Capturing group variability using IVA: A simulation study and graph-theoretical analysis

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.

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.

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 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.

Independent vector analysis followed by HMM-based feature enhancement for robust speech recognition

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.'

With the development of nondestructive detection, the emerging testing techniques provide new challenges to signal analysis and interpretation approach applied to the inspection evaluation. Some researchers have developed the methods that focus on feature analysis of detected signals. This article presents a new feature analysis by the Independent Component Analysis (ICA) approach to evaluate the defects tested by the pulsed eddy current (PEC) technique. ICA is a high-order statistics technique used to separate multi-unknown sources, which has been successfully applied to facial image identification and separation of the components of 1D signal. In this article, the ICA approach is utilized to project the response signals of various defects into the independent components (ICs) feature subspace by signal representation model. Dependent on the selected ICs, each defect is represented by different projected coefficients, which are proposed to discriminate and classify the defects that belong to three categories. The improved ICA model is proposed to improve the classification of two similar categories of single defects: metal loss and subsurface defects. The evaluation using the series of experimental data has validated the classification of single defects and the defects with lift-off effect by our ICA approach. The comparison with Principal component analysis (PCA)–based approach further verified the better performance of the ICA-based model.

Electrocardiogram (ECG) signals are normally contaminated by various physiological and nonphysiological artifacts. Among these artifacts baseline wandering, electrode movement and muscle artifacts are particularly difficult to remove. Independent component analysis (ICA) is a well-known technique of blind source separation (BSS) and is extensively used in literature for ECG artifact elimination. In this article, the independent vector analysis (IVA) is used for artifact removal in the ECG data. This technique takes advantage of both the canonical correlation analysis (CCA) and the ICA due to the utilization of second-order and high order statistics for un-mixing of the recorded mixed data. The utilization of recorded signals along with their delayed versions makes the IVA-based technique more practical. The proposed technique is evaluated on real and simulated ECG signals and it shows that the proposed technique outperforms the CCA and ICA because it removes the artifacts while altering the ECG signals minimally.

Dynamic functional connectivity analysis is an effective way to capture the networks that are functionally associated and continuously changing over the scanning period. However, these methods mostly analyze the dynamic associations across the activation patterns of the spatial networks while assuming that the spatial networks are stationary. Hence, a model that allows for the variability in both domains and reduces the assumptions imposed on the data provides an effective way for extracting spatiotemporal networks. Independent vector analysis (IVA) is a joint blind source separation technique that allows for estimation of spatial and temporal features while successfully preserving variability. However, its performance is affected for higher number of datasets. Hence, we develop an effective two-stage method to extract time-varying spatial and temporal features using IVA, mitigating the problems with higher number of datasets while preserving the variability across subjects and time. The first stage is used to extract reference signals using group-independent component analysis (GICA) that are used in a parameter-tuned constrained IVA framework to estimate time-varying representations of these signals by preserving the variability through tuning the constraint parameter. This approach effectively captures variability across time from a large-scale resting-state fMRI data acquired from healthy controls and patients with schizophrenia and identifies more functionally relevant connections that are significantly different among healthy controls and patients with schizophrenia, compared with the widely used GICA method alone.

Individuals with Autism Spectrum Conditions (ASC) have difficulties in social interaction and communication, which is reflected in hypoactivation of brain regions engaged in social processing, such as medial prefrontal cortex (mPFC), amygdala and insula. Resting state studies in ASC have identified reduced connectivity of the default mode network (DMN), which includes mPFC, suggesting that other resting state networks incorporating ‘social’ brain regions may also be abnormal. Using Seed-based Connectivity and Group Independent Component Analysis (ICA) approaches, we looked at resting functional connectivity in ASC between specific ‘social’ brain regions, as well as within and between whole networks incorporating these regions. We found reduced functional connectivity within the DMN in individuals with ASC, using both ICA and seed-based approaches. Two further networks identified by ICA, the salience network, incorporating the insula and a medial temporal lobe network, incorporating the amygdala, showed reduced inter-network connectivity. This was underlined by reduced seed-based connectivity between the insula and amygdala. The results demonstrate significantly reduced functional connectivity within and between resting state networks incorporating ‘social’ brain regions. This reduced connectivity may result in difficulties in communication and integration of information across these networks, which could contribute to the impaired processing of social signals in ASC.

Identification of homogeneous subgroups of subjects plays a key role in the study of precision medicine. While there are a number of approaches based on the clustering of low-level features such as behavioral variables, work that makes use of fully multivariate nature of medical imaging data is very limited. Given that the individual variability in brain functional networks obtained from functional magnetic resonance imaging (fMRI) data is noted as being both significant and consistent like fingerprints, its use provides a particularly appealing approach to this challenging problem. We present a completely data-driven approach, subgroup identification using independent vector analysis (SI-IVA), which leverages the desirable properties of IVA to uncover the relationship across subjects along with the discovery of subgroup structures revealed by Gershgorin disc theorem. We show that SI-IVA outperforms an eigenanalysis-based approach by simulations. We then apply the method to real fMRI data obtained from patients of during resting state to identify group differences in multiple relevant brain regions including primary somatosensory and motor cortex, which demonstrates that SI-IVA provides interpretable and meaningful results.

A data-driven unsupervised learning such as an independent component analysis was gainfully applied to bloodoxygenation- level-dependent (BOLD) functional magnetic resonance imaging (fMRI) data compared to a model-based general linear model (GLM). This is due to an ability of this unsupervised learning method to extract a meaningful neuronal activity from BOLD signal that is a mixture of confounding non-neuronal artifacts such as head motions and physiological artifacts as well as neuronal signals. In this study, we support this claim by identifying neuronal underpinnings of cigarette craving and cigarette resistance. The fMRI data were acquired from heavy cigarette smokers (n = 14) while they alternatively watched images with and without cigarette smoking. During acquisition of two fMRI runs, they were asked to crave when they watched cigarette smoking images or to resist the urge to smoke. Data driven approaches of group independent component analysis (GICA) method based on temporal concatenation (TC) and TCGICA with an extension of iterative dual-regression (TC-GICA-iDR) were applied to the data. From the results, cigarette craving and cigarette resistance related neuronal activations were identified in the visual area and superior frontal areas, respectively with a greater statistical significance from the TC-GICA-iDR method than the TC-GICA method. On the other hand, the neuronal activity levels in many of these regions were not statistically different from the GLM method between the cigarette craving and cigarette resistance due to potentially aberrant BOLD signals.

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.

Independent vector analysis (IVA) can be viewed as an extension of independent component analysis (ICA) to multiple datasets. It exploits the statistical dependency between different datasets through mutual information. In the context of motor imagery classification based on electroencephalogram (EEG) signals for the brain-computer interface (BCI), several methods have been proposed to extract features efficiently, mainly based on common spatial patterns, filter banks, and deep learning. However, most methods use only one dataset at a time, which may not be sufficient for dealing with a multi-source retrieving problem in certain scenarios. From this perspective, this paper proposes an original approach for feature extraction through multiple datasets based on IVA to improve the classification of EEG-based motor imagery movements. The IVA components were used as features to classify imagined movements using consolidated classifiers (support vector machines and K-nearest neighbors) and deep classifiers (EEGNet and EEGInception). The results show an interesting performance concerning the clustering of MI-based BCI patients, and the proposed method reached an average accuracy of 86.7%.

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.