Independent Vector Analysis Algorithm Research Articles

Constrained Independent Vector Analysis with Reference for Multi-Subject fMRI Analysis.

Independent component analysis (ICA) is now a widely used solution for the analysis of multi-subject functional magnetic resonance imaging (fMRI) data. Independent vector analysis (IVA) generalizes ICA to multiple datasets (multi-subject data). Along with higher-order statistical information in ICA, it leverages the statistical dependence across the datasets as an additional type of statistical diversity. As such, IVA preserves variability in the estimation of single-subject maps but its performance might suffer when the number of datasets increases. Constrained IVA is an effective way to bypass computational issues and improve the quality of separation by incorporating available prior information. Existing constrained IVA approaches often rely on user-defined threshold values to define the constraints. However, an improperly selected threshold can have a negative impact on the final results. This paper proposes two novel methods for constrained IVA: one using an adaptive-reverse scheme to select variable thresholds for the constraints and a second one based on a threshold-free formulation by leveraging the unique structure of IVA. Notably, the proposed algorithms do not require all components to be constrained, utilizing free components to model interferences and components that might not be in the reference set. We demonstrate that our solutions provide an attractive solution to multi-subject fMRI analysis both by simulations and through analysis of resting state fMRI data collected from 98 subjects - the highest number of subjects ever used by IVA algorithms. Our results show that both proposed approaches obtain significantly better separation quality and model match while providing computationally efficient and highly reproducible solutions.

The effect of source sparsity on independent vector analysis for blind source separation

In this paper, the effect of source sparsity on the performance of the independent vector analysis (IVA) algorithm for blind source separation is investigated. The IVA algorithm was originally developed under the assumption of statistical independence between the sources and has made great advances in recent years. However, its performance under different sparsity conditions is rarely studied. This study begins by mathematically analyzing the performance of IVA in permutation alignment, which is proved to directly correlate with the degree of frame-level W-disjoint orthogonality (F-WDO) of the sources. We further prove that IVA can theoretically achieve the optimal separation in the cases where the sources are F-WDO. Experimental results show a strong positive correlation between a quantitative measure of F-WDO and the IVA algorithm’s performance under various conditions.

An Efficient Convolutional Blind Source Separation Algorithm for Speech Signals under Chaotic Masking

As the main method of information transmission, it is particularly important to ensure the security of speech communication. Considering the more complex multipath channel transmission situation in the wireless communication of speech signals and separating or extracting the source signal from the convolutional signal are crucial steps in obtaining source information. In this paper, chaotic masking technology is used to guarantee the transmission safety of speech signals, and a fast fixed-point independent vector analysis algorithm is used to solve the problem of convolutional blind source separation. First, the chaotic masking is performed before the speech signal is sent, and the convolutional mixing process of multiple signals is simulated by impulse response filter. Then, the observed signal is transformed to the frequency domain by short-time Fourier transform, and instantaneous blind source separation is performed using a fast fixed-point independent vector analysis algorithm. The algorithm can preserve the high-order statistical correlation between frequencies to solve the permutation ambiguity problem in independent component analysis. Simulation experiments show that this algorithm can efficiently complete the blind extraction of convolutional signals, and the quality of recovered speech signals is better. It provides a solution for the secure transmission and effective separation of speech signals in multipath transmission channels.

An Expectation–Maximization-Based IVA Algorithm for Speech Source Separation Using Student’s t Mixture Model Based Source Priors

The performance of the independent vector analysis (IVA) algorithm depends on the choice of the source prior to better model the speech signals as it employs a multivariate source prior to retain the dependency between frequency bins of each source. Identical source priors are frequently used for the IVA methods; however, different speech sources will generally have different statistical properties. In this work, instead of identical source priors, a novel Student’s t mixture model based source prior is introduced for the IVA algorithm that can adapt to the statistical properties of different speech sources and thereby enhance the separation performance of the IVA algorithm. The unknown parameters of the source prior and unmixing matrices are estimated together by deriving an efficient expectation maximization (EM) algorithm. Useful improvement in the separation performance in different realistic scenarios is confirmed by experimental studies on real datasets.

Decoupled Independent Vector Analysis Algorithm for Convolutive Blind Source Separation without Orthogonality Constraint on the Demixing Matrices

In this paper, we consider the problem of convolutive blind source separation in frequency domain and introduce a solution to the problem in an independent vector analysis (IVA) framework. IVA utilizes both the statistical independence of different sources in each frequency bin and the statistical dependence of the same source in different frequency bins. However, most of previous works impose orthogonality constraint on the rows of each separation matrix which may undermine the separation performance. In this work, we propose a nonorthogonal IVA algorithm based on decoupled relative Newton method. This proposed algorithm updates the separation matrices row by row, and unlike deflation separation algorithm, there is no separation error accumulation arising. Simulation results are provided to show the superior convergence behavior and separation performance of the proposed algorithm.

An Acoustic Signal Enhancement Method Based on Independent Vector Analysis for Moving Target Classification in the Wild.

In this paper, we study how to improve the performance of moving target classification by using an acoustic signal enhancement method based on independent vector analysis (IVA) in the unattended ground sensor (UGS) system. Inspired by the IVA algorithm, we propose an improved IVA method based on a microphone array for acoustic signal enhancement in the wild, which adopts a particular multivariate generalized Gaussian distribution as the source prior, an adaptive variable step strategy for the learning algorithm and discrete cosine transform (DCT) to convert the time domain observed signals to the frequency domain. We term the proposed method as DCT-G-IVA. Moreover, we design a target classification system using the improved IVA method for signal enhancement in the UGS system. Different experiments are conducted to evaluate the proposed method for acoustic signal enhancement by comparing with the baseline methods in our classification system under different wild environments. The experimental results validate the superiority of the DCT-G-IVA enhancement method in the classification system for moving targets in the presence of dynamic wind noise.

Adaptive independent vector analysis for multi-subject complex-valued fMRI data

BackgroundComplex-valued fMRI data can provide additional insights beyond magnitude-only data. However, independent vector analysis (IVA), which has exhibited great potential for group analysis of magnitude-only fMRI data, has rarely been applied to complex-valued fMRI data. The main challenges in this application include the extremely noisy nature and large variability of the source component vector (SCV) distribution. New methodTo address these challenges, we propose an adaptive fixed-point IVA algorithm for analyzing multiple-subject complex-valued fMRI data. We exploited a multivariate generalized Gaussian distribution (MGGD)- based nonlinear function to match varying SCV distributions in which the MGGD shape parameter was estimated using maximum likelihood estimation. To achieve our de-noising goal, we updated the MGGD-based nonlinearity in the dominant SCV subspace, and employed a post-IVA de-noising strategy based on phase information in the IVA estimates. We also incorporated the pseudo-covariance matrix of fMRI data into the algorithm to emphasize the noncircularity of complex-valued fMRI sources. ResultsResults from simulated and experimental fMRI data demonstrated the efficacy of our method. Comparison with existing method(s)Our approach exhibited significant improvements over typical complex-valued IVA algorithms, especially during higher noise levels and larger spatial and temporal changes. As expected, the proposed complex-valued IVA algorithm detected more contiguous and reasonable activations than the magnitude-only method for task-related (393%) and default mode (301%) spatial maps. ConclusionsThe proposed approach is suitable for decomposing multi-subject complex-valued fMRI data, and has great potential for capturing additional subject variability.

Independent vector analysis with a generalized multivariate Gaussian source prior for frequency domain blind source separation

Independent vector analysis (IVA) is designed to retain the dependency within individual source vectors, while removing the dependency between different source vectors. It can theoretically avoid the permutation problem inherent to independent component analysis (ICA). The dependency in each source vector is retained by adopting a multivariate source prior instead of a univariate source prior. In this paper, a multivariate generalized Gaussian distribution is adopted as the source prior which can exploit frequency domain energy correlation within each source vector. As such, it can utilize more information describing the dependency structure and provide improved source separation performance. This proposed source prior is suitable for the whole family of IVA algorithms and found to be more robust in applications where non-stationary signals are separated than the one preferred by Lee. Experimental results on real speech signals confirm the advantage of adopting the proposed source prior on three types of IVA algorithm.

Independent vector analysis with multivariate student's t ‐distribution source prior for speech separation

The independent vector analysis algorithm can theoretically avoid the permutation problem in frequency domain blind source separation by using a multivariate source prior to retain the dependency between different frequency bins of each source. A super-Gaussian multivariate Student's t-distribution is adopted as the source prior to model the spectrum of speech signals and to mitigate imprecise variance knowledge as is commonplace in non-stationary signal processing. Moreover, the new multivariate source prior can be interpreted as a joint distribution constructed by a t-copula, which can describe the nonlinear inter-frequency dependency. Experimental results using 50 speech mixtures formed from the TIMIT database confirm the advantages of the proposed algorithm.

Independent Vector Analysis: Identification Conditions and Performance Bounds

Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has also been shown to be a generalization of Hotelling's canonical correlation analysis. In this paper, we provide the identification conditions for a general IVA formulation, which accounts for linear, nonlinear, and sample-to-sample dependencies. The identification conditions are a generalization of previous results for ICA and for IVA when samples are independently and identically distributed. Furthermore, a principal aim of IVA is the identification of dependent sources between datasets. Thus, we provide the additional conditions for when the arbitrary ordering of the sources within each dataset is common. Performance bounds in terms of the Cramer-Rao lower bound are also provided for the demixing matrices and interference to source ratio. The performance of two IVA algorithms are compared to the theoretical bounds.

Non-unitary matrix joint diagonalization for complex independent vector analysis

Independent vector analysis (IVA) is a special form of independent component analysis (ICA), which has demonstrated its prominent performance in solving convolutive blind source separation (BSS) problems in the frequency domain. Most IVA algorithms are based on optimizing certain contrast functions, where the main difficulty of these approaches lies in finding a reliable and fast estimation of the unknown distribution of sources. Despite the rich availability of efficient tensorial approaches to the standard ICA problem, these methods have not been explored considerably for IVA. In this article, we propose a matrix joint diagonalization approach to solve the complex IVA problem. The new factorization neither relies on a whitening process, nor does it require an estimate of the joint probability distribution of the dependent signal groups. The latter is in contrast to most IVA approaches up to date. The underlying geometry of the problem is investigated together with a critical point analysis of the resulting cost function. A conjugate gradient algorithm on the appropriate manifold setting is developed.

Audio video based fast fixed-point independent vector analysis for multisource separation in a room environment

Fast fixed-point independent vector analysis (FastIVA) is an improved independent vector analysis (IVA) method, which can achieve faster and better separation performance than original IVA. As an example IVA method, it is designed to solve the permutation problem in frequency domain independent component analysis by retaining the higher order statistical dependency between frequencies during learning. However, the performance of all IVA methods is limited due to the dimensionality of the parameter space commonly encountered in practical frequency-domain source separation problems and the spherical symmetry assumed with the source model. In this article, a particular permutation problem encountered in using the FastIVA algorithm is highlighted, namely the block permutation problem. Therefore a new audio video based fast fixed-point independent vector analysis algorithm is proposed, which uses video information to provide a smart initialization for the optimization problem. The method cannot only avoid the ill convergence resulting from the block permutation problem but also improve the separation performance even in noisy and high reverberant environments. Different multisource datasets including the real audio video corpus AV16.3 are used to verify the proposed method. For the evaluation of the separation performance on real room recordings, a new pitch based evaluation criterion is also proposed.

Independent vector analysis for source separation using a mixture of gaussians prior.

Convolutive mixtures of signals, which are common in acoustic environments, can be difficult to separate into their component sources. Here we present a uniform probabilistic framework to separate convolutive mixtures of acoustic signals using independent vector analysis (IVA), which is based on a joint distribution for the frequency components originating from the same source and is capable of preventing permutation disorder. Different gaussian mixture models (GMM) served as source priors, in contrast to the original IVA model, where all sources were modeled by identical multivariate Laplacian distributions. This flexible source prior enabled the IVA model to separate different type of signals. Three classes of models were derived and tested: noiseless IVA, online IVA, and noisy IVA. In the IVA model without sensor noise, the unmixing matrices were efficiently estimated by the expectation maximization (EM) algorithm. An online EM algorithm was derived for the online IVA algorithm to track the movement of the sources and separate them under nonstationary conditions. The noisy IVA model included the sensor noise and combined denoising with separation. An EM algorithm was developed that found the model parameters and separated the sources simultaneously. These algorithms were applied to separate mixtures of speech and music. Performance as measured by the signal-to-interference ratio (SIR) was substantial for all three models.

Independent vector analysis (IVA) for group fMRI processing of subcortical area

During functional MRI (fMRI) studies, blood oxygenation-level dependent (BOLD) signal associated with neuronal activity acquired from multiple individuals are subject to the derivation of group-averaged brain activation patterns. Unlike other cortical areas, subcortical areas such as the thalamus and basal ganglia often manifest smaller, biphasic BOLD signal that are aberrant from signals originating from cortices. Independent component analysis (ICA) can offer session/individual specific brain activation maps without a priori assumptions regarding the timing or pattern of the signal responses. The small activation loci within the subcortical areas are sparsely distributed among the subjects, and a conventional group processing method based on the general linear model (GLM) or ICA may fail to characterize the activation loci. In this paper, we present an independent vector analysis (IVA) to overcome these limitations by offering an analysis of additional dependent components (compared to the ICA-based method) that are assigned for use in the automated grouping of dependent (i.e. similar) activation patterns across subjects. The proposed IVA algorithm was applied to simulated data, and its utility was confirmed from real fMRI data employing a trial-based hand motor task. A GLM and the group ICA of the fMRI toolbox (GIFT) were also applied for comparison. From the analysis of activation patterns within subcortical areas, in which the hemodynamic responses (HRs) often deviate from a canonical, model-driven HR, IVA detected task-related activation loci that were not detected through GLM and GIFT. IVA may offer a unique advantage for inferring group activation originating from subcortical areas.

On the Assumption of Spherical Symmetry and Sparseness for the Frequency-Domain Speech Model

A new independent component analysis (ICA) formulation called independent vector analysis (IVA) was proposed in order to solve the permutation problem in convolutive blind source separation (BSS). Instead of running ICA in each frequency bin separately and correcting the disorder with an additional algorithmic scheme afterwards, IVA exploited the dependency among the frequency components of a source and dealt with them as a multivariate source by modeling it with sparse and spherically, or radially, symmetric joint probability density functions (pdfs). In this paper, we compare the speech separation performances of IVA by using a group of l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> -norm-invariant sparse pdfs where the value of and the sparseness can be controlled. Also, we derive an IVA algorithm from a nonparametric perspective with the constraint of spherical symmetry and high dimensionality. Simulation results confirm the efficiency of assuming sparseness and spherical symmetry for the speech model in the frequency domain.

Fast fixed-point independent vector analysis algorithms for convolutive blind source separation

A new type of independent component analysis (ICA) model showed excellence in tackling the blind source separation problem in the frequency domain. The new model, called independent vector analysis, is an extension of ICA for (independent) multivariate sources where the sources are mixed component-wise. In this work we examine available contrasts for the new formulation that can solve the frequency-domain blind source separation problem. Also, we introduce a quadratic Taylor polynomial in the notations of complex variables which is very useful in directly applying Newton's method to a contrast function of complex-valued variables. The use of the form makes the derivation of a Newton update rule simple and clear. Fast fixed-point blind source separation algorithms are derived and the performance is shown by experimental results.