition results. The NMF decomposition weights are encouraged to satisfy some prior information that is related to the nature of the source signals. The priors are modeled using Gaussian mixture models or hidden Markov models. These priors basically represent valid weight combination sequences that the basis vectors can receive for a certain type of source signal. The prior models are incorporated with the NMF cost function using either log-likelihood or minimum mean squared error estimation (MMSE). We also incorporate the prior information as a post processing. We incorporate the smoothness prior on the NMF solutions by using post smoothing processing. We also introduce post enhancement using MMSE estimation to obtain better separation for the source signals. In this thesis, we also improve the NMF training for the basis models. In cases when enough training data are not available, we introduce two di erent adaptation methods for the trained basis to better t the sources in the mixed signal. We also improve the training procedures for the sources by learning more discriminative dictionaries for the source signals. In addition, to consider a larger context in the models, we concatenate neighboring spectra together and train basis sets from them instead of a single frame which makes it possible to directly model the relation between consequent spectral frames. Experimental results show that the proposed approaches improve the performance of using NMF in source separation applications

Gaussian Framework for Interference Reduction in Live Recordings

Here typical live full-length music recordings are considered. In this scenarios, some instrumental voices are captured by microphones intended to other voices, leading to so-called “interferences”. Reducing this phenomenon is desirable because it opens new possibilities for sound engineers and also it has been proven that it increase performances of music analysis and processing tools (e.g. pitch tracking). In this work we propose an fast NMF-based algorithm to solve this problem.ope

Audio source separation for music in low-latency and high-latency scenarios

Aquesta tesi proposa mètodes per tractar les limitacions de les tècniques existents de separació de fonts musicals en condicions de baixa i alta latència. En primer lloc, ens centrem en els mètodes amb un baix cost computacional i baixa latència. Proposem l'ús de la regularització de Tikhonov com a mètode de descomposició de l'espectre en el context de baixa latència. El comparem amb les tècniques existents en tasques d'estimació i seguiment dels tons, que són passos crucials en molts mètodes de separació. A continuació utilitzem i avaluem el mètode de descomposició de l'espectre en tasques de separació de veu cantada, baix i percussió. En segon lloc, proposem diversos mètodes d'alta latència que milloren la separació de la veu cantada, gràcies al modelatge de components específics, com la respiració i les consonants. Finalment, explorem l'ús de correlacions temporals i anotacions manuals per millorar la separació dels instruments de percussió i dels senyals musicals polifònics complexes.Esta tesis propone métodos para tratar las limitaciones de las técnicas existentes de separación de fuentes musicales en condiciones de baja y alta latencia. En primer lugar, nos centramos en los métodos con un bajo coste computacional y baja latencia. Proponemos el uso de la regularización de Tikhonov como método de descomposición del espectro en el contexto de baja latencia. Lo comparamos con las técnicas existentes en tareas de estimación y seguimiento de los tonos, que son pasos cruciales en muchos métodos de separación. A continuación utilizamos y evaluamos el método de descomposición del espectro en tareas de separación de voz cantada, bajo y percusión. En segundo lugar, proponemos varios métodos de alta latencia que mejoran la separación de la voz cantada, gracias al modelado de componentes que a menudo no se toman en cuenta, como la respiración y las consonantes. Finalmente, exploramos el uso de correlaciones temporales y anotaciones manuales para mejorar la separación de los instrumentos de percusión y señales musicales polifónicas complejas.This thesis proposes specific methods to address the limitations of current music source separation methods in low-latency and high-latency scenarios. First, we focus on methods with low computational cost and low latency. We propose the use of Tikhonov regularization as a method for spectrum decomposition in the low-latency context. We compare it to existing techniques in pitch estimation and tracking tasks, crucial steps in many separation methods. We then use the proposed spectrum decomposition method in low-latency separation tasks targeting singing voice, bass and drums. Second, we propose several high-latency methods that improve the separation of singing voice by modeling components that are often not accounted for, such as breathiness and consonants. Finally, we explore using temporal correlations and human annotations to enhance the separation of drums and complex polyphonic music signals

Algoritmos de procesado de señal basados en Non-negative Matrix Factorization aplicados a la separación, detección y clasificación de sibilancias en señales de audio respiratorias monocanal

La auscultación es el primer examen clínico que un médico lleva a cabo para evaluar el estado del sistema respiratorio, debido a que es un método no invasivo, de bajo coste, fácil de realizar y seguro para el paciente. Sin embargo, el diagnóstico que se deriva de la auscultación sigue siendo un diagnóstico subjetivo que se encuentra condicionado a la habilidad, experiencia y entrenamiento de cada médico en la escucha e interpretación de las señales de audio respiratorias. En consecuencia, se producen un alto porcentaje de diagnósticos erróneos que ponen en riesgo la salud de los pacientes e incrementan el coste asociado a los centros de salud. Esta Tesis propone nuevos métodos basados en Non-negative Matrix Factorization aplicados a la separación, detección y clasificación de sonidos sibilantes para proporcionar una vía de información complementaria al médico que ayude a mejorar la fiabilidad del diagnóstico emitido por el especialista. Auscultation is the first clinical examination that a physician performs to evaluate the condition of the respiratory system, because it is a non-invasive, low-cost, easy-to-perform and safe method for the patient. However, the diagnosis derived from auscultation remains a subjective diagnosis that is conditioned by the ability, experience and training of each physician in the listening and interpretation of respiratory audio signals. As a result, a high percentage of misdiagnoses are produced that endanger the health of patients and increase the cost associated with health centres. This Thesis proposes new methods based on Non-negative Matrix Factorization applied to separation, detection and classification of wheezing sounds in order to provide a complementary information pathway to the physician that helps to improve the reliability of the diagnosis made by the doctor.Tesis Univ. Jaén. Departamento INGENIERÍA DE TELECOMUNICACIÓ

Automatic Music Transcription using Structure and Sparsity

PhdAutomatic Music Transcription seeks a machine understanding of a musical signal in terms of pitch-time activations. One popular approach to this problem is the use of spectrogram decompositions, whereby a signal matrix is decomposed over a dictionary of spectral templates, each representing a note. Typically the decomposition is performed using gradient descent based methods, performed using multiplicative updates based on Non-negative Matrix Factorisation (NMF). The final representation may be expected to be sparse, as the musical signal itself is considered to consist of few active notes. In this thesis some concepts that are familiar in the sparse representations literature are introduced to the AMT problem. Structured sparsity assumes that certain atoms tend to be active together. In the context of AMT this affords the use of subspace modelling of notes, and non-negative group sparse algorithms are proposed in order to exploit the greater modelling capability introduced. Stepwise methods are often used for decomposing sparse signals and their use for AMT has previously been limited. Some new approaches to AMT are proposed by incorporation of stepwise optimal approaches with promising results seen. Dictionary coherence is used to provide recovery conditions for sparse algorithms. While such guarantees are not possible in the context of AMT, it is found that coherence is a useful parameter to consider, affording improved performance in spectrogram decompositions

Learning Sparse Orthogonal Wavelet Filters

The wavelet transform is a well studied and understood analysis technique used in signal processing. In wavelet analysis, signals are represented by a sum of self-similar wavelet and scaling functions. Typically, the wavelet transform makes use of a fixed set of wavelet functions that are analytically derived. We propose a method for learning wavelet functions directly from data. We impose an orthogonality constraint on the functions so that the learned wavelets can be used to perform both analysis and synthesis. We accomplish this by using gradient descent and leveraging existing automatic differentiation frameworks. Our learned wavelets are able to capture the structure of the data by exploiting sparsity. We show that the learned wavelets have similar structure to traditional wavelets. Machine learning has proven to be a powerful tool in signal processing and computer vision. Recently, neural networks have become a popular and successful method used to solve a variety of tasks. However, much of the success is not well understood, and the neural network models are often treated as black boxes. This thesis provides insight into the structure of neural networks. In particular, we consider the connection between convolutional neural networks and multiresolution analysis. We show that the wavelet transform shares similarities to current convolutional neural network architectures. We hope that viewing neural networks through the lens of multiresolution analysis may provide some useful insights. We begin the thesis by motivating our method for one-dimensional signals. We then show that we can easily extend the framework to multidimensional signals. Our learning method is evaluated on a variety of supervised and unsupervised tasks, such as image compression and audio classification. The tasks are chosen to compare the usefulness of the learned wavelets to traditional wavelets, as well as provide a comparison to existing neural network architectures. The wavelet transform used in this thesis has some drawbacks and limitations, caused in part by the fact that we make use of separable real filters. We address these shortcomings by exploring an extension of the wavelet transform known as the dual-tree complex wavelet transform. Our wavelet learning model is extended into the dual-tree domain with few modifications, overcoming the limitations of our standard model. With this new model we are able to show that localized, oriented filters arise from natural images