Ronald Phlypo

Dynamic changes of spatial functional network connectivity in healthy individuals and schizophrenia patients using independent vector analysis

Recent work on both task-induced and resting-state functional magnetic resonance imaging (fMRI) data suggests that functional connectivity may fluctuate, rather than being stationary during an entire scan. Most dynamic studies are based on second-order statistics between fMRI time series or time courses derived from blind source separation, e.g., independent component analysis (ICA), to investigate changes of temporal interactions among brain regions. However, fluctuations related to spatial components over time are of interest as well. In this paper, we examine higher-order statistical dependence between pairs of spatial components, which we define as spatial functional network connectivity (sFNC), and changes of sFNC across a resting-state scan. We extract time-varying components from healthy controls and patients with schizophrenia to represent brain networks using independent vector analysis (IVA), which is an extension of ICA to multiple data sets and enables one to capture spatial variations. Based on mutual information among IVA components, we perform statistical analysis and Markov modeling to quantify the changes in spatial connectivity. Our experimental results suggest significantly more fluctuations in patient group and show that patients with schizophrenia have more variable patterns of spatial concordance primarily between the frontoparietal, cerebellar and temporal lobe regions. This study extends upon earlier studies showing temporal connectivity differences in similar areas on average by providing evidence that the dynamic spatial interplay between these regions is also impacted by schizophrenia.

Independent Component Analysis for Brain fMRI Does Indeed Select for Maximal Independence

A recent paper by Daubechies et al. claims that two independent component analysis (ICA) algorithms, Infomax and FastICA, which are widely used for functional magnetic resonance imaging (fMRI) analysis, select for sparsity rather than independence. The argument was supported by a series of experiments on synthetic data. We show that these experiments fall short of proving this claim and that the ICA algorithms are indeed doing what they are designed to do: identify maximally independent sources.

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 a subject of significant research interest. IVA has also been shown to be a generalization of Hotellings 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 identification of dependent sources between datasets. Thus, we provide additional conditions for when the arbitrary ordering of the estimated sources can be common across datasets. Performance bounds in terms of the Cramér-Rao lower bound are also provided for demixing matrices and interference to source ratio. The performance of two IVA algorithms are compared to the theoretical bounds.

Independent vector analysis, the Kotz distribution, and performance bounds

The recent extensions of independent component analysis (ICA) to exploit source dependence across multiple datasets, termed independent vector analysis (IVA), have thus far only considered two multivariate source distribution models: the Gaussian and a second-order uncorrelated Laplacian distribution. In this paper, we introduce the use of the Kotz distribution family as a more flexible source distribution model which exploits both second and higher-order statistics. The Cramér-Rao lower bound (CRLB) for IVA performance prediction is shown to be analogous to the bound for blind source separation (BSS). Lastly, we provide an analytic expression for the CRLB when the sources follow the multivariate power exponential (MPE) subclass of distributions within the Kotz family.

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

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.

Blind Source Separation by Entropy Rate Minimization

By assuming latent sources are statistically independent, independent component analysis separates underlying sources from a given linear mixture. Since in many applications, latent sources are both non-Gaussian and have sample dependence, it is desirable to exploit both properties jointly. In this paper, we use mutual information rate to construct a general framework for analysis and derivation of algorithms that take both properties into account. We discuss two types of source models for entropy rate estimation-a Markovian and an invertible filter model-and give the general independent component analysis cost function, update rule, and performance analysis based on these. We also introduce four algorithms based on these two models, and show that their performance can approach the Cramér-Rao lower bound. In addition, we demonstrate that the algorithms with flexible models exhibit very desirable performance for “natural” data.

Independent Vector Analysis for Gradient Artifact Removal in Concurrent EEG-fMRI Data.

We consider the problem of removing gradient artifact from electroencephalogram (EEG) signal, recorded concurrently with functional magnetic resonance imaging (fMRI) acquisition. We estimate the artifact by exploiting its quasi-periodicity over the epochs and its similarity over the different channels by using independent vector analysis, a recent extension of independent component analysis for multiple datasets. The method fully makes use of the spatio-temporal information by using spatial dependences across channels to estimate the artifact for a particular channel. Thus, it provides robustness with respect to uncontrollable changes such as head movement and fluctuations in the B0 field during the acquisition. Results using both simulated data with gradient artifact and EEG data collected concurrently with fMRI show the desirable performance of the new method.

Algorithms for Markovian source separation by entropy rate minimization

Since in many blind source separation applications, latent sources are both non-Gaussian and have sample dependence, it is desirable to exploit both non-Gaussianity and sample dependency. In this paper, we use the Markov model to construct a general framework for the analysis and derivation of algorithms that take both properties into account. We also present two algorithms using two effective source priors. The first one is a multivariate generalized Gaussian distribution and the second is an autoregressive model driven by a generalized Gaussian distributed process. We derive the Cramér-Rao lower bound and demonstrate that the performance of the algorithms approach the lower bound especially when the underlying model matches the parametric model. We also demonstrate that a flexible semi-parametric approach exhibits very desirable performance.

Complex Independent Component Analysis Using Three Types of Diversity: Non-Gaussianity, Nonwhiteness, and Noncircularity

By assuming latent sources are statistically independent, independent component analysis (ICA) separates underlying sources from a given linear mixture. Since in many applications, latent sources are non-Gaussian, noncircular, and have sample dependence, it is desirable to exploit all these properties jointly. Mutual information rate, which leads to the minimization of entropy rate, provides a natural cost for the task. In this paper, we establish the theory for complex-valued ICA giving Cramér-Rao lower bound and identification conditions, and present a new algorithm that takes all these properties into account. We propose an effective estimator of entropy rate and a complex-valued entropy rate bound minimization algorithm based on it. We show that the new method exploits all these properties effectively by comparing the estimation performance with the Cramér-Rao lower bound and by a number of examples.

An efficient entropy rate estimator for complex-valued signal processing: Application to ICA

Estimating likelihood or entropy rate is one of the key issues in many signal processing problems. Mutual information rate, which leads to the minimization of entropy rate, provides a natural cost for achieving blind source separation (BSS). In many complex-valued BSS applications, the latent sources are non-Gaussian, noncircular, and possess sample dependence. Consequently, an effective estimator of entropy rate that jointly considers all three properities of the sources is required. In this paper, we propose such an entropy rate estimator that assumes the sources are generated by invertible filters. With this new entropy rate estimator, we propose a complex entropy rate bound minimization algorithm. Simulation results show that the new method exploits all three properties effectively.