Joint Analysis of Multiple Datasets by Cross-Cumulant Tensor (Block) Diagonalization

International audienceIn this paper, we propose approximate diagonalization of a cross-cumulant tensor as a means to achieve independent component analysis (ICA) in several linked datasets. This approach generalizes existing cumulant-based independent vector analysis (IVA). It leads to uniqueness, identifiability and resilience to noise that exceed those in the literature, in certain scenarios. The proposed method can achieve blind identification of underdetermined mixtures when single-dataset cumulant-based methods that use the same order of statistics fall short. In addition, it is possible to analyse more than two datasets in a single tensor factorization. The proposed approach readily extends to independent subspace analysis (ISA), by tensor block-diagonalization. The proposed approach can be used as-is or as an ingredient in various data fusion frameworks, using coupled decompositions. The core idea can be used to generalize existing ICA methods from one dataset to an ensemble

Underdetermined convolutive source separation using two dimensional non-negative factorization techniques

PhD ThesisIn this thesis the underdetermined audio source separation has been considered, that is, estimating the original audio sources from the observed mixture when the number of audio sources is greater than the number of channels. The separation has been carried out using two approaches; the blind audio source separation and the informed audio source separation. The blind audio source separation approach depends on the mixture signal only and it assumes that the separation has been accomplished without any prior information (or as little as possible) about the sources. The informed audio source separation uses the exemplar in addition to the mixture signal to emulate the targeted speech signal to be separated. Both approaches are based on the two dimensional factorization techniques that decompose the signal into two tensors that are convolved in both the temporal and spectral directions. Both approaches are applied on the convolutive mixture and the high-reverberant convolutive mixture which are more realistic than the instantaneous mixture. In this work a novel algorithm based on the nonnegative matrix factor two dimensional deconvolution (NMF2D) with adaptive sparsity has been proposed to separate the audio sources that have been mixed in an underdetermined convolutive mixture. Additionally, a novel Gamma Exponential Process has been proposed for estimating the convolutive parameters and number of components of the NMF2D/ NTF2D, and to initialize the NMF2D parameters. In addition, the effects of different window length have been investigated to determine the best fit model that suit the characteristics of the audio signal. Furthermore, a novel algorithm, namely the fusion K models of full-rank weighted nonnegative tensor factor two dimensional deconvolution (K-wNTF2D) has been proposed. The K-wNTF2D is developed for its ability in modelling both the spectral and temporal changes, and the spatial covariance matrix that addresses the high reverberation problem. Variable sparsity that derived from the Gibbs distribution is optimized under the Itakura-Saito divergence and adapted into the K-wNTF2D model. The tensors of this algorithm have been initialized by a novel initialization method, namely the SVD two-dimensional deconvolution (SVD2D). Finally, two novel informed source separation algorithms, namely, the semi-exemplar based algorithm and the exemplar-based algorithm, have been proposed. These algorithms based on the NMF2D model and the proposed two dimensional nonnegative matrix partial co-factorization (2DNMPCF) model. The idea of incorporating the exemplar is to inform the proposed separation algorithms about the targeted signal to be separated by initializing its parameters and guide the proposed separation algorithms. The adaptive sparsity is derived for both ii of the proposed algorithms. Also, a multistage of the proposed exemplar based algorithm has been proposed in order to further enhance the separation performance. Results have shown that the proposed separation algorithms are very promising, more flexible, and offer an alternative model to the conventional methods

A mixture model with a reference-based automatic selection of components for disease classification from protein and/or gene expression levels

Background Bioinformatics data analysis is often using linear mixture model representing samples as additive mixture of components. Properly constrained blind matrix factorization methods extract those components using mixture samples only. However, automatic selection of extracted components to be retained for classification analysis remains an open issue. Results The method proposed here is applied to well-studied protein and genomic datasets of ovarian, prostate and colon cancers to extract components for disease prediction. It achieves average sensitivities of: 96.2 (sd=2.7%), 97.6% (sd=2.8%) and 90.8% (sd=5.5%) and average specificities of: 93.6% (sd=4.1%), 99% (sd=2.2%) and 79.4% (sd=9.8%) in 100 independent two-fold cross-validations. Conclusions We propose an additive mixture model of a sample for feature extraction using, in principle, sparseness constrained factorization on a sample-by-sample basis. As opposed to that, existing methods factorize complete dataset simultaneously. The sample model is composed of a reference sample representing control and/or case (disease) groups and a test sample. Each sample is decomposed into two or more components that are selected automatically (without using label information) as control specific, case specific and not differentially expressed (neutral). The number of components is determined by cross-validation. Automatic assignment of features (m/z ratios or genes) to particular component is based on thresholds estimated from each sample directly. Due to the locality of decomposition, the strength of the expression of each feature across the samples can vary. Yet, they will still be allocated to the related disease and/or control specific component. Since label information is not used in the selection process, case and control specific components can be used for classification. That is not the case with standard factorization methods. Moreover, the component selected by proposed method as disease specific can be interpreted as a sub-mode and retained for further analysis to identify potential biomarkers. As opposed to standard matrix factorization methods this can be achieved on a sample (experiment)-by-sample basis. Postulating one or more components with indifferent features enables their removal from disease and control specific components on a sample-by-sample basis. This yields selected components with reduced complexity and generally, it increases prediction accuracy

Probabilistic Modeling Paradigms for Audio Source Separation

This is the author's final version of the article, first published as E. Vincent, M. G. Jafari, S. A. Abdallah, M. D. Plumbley, M. E. Davies. Probabilistic Modeling Paradigms for Audio Source Separation. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 7, pp. 162-185. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch007file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04Most sound scenes result from the superposition of several sources, which can be separately perceived and analyzed by human listeners. Source separation aims to provide machine listeners with similar skills by extracting the sounds of individual sources from a given scene. Existing separation systems operate either by emulating the human auditory system or by inferring the parameters of probabilistic sound models. In this chapter, the authors focus on the latter approach and provide a joint overview of established and recent models, including independent component analysis, local time-frequency models and spectral template-based models. They show that most models are instances of one of the following two general paradigms: linear modeling or variance modeling. They compare the merits of either paradigm and report objective performance figures. They also,conclude by discussing promising combinations of probabilistic priors and inference algorithms that could form the basis of future state-of-the-art systems

Dictionary Learning for Sparse Representations With Applications to Blind Source Separation.

During the past decade, sparse representation has attracted much attention in the signal processing community. It aims to represent a signal as a linear combination of a small number of elementary signals called atoms. These atoms constitute a dictionary so that a signal can be expressed by the multiplication of the dictionary and a sparse coefficients vector. This leads to two main challenges that are studied in the literature, i.e. sparse coding (find the coding coefficients based on a given dictionary) and dictionary design (find an appropriate dictionary to fit the data). Dictionary design is the focus of this thesis. Traditionally, the signals can be decomposed by the predefined mathematical transform, such as discrete cosine transform (DCT), which forms the so-called analytical approach. In recent years, learning-based methods have been introduced to adapt the dictionary from a set of training data, leading to the technique of dictionary learning. Although this may involve a higher computational complexity, learned dictionaries have the potential to offer improved performance as compared with predefined dictionaries. Dictionary learning algorithm is often achieved by iteratively executing two operations: sparse approximation and dictionary update. We focus on the dictionary update step, where the dictionary is optimized with a given sparsity pattern. A novel framework is proposed to generalize benchmark mechanisms such as the method of optimal directions (MOD) and K-SVD where an arbitrary set of codewords and the corresponding sparse coefficients are simultaneously updated, hence the term simultaneous codeword optimization (SimCO). Moreover, its extended formulation ‘regularized SimCO’ mitigates the major bottleneck of dictionary update caused by the singular points. First and second order optimization procedures are designed to solve the primitive and regularized SimCO. In addition, a tree-structured multi-level representation of dictionary based on clustering is used to speed up the optimization process in the sparse coding stage. This novel dictionary learning algorithm is also applied for solving the underdetermined blind speech separation problem, leading to a multi-stage method, where the separation problem is reformulated as a sparse coding problem, with the dictionary being learned by an adaptive algorithm. Using mutual coherence and sparsity index, the performance of a variety of dictionaries for underdetermined speech separation is compared and analyzed, such as the dictionaries learned from speech mixtures and ground truth speech sources, as well as those predefined by mathematical transforms. Finally, we propose a new method for joint dictionary learning and source separation. Different from the multistage method, the proposed method can simultaneously estimate the mixing matrix, the dictionary and the sources in an alternating and blind manner. The advantages of all the proposed methods are demonstrated over the state-of-the-art methods using extensive numerical tests

Blind source separation using statistical nonnegative matrix factorization

PhD ThesisBlind Source Separation (BSS) attempts to automatically extract and track a signal of interest in real world scenarios with other signals present. BSS addresses the problem of recovering the original signals from an observed mixture without relying on training knowledge. This research studied three novel approaches for solving the BSS problem based on the extensions of non-negative matrix factorization model and the sparsity regularization methods. 1) A framework of amalgamating pruning and Bayesian regularized cluster nonnegative tensor factorization with Itakura-Saito divergence for separating sources mixed in a stereo channel format: The sparse regularization term was adaptively tuned using a hierarchical Bayesian approach to yield the desired sparse decomposition. The modified Gaussian prior was formulated to express the correlation between different basis vectors. This algorithm automatically detected the optimal number of latent components of the individual source. 2) Factorization for single-channel BSS which decomposes an information-bearing matrix into complex of factor matrices that represent the spectral dictionary and temporal codes: A variational Bayesian approach was developed for computing the sparsity parameters for optimizing the matrix factorization. This approach combined the advantages of both complex matrix factorization (CMF) and variational -sparse analysis. BLIND SOURCE SEPARATION USING STATISTICAL NONNEGATIVE MATRIX FACTORIZATION ii 3) An imitated-stereo mixture model developed by weighting and time-shifting the original single-channel mixture where source signals can be modelled by the AR processes. The proposed mixing mixture is analogous to a stereo signal created by two microphones with one being real and another virtual. The imitated-stereo mixture employed the nonnegative tensor factorization for separating the observed mixture. The separability analysis of the imitated-stereo mixture was derived using Wiener masking. All algorithms were tested with real audio signals. Performance of source separation was assessed by measuring the distortion between original source and the estimated one according to the signal-to-distortion (SDR) ratio. The experimental results demonstrate that the proposed uninformed audio separation algorithms have surpassed among the conventional BSS methods; i.e. IS-cNTF, SNMF and CMF methods, with average SDR improvement in the ranges from 2.6dB to 6.4dB per source.Payap Universit

Tensor based singular spectrum analysis for automatic scoring of sleep EEG

A new supervised approach for decomposition of single channel signal mixtures is introduced in this paper. The performance of the traditional singular spectrum analysis (SSA) algorithm is significantly improved by applying tensor decomposition instead of traditional singular value decomposition (SVD). As another contribution to this subspace analysis method, the inherent frequency diversity of the data has been effectively exploited to highlight the subspace of interest. As an important application, sleep EEG has been analysed and the stages of sleep for the subjects in normal condition, with sleep restriction, and with sleep extension have been accurately estimated and compared with the results of sleep scoring by clinical experts