Multivariate analysis methods such as independent component analysis (ICA) have been applied to the analysis of functional magnetic resonance imaging (fMRI) data to study brain function. Because of the high dimensionality and high noise level of the fMRI data, order selection, i.e., estimation of the number of informative components, is critical to reduce… (More)
Independent component analysis (ICA) has become an increasingly utilized approach for analyzing brain imaging data. In contrast to the widely used general linear model (GLM) that requires the user to parameterize the data (e.g. the brain's response to stimuli), ICA, by relying upon a general assumption of independence, allows the user to be agnostic… (More)
A novel (differential) entropy estimator is introduced where the maximum entropy bound is used to approximate the entropy given the observations, and is computed using a numerical procedure thus resulting in accurate estimates for the entropy. We show that such an estimator exists for a wide class of measuring functions, and provide a number of design… (More)
Spatial independent component analysis (ICA) applied to functional magnetic resonance imaging (fMRI) data identifies functionally connected networks by estimating spatially independent patterns from their linearly mixed fMRI signals. Several multi-subject ICA approaches estimating subject-specific time courses (TCs) and spatial maps (SMs) have been… (More)
We propose a new entropy rate estimator for a second and/or higher-order correlated source by modeling it as the output of a linear filter, which can be mixed-phase, driven by Gaussian or non-Gaussian noise. Based on this estimator, we develop a new spatiotemporal blind source separation (BSS) algorithm, full BSS (FBSS), by minimizing the entropy rate of… (More)
Although the impact of serial correlation (autocorrelation) in residuals of general linear models for fMRI time-series has been studied extensively, the effect of autocorrelation on functional connectivity studies has been largely neglected until recently. Some recent studies based on results from economics have questioned the conventional estimation of… (More)
We investigate the approximation ability of a multilayer perceptron (MLP) network when it is extended to the complex domain. The main challenge for processing complex data with neural networks has been the lack of bounded and analytic complex nonlinear activation functions in the complex domain, as stated by Liouville's theorem. To avoid the conflict… (More)
A number of complex nonlinear functions are proposed for the independent component analysis (ICA) of complex-valued data. We discuss the properties of these nonlinearities and show their efficiency in generating the higher order statistics needed for ICA.