Non-unitary matrix joint diagonalization for complex independent vector 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.

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 followed by HMM-based feature enhancement for robust speech recognition

When applied to functional magnetic resonance imaging (fMRI) data, independent vector analysis (IVA) provides superior performance in capturing subject variability within one group, as compared to the widely used group independent component analysis (ICA) approach. However, the effectiveness of IVA algorithms in preserving variability between different groups of subjects has not been studied yet, although it is of great interest in most fMRI studies, especially for identifying biomarkers for diagnosis of mental disorders. In this paper, we introduce a methodology that uses graph-theoretical analysis and statistical analysis for assessing the ability of IVA algorithms to capture group variability. We generate multi-subject fMRI-like datasets with increasing spatial variability for a selected component between two groups and compare a robust IVA algorithm to group ICA approach. Our experimental results show that IVA can successfully preserve group variability, indicating its potential in extracting biomarkers across groups of subjects in fMRI analysis.

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.

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.'

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.

The issue of convolutive blind source separation (BSS) is addressed in this paper. Independent low-rank matrix analysis (ILRMA), unifying frequency-domain independent component analysis (FDICA) and nonnegative matrix factorization (NMF), is a method that has recently proposed to model low-rank structure of source spectra by using NMF in addition to independence between sources used in FDICA and independent vector analysis (IVA). Although ILRMA has been shown to provide better separation performance than FDICA and IVA, the frequency components of each source are assumed to be independent in ILRMA due to NMF modeling of source spectra, which may degrade its performance when the short-term Fourier transform (STFT) is unable to decorrelate the frequency components for each source. This paper therefore presents a new BSS method that unifies IVA and positive semidefinite tensor factorization (PSDTF). PSDTF models not only power spectra in the same way NMF does but also models the correlations between frequency bins in each source. The proposed method can be viewed as a multichannel extension of PSDTF and exploits both the independence between sources and the inter-frequency correlations as a clue for separating mixtures. Experimental results indicate the improved performance of our approach.

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%.

We present a new approach to independent component analysis (ICA) by extending the formulation of univariate source signals to multivariate source signals. The new approach is termed independent vector analysis (IVA). In the model, we assume that linear mixing model exists in each dimension separately, and the latent sources are independent of the others. In contrast to ICA, the sources are random vectors, not just single variables, which means the elements of a random vector are closely related to the others. Thus, we assume the dependency between the elements of a source vector. In this manner, we define dependence between vectors as Kullback-Leibler divergence between the total joint probability of vectors and the product of marginal probabilities of vectors. Then, the model allows independence between multivariate source signals represented as random vectors, and dependence between the source signals within the vector representation. The proposed vector density model can for example capture variance dependencies within a vector source signal. There are several applications of this new formulation. In the separation of acoustic sources, the algorithm mitigates the permutation problem, i.e. the usual ICA algorithms applied in to the frequency domain mixture data suffer from the unknown permutation of the output signals. Although there are several engineering solutions to fix this problem after the ICA stage, the proposed method provides a natural solution to the problem by capturing the inherent dependencies of the acoustic signals. It therefore avoids the permutation problem and allows the separation of sources in very challenging environments for many sound sources.

The analysis of multiparametric geophysical and geochemical datasets presents significant challenges due to the diverse nature of measurements and their potential interactions. The development of advanced statistical and data mining techniques has enabled researchers to identify and characterise complex patterns within such datasets. This work builds upon a previous study that applied Independent Vector Analysis (IVA) to analyse multiparametric measurements collected at Teide volcano crater (Tenerife, Canary Islands) between 2020 and 2024. Our main goal is to extend the initial findings by identifying endogenous and exogenous factors influencing the observed patterns and characterising their temporal behaviour.The dataset includes spontaneous potential, CO2 and H2S fluxes, and thermal gradient measurements taken within the crater of Teide volcano on 38 fixed points. The application of IVA, which is an extension of Independent Component Analysis (ICA), allows for a multivariate approach that leverages vectorial data instead of scalar quantities. This method has proven effective for disentangling spatio-temporal interactions and isolating independent processes that govern the observed geophysical and geochemical variations.Based on previous preliminary results, this study incorporates new data collected during 2023 and 2024, allowing a better definition of the spatio-temporal patterns. Using the IVA, we identify and quantify evolving endogenous patterns potentially related to magmatic processes. Simultaneously, we assess the influence of exogenous factors such as seasonal temperature fluctuations and hydrological changes.Our results highlight the robustness of IVA in separating and characterising independent processes contributing to spatio-temporal multivariate datasets, such as the specific case of the Teide volcano. The results reveal a strong correlation between spontaneous potential anomalies and localised gas emissions, validating this methodology in volcanic environments. Moreover, this extended study underscores the importance of integrating temporal dynamics into multivariate analyses to improve the understanding of volcanic systems.This work demonstrates the potential of IVA as a powerful tool for analysing repeated geophysical and geochemical surveys. It offers significant advantages for monitoring active volcanic systems. Future applications could include adding more datasets, such as remote sensing and/or other geophysical or geochemical parameters, to understand volcanic processes comprehensively.

We propose a blind source separation method that yields high-quality speech with low distortion. Time-frequency (TF) masking can effectively reduce interference, but it produces nonlinear distortion. By contrast, linear filtering using a separation matrix such as independent vector analysis (IVA) can avoid nonlinear distortion, but the separation performance is reduced under reverberant conditions. The tandem connectionist approach combines several separation methods and it has been used frequently to compensate for the disadvantages of these methods. In this study, we propose associative memory model (AMM)-based linear filtering and a tandem connectionist framework, which applies TF masking followed by linear filtering. By using AMM trained with speech spectra to optimize the separation matrix, the proposed linear filtering method considers the properties of speech that are not considered explicitly in IVA, such as the harmonic components of spectra. TF masking is applied in the proposed tandem connectionist framework to reduce unwanted components that hinder the optimization of the separation matrix, and it is approximated by using a linear separation matrix to reduce nonlinear distortion. The results obtained in simultaneous speech separation experiments demonstrate that although the proposed linear filtering method can increase the signal-to-distortion ratio (SDR) and signal-to-interference ratio (SIR) compared with IVA, the proposed tandem connectionist framework can obtain greater increases in SDR and SIR, and it reduces the phoneme error rate more than the proposed linear filtering method.

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