An Effective Iterative Solution for Independent Vector Analysis With Convergence Guarantees

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.

The noncircular fast independent vector analysis (nc-FastIVA) algorithm is an effective approach to achieve the joint blind source separation (JBSS) problem. However, the original nc-FastIVA algorithm does not take noise into account. In this letter, a new fixed-point algorithm is proposed for more realistic cases when noise is present. Simulations show that the proposed method can have better performance than the original nc-FastIVA algorithm for solving the noisy JBSS problem.

Complex-valued independent vector analysis: Application to multivariate Gaussian model

Joint blind source separation (JBSS) is a means to extract common sources simultaneously found across multiple datasets, e.g., electroencephalogram (EEG) and kinematic data jointly recorded during reaching movements. Existing JBSS approaches are designed to handle multidimensional datasets, yet to our knowledge, there is no existing means to examine common components that may be found across a unidimensional dataset and a multidimensional one. In this paper, we propose a simple, yet effective method to achieve the goal of JBSS when concurrent multidimensional EEG and unidimensional kinematic datasets are available, by combining ensemble empirical mode decomposition (EEMD) with independent vector analysis (IVA). We demonstrate the performance of the proposed method through numerical simulations and application to data collected from reaching movements in Parkinson's disease. The proposed method is a promising JBSS tool for real-world biomedical signal processing applications.

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

Independent Vector Analysis (IVA) has become a widely used approach for blind source separation in functional Magnetic Resonance Imaging (fMRI) data analysis. However, IVA requires prior specification of the number of sources (model order), which often needs to be overestimated. This is further associated with higher computational complexity and the need to identify target components, as their order is random. To address this problem, we explore an alternative framework based on source extraction, which targets a particular Source of Interest (SOI). Specifically, we employ the informed FastIVE (iFIVE) algorithm, which utilizes a prior spatial template to steer the extraction towards the desired component, enhancing both separation quality and convergence stability. Experiments on simulated fMRI demonstrate that iFIVE achieves superior extraction accuracy and significantly reduced computational requirements compared to state-of-the-art blind and constrained IVA methods.

To solve the problem of joint blind equalization and source separation, two new quasi-Newton 'adaptive algorithms with rapid convergence property are proposed based upon the cross-correlation and constant modulus (CC-CM) criterion, namely the block-Shanno cross-correlation and constant modulus algorithm (BS-CCCMA) and the fast quasi-Newton cross-correlation and constant modulus algorithm (FQN-CCCMA). Simulations studies are used to show that the convergence properties of these algorithms are much improved upon those of the conventional LMS-CCCMA algorithm.

Analysis of time-evolving data is crucial to understand the functioning of dynamic systems such as the brain. For instance, analysis of functional magnetic resonance imaging (fMRI) data collected during a task may reveal spatial regions of interest, and how they evolve during the task. However, capturing underlying spatial patterns as well as their change in time is challenging. The traditional approach in fMRI data analysis is to assume that underlying spatial regions of interest are static. In this article, using fractional amplitude of low-frequency fluctuations (fALFF) as an effective way to summarize the variability in fMRI data collected during a task, we arrange time-evolving fMRI data as a subjects by voxels by time windows tensor, and analyze the tensor using a tensor factorization-based approach called a PARAFAC2 model to reveal spatial dynamics. The PARAFAC2 model jointly analyzes data from multiple time windows revealing subject-mode patterns, evolving spatial regions (also referred to as networks) and temporal patterns. We compare the PARAFAC2 model with matrix factorization-based approaches relying on independent components, namely, joint independent component analysis (ICA) and independent vector analysis (IVA), commonly used in neuroimaging data analysis. We assess the performance of the methods in terms of capturing evolving networks through extensive numerical experiments demonstrating their modeling assumptions. In particular, we show that (i) PARAFAC2 provides a compact representation in all modes, i.e., subjects, time, and voxels, revealing temporal patterns as well as evolving spatial networks, (ii) joint ICA is as effective as PARAFAC2 in terms of revealing evolving networks but does not reveal temporal patterns, (iii) IVA's performance depends on sample size, data distribution and covariance structure of underlying networks. When these assumptions are satisfied, IVA is as accurate as the other methods, (iv) when subject-mode patterns differ from one time window to another, IVA is the most accurate. Furthermore, we analyze real fMRI data collected during a sensory motor task, and demonstrate that a component indicating statistically significant group difference between patients with schizophrenia and healthy controls is captured, which includes primary and secondary motor regions, cerebellum, and temporal lobe, revealing a meaningful spatial map and its temporal change.

A novel method is proposed to improve the performance of independent vector analysis (IVA) for blind signal separation of acoustic mixtures. IVA is a frequency-domain approach that successfully resolves the well-known permutation problem by applying a spherical dependency model to all pairs of frequency bins. The dependency model of IVA is equivalent to a single clique in an undirected graph; a clique in graph theory is defined as a subset of vertices in which any pair of vertices is connected by an undirected edge. Therefore, IVA imposes the same amount of statistical dependency on every pair of frequency bins, which may not match the characteristics of real-world signals. The proposed method allows variable amounts of statistical dependencies according to the correlation coefficients observed in real acoustic signals and, hence, enables more accurate modeling of statistical dependencies. A number of cliques constitutes the new dependency graph so that neighboring frequency bins are assigned to the same clique, while distant bins are assigned to different cliques. The permutation ambiguity is resolved by overlapped frequency bins between neighboring cliques. For speech signals, we observed especially strong correlations across neighboring frequency bins and a decrease in these correlations with an increase in the distance between bins. The clique sizes are either fixed, or determined by the reciprocal of the mel-frequency scale to impose a wider dependency on low-frequency components. Experimental results showed improved performances over conventional IVA. The signal-to-interference ratio improved from 15.5 to 18.8 dB on average for seven different source locations. When we varied the clique sizes according to the observed correlations, the stability of the proposed method increased with a large number of cliques.

Speeches in real world environment are normally mixed together convolutedly. The speech mixtures are not instantaneous at all. Rather speeches are mixed component wise. Independent Vector Analysis (IVA) is an approach for separating convolutive mixture in frequency domain. Entropy estimation is an important part of IVA. In this paper, IVA is implemented by estimating entropy using recursive copula splitting. It measures entropy by decomposing probability density function (PDF) into a product of marginal (1D) densities and a copula. This entropy estimator improves IVA performance in different types of real world speech mixtures. We have proved that by estimating entropy using recursive copula splitting makes IVA algorithm simple and more efficient.'

Independent vector analysis (IVA) generalizes independent component analysis (ICA) to multiple datasets, and when used with a multivariate Gaussian model (IVA-G), provides a powerful tool for joint analysis of multiple datasets in an array of applications. While IVA-G enjoys uniqueness guarantees, the current solution to the problem exhibits significant variability across runs necessitating the use of a scheme for selecting the most consistent one, which is costly. In this paper, we present a penalized maximum-likelihood framework for the problem, which enables us to derive a non-convex cost function that depends on the precision matrices of the source component vectors, the main mechanism by which IVA-G leverages correlation across the datasets. By adding a quadratic regularization, a block-coordinate proximal algorithm is shown to offer a suitable solution to this minimization problem. The proposed method also provides convergence guarantees that are lacking in other state-of-the-art approaches to the problem. This also allows us to obtain overall slightly better performance, and in particular, we show that our method yields better estimation in average than the current IVA-G algorithm for various source numbers, datasets, and degrees of correlation across the data.

The independent vector analysis (IVA) algorithm employs a multivariate source prior to retain the dependency between different frequency bins of each source and thereby avoids the permutation problem that is inherent to blind source separation (BSS). In this paper, a multivariate Student's t distribution is adopted as the source prior, which because of its heavy tail nature can better model the large amplitude information in the frequency bins. Therefore it can improve the separation performance and the convergence speed of the IVA and fast version of the IVA (FastIVA) algorithms as compared with the IVA algorithm based on another multivariate super Gaussian source prior. Separation performance with real binaural room impulse responses (BRIRs) is evaluated by detailed simulation studies when using the different source priors, and the experimental results confirm that the IVA and the FastIVA with the proposed multivariate Student's t source prior can consistently achieve improved and faster separation performance.

In this paper, we present a quasi-Newton (QN) algorithm for joint independent subspace analysis (JISA). JISA is a recently proposed generalization of independent vector analysis (IVA). JISA extends classical blind source separation (BSS) to jointly resolve several BSS problems by exploiting statistical dependence between latent sources across mixtures, as well as relaxing the assumption of statistical independence within each mixture. Algebraically, JISA based on second-order statistics amounts to coupled block diagonalization of a set of covariance and cross-covariance matrices, as well as block diagonalization of a single permuted covariance matrix. The proposed QN algorithm achieves asymptotically the minimal mean square error (MMSE) in the separation of multidimensional Gaussian components. Numerical experiments demonstrate convergence and source separation properties of the proposed algorithm.KeywordsBlind source separationIndependent vector analysisIndependent subspace analysisJoint block diagonalization

Steady state visual evoked potentials (SSVEPs) have been identified as an effective solution for brain computer interface (BCI) systems as well as for neurocognitive investigations. SSVEPs can be observed in the scalp-based recordings of electroencephalogram signals, and are one component buried amongst the normal brain signals and complex noise. We present a novel method for enhancing and improving detection of SSVEPs by leveraging the rich joint blind source separation framework using independent vector analysis (IVA). IVA exploits the diversity within each dataset while preserving dependence across all the datasets. This approach is shown to enhance the detection of SSVEP signals across a range of frequencies and subjects for BCI systems. Furthermore, we show that IVA enables improved topographic mapping of the SSVEP propagation providing a promising new tool for neuroscience and neurocognitive research.