Differentiable Max-Directivity Beamforming Normalization for Independent Vector Analysis

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 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 followed by HMM-based feature enhancement for robust speech recognition

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.

Various methods are proposed to estimate the DOA (direction of arrival) of source signal. MUSIC method uses the peak point of MUSIC spectrum to estimate DOA. The method that uses the image of video camera to estimate DOA is also proposed. Mixing matrix can be calculated by arranging the frequency transfer function calculated from DOA and separation matrix of source signal is equal to the inverse of mixing matrix. However, if the frequency range of source signal is wide, calculation accuracy of the separation matrix is worse since mixing matrix becomes adverse condition in low frequency. ILRMA can estimate wideband source signals precisely by updating signal power and separation matrix alternatively. ILRMA is characterized by learning the signal power in time-frequency domain using low rank approximation. However, if source signals are high rank, the learning error of signal power occurs in using ILRMA. To resolve these problems, this paper proposes a new method, which can improve separation accuracy by using the prior information of DOA. In this method, regularization term calculated from DOA is added to NMF's objective function. By adding this regularization term, signal power can be calculated correctly even if source signals are high rank. In order to verify the estimation accuracy of source signals in using proposed method, numerical experiment was conducted and the estimation accuracy in using proposed method was compared with that in using ILRMA under the condition that DOA was already-known. In this experiment, three source signals and six noises were mixed and three sensors received the mixed signals. The estimation accuracy of source signals by proposed method was better than ILRMA. This experimental result proves that proposed method can improve the estimation accuracy of source signals by using DOA even if source signals are high rank and exist in wideband frequency range.

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 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.

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.'

This paper presents a brief overview of narrowband direction of arrival (DOA) estimation algorithms and techniques. A comprehensive study is carried out in this paper to investigate and evaluate the performance of variety of algorithms for DOA estimation. Two categories of DOA estimation algorithms are considered for discussion which are Classical methods and Subspace based techniques. Classical methods include Sum-and-Delay method and Capon’s Minimum Variance Distortionless Response (MVDR) while Subspace based techniques are multiple signal classification (MUSIC) and The Minimum Norm Technique. Also ESPIRIT technique is evaluated. Inefficiencies are pointed out and solutions are suggested to overcome these shortfalls. Simulation results shows that the MUSIC algorithm is able to better represent the DOAs of signals with more prominent peaks. The Min-Norm algorithm also identifies the DOAs of signals similar to the MUSIC algorithm, but produces spurious peaks at other locations. The MVDR method identifies the DOAs of signals, but the locations are not represented by sharp peaks, due to spectral leakage. The classical beamformer also produces several spurious peaks. MUSIC show higher accuracy and resolution than the other algorithms. It should be noted that MUSIC is more applicable because it can be used for different array geometries.

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.

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.

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.

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.

Independent vector analysis (IVA) is a frequency domain blind source separation (FDBSS) technique that has proven efficient in separating independent speech signals from their convolutive mixtures. In particular, it addresses the problematic permutation problem by using a multivariate source prior. The multivariate source prior models statistical inter dependency across the frequency bins of each source and the performance of the method is dependent upon the choice of source prior. The online form of the IVA is suitable for practical real time systems. Previous online algorithms use a learning rate that does not introduce a robust way to control the learning as a function of the proximity to the target solution. In this work, we propose a new adaptive learning scheme to improve the convergence speed and steady state separation performance. The speech signals are modelled by two different source priors; a super-Gaussian distribution and a generalized Gaussian distribution. The experimental results confirm improved performance with real room impulse responses and real recorded speech signals.

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.