Tülay Adali

A method for making group inferences from functional MRI data using independent component analysis.

Independent component analysis (ICA) is a promising analysis method that is being increasingly applied to fMRI data. A principal advantage of this approach is its applicability to cognitive paradigms for which detailed models of brain activity are not available. Independent component analysis has been successfully utilized to analyze single‐subject fMRI data sets, and an extension of this work would be to provide for group inferences. However, unlike univariate methods (e.g., regression analysis, Kolmogorov–Smirnov statistics), ICA does not naturally generalize to a method suitable for drawing inferences about groups of subjects. We introduce a novel approach for drawing group inferences using ICA of fMRI data, and present its application to a simple visual paradigm that alternately stimulates the left or right visual field. Our group ICA analysis revealed task‐related components in left and right visual cortex, a transiently task‐related component in bilateral occipital/parietal cortex, and a non‐task‐related component in bilateral visual association cortex. We address issues involved in the use of ICA as an fMRI analysis method such as: (1) How many components should be calculated? (2) How are these components to be combined across subjects? (3) How should the final results be thresholded and/or presented? We show that the methodology we present provides answers to these questions and lay out a process for making group inferences from fMRI data using independent component analysis. Hum. Brain Mapping 14:140–151, 2001.

A review of group ICA for fMRI data and ICA for joint inference of imaging, genetic, and ERP data.

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 brains response to stimuli), ICA, by relying upon a general assumption of independence, allows the user to be agnostic regarding the exact form of the response. In addition, ICA is intrinsically a multivariate approach, and hence each component provides a grouping of brain activity into regions that share the same response pattern thus providing a natural measure of functional connectivity. There are a wide variety of ICA approaches that have been proposed, in this paper we focus upon two distinct methods. The first part of this paper reviews the use of ICA for making group inferences from fMRI data. We provide an overview of current approaches for utilizing ICA to make group inferences with a focus upon the group ICA approach implemented in the GIFT software. In the next part of this paper, we provide an overview of the use of ICA to combine or fuse multimodal data. ICA has proven particularly useful for data fusion of multiple tasks or data modalities such as single nucleotide polymorphism (SNP) data or event-related potentials. As demonstrated by a number of examples in this paper, ICA is a powerful and versatile data-driven approach for studying the brain.

Estimating the Number of Independent Components for Functional Magnetic Resonance Imaging Data

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 over/underfitting in such methods. Dependence among fMRI data samples in the spatial and temporal domain limits the usefulness of the practical formulations of information‐theoretic criteria (ITC) for order selection, since they are based on likelihood of independent and identically distributed (i.i.d.) data samples. To address this issue, we propose a subsampling scheme to obtain a set of effectively i.i.d. samples from the dependent data samples and apply the ITC formulas to the effectively i.i.d. sample set for order selection. We apply the proposed method on the simulated data and show that it significantly improves the accuracy of order selection from dependent data. We also perform order selection on fMRI data from a visuomotor task and show that the proposed method alleviates the over‐estimation on the number of brain sources due to the intrinsic smoothness and the smooth preprocessing of fMRI data. We use the software package ICASSO (Himberg et al. [ 2004 ]: Neuroimage 22:1214–1222) to analyze the independent component (IC) estimates at different orders and show that, when ICA is performed at overestimated orders, the stability of the IC estimates decreases and the estimation of task related brain activations show degradation. Hum Brain Mapp, 2007.

Spatial and Temporal Independent Component Analysis of Functional MRI Data Containing a Pair of Task-Related Waveforms

Independent component analysis (ICA) is a technique that attempts to separate data into maximally independent groups. Achieving maximal independence in space or time yields two varieties of ICA meaningful for functional MRI (fMRI) applications: spatial ICA (SICA) and temporal ICA (TICA). SICA has so far dominated the application of ICA to fMRI. The objective of these experiments was to study ICA with two predictable components present and evaluate the importance of the underlying independence assumption in the application of ICA. Four novel visual activation paradigms were designed, each consisting of two spatiotemporal components that were either spatially dependent, temporally dependent, both spatially and temporally dependent, or spatially and temporally uncorrelated, respectively. Simulated data were generated and fMRI data from six subjects were acquired using these paradigms. Data from each paradigm were analyzed with regression analysis in order to determine if the signal was occurring as expected. Spatial and temporal ICA were then applied to these data, with the general result that ICA found components only where expected, e.g., S(T)ICA “failed” (i.e., yielded independent components unrelated to the “self‐evident” components) for paradigms that were spatially (temporally) dependent, and “worked” otherwise. Regression analysis proved a useful “check” for these data, however strong hypotheses will not always be available, and a strength of ICA is that it can characterize data without making specific modeling assumptions. We report a careful examination of some of the assumptions behind ICA methodologies, provide examples of when applying ICA would provide difficult‐to‐interpret results, and offer suggestions for applying ICA to fMRI data especially when more than one task‐related component is present in the data.Hum. Brain Mapping 13:43–53, 2001.

Comparison of multi-subject ICA methods for analysis of fMRI data.

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 developed, however, there has not yet been a full comparison of the implications of their use. Here, we provide extensive comparisons of four multi‐subject ICA approaches in combination with data reduction methods for simulated and fMRI task data. For multi‐subject ICA, the data first undergo reduction at the subject and group levels using principal component analysis (PCA). Comparisons of subject‐specific, spatial concatenation, and group data mean subject‐level reduction strategies using PCA and probabilistic PCA (PPCA) show that computationally intensive PPCA is equivalent to PCA, and that subject‐specific and group data mean subject‐level PCA are preferred because of well‐estimated TCs and SMs. Second, aggregate independent components are estimated using either noise‐free ICA or probabilistic ICA (PICA). Third, subject‐specific SMs and TCs are estimated using back‐reconstruction. We compare several direct group ICA (GICA) back‐reconstruction approaches (GICA1‐GICA3) and an indirect back‐reconstruction approach, spatio‐temporal regression (STR, or dual regression). Results show the earlier group ICA (GICA1) approximates STR, however STR has contradictory assumptions and may show mixed‐component artifacts in estimated SMs. Our evidence‐based recommendation is to use GICA3, introduced here, with subject‐specific PCA and noise‐free ICA, providing the most robust and accurate estimated SMs and TCs in addition to offering an intuitive interpretation. Hum Brain Mapp, 2011.

Unmixing fMRI with independent component analysis

Independent component analysis (ICA) is a statistical method used to discover hidden factors (sources or features) from a set of measurements or observed data such that the sources are maximally independent. Typically, it assumes a generative model where observations are assumed to be linear mixtures of independent sources and works with higher-order statistics to achieve independence. ICA has recently demonstrated considerable promise in characterizing functional magnetic resonance imaging (fMRI) data, primarily due to its intuitive nature and ability for flexible characterization of the brain function. In this article, ICA is introduced and its application to fMRI data analysis is reviewed.

Multisubject Independent Component Analysis of fMRI: A Decade of Intrinsic Networks, Default Mode, and Neurodiagnostic Discovery

Since the discovery of functional connectivity in fMRI data (i.e., temporal correlations between spatially distinct regions of the brain) there has been a considerable amount of work in this field. One important focus has been on the analysis of brain connectivity using the concept of networks instead of regions. Approximately ten years ago, two important research areas grew out of this concept. First, a network proposed to be “a default mode of brain function” since dubbed the default mode network was proposed by Raichle. Secondly, multisubject or group independent component analysis (ICA) provided a data-driven approach to study properties of brain networks, including the default mode network. In this paper, we provide a focused review of how ICA has contributed to the study of intrinsic networks. We discuss some methodological considerations for group ICA and highlight multiple analytic approaches for studying brain networks. We also show examples of some of the differences observed in the default mode and resting networks in the diseased brain. In summary, we are in exciting times and still just beginning to reap the benefits of the richness of functional brain networks as well as available analytic approaches.

fMRI activation in a visual-perception task: network of areas detected using the general linear model and independent components analysis.

The Motor-Free Visual Perception Test, revised (MVPT-R), provides a measure of visual perceptual processing. It involves different cognitive elements including visual discrimination, spatial relationships, and mental rotation. We adapted the MVPT-R to an event-related functional MRI (fMRI) environment to investigate the brain regions involved in the interrelation of these cognitive elements. Two complementary analysis methods were employed to characterize the fMRI data: (a) a general linear model SPM approach based upon a model of the time course and a hemodynamic response estimate and (b) independent component analysis (ICA), which does not constrain the specific shape of the time course per se, although we did require it to be at least transiently task-related. Additionally, we implemented ICA in a novel way to create a group average that was compared with the SPM group results. Both methods yielded similar, but not identical, results and detected a network of robustly activated visual, inferior parietal, and frontal eye-field areas as well as thalamus and cerebellum. SPM appeared to be the more sensitive method and has a well-developed theoretical approach to thresholding. The ICA method segregated functional elements into separate maps and identified additional regions with extended activation in response to presented events. The results demonstrate the utility of complementary analyses for fMRI data and suggest that the cerebellum may play a significant role in visual perceptual processing. Additionally, results illustrate functional connectivity between frontal eye fields and prefrontal and parietal regions.

Different activation dynamics in multiple neural systems during simulated driving

Driving is a complex behavior that recruits multiple cognitive elements. We report on an imaging study of simulated driving that reveals multiple neural systems, each of which have different activation dynamics. The neural correlates of driving behavior are identified with fMRI and their modulation with speed is investigated. We decompose the activation into interpretable pieces using a novel, generally applicable approach, based upon independent component analysis. Some regions turn on or off, others exhibit a gradual decay, and yet others turn on transiently when starting or stopping driving. Signal in the anterior cingulate cortex, an area often associated with error monitoring and inhibition, decreases exponentially with a rate proportional to driving speed, whereas decreases in frontoparietal regions, implicated in vigilance, correlate with speed. Increases in cerebellar and occipital areas, presumably related to complex visuomotor integration, are activated during driving but not associated with driving speed. Hum. Brain Mapping 16:158–167, 2002.

Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety

Complex-valued signals occur in many areas of science and engineering and are thus of fundamental interest. In the past, it has often been assumed, usually implicitly, that complex random signals are proper or circular. A proper complex random variable is uncorrelated with its complex conjugate, and a circular complex random variable has a probability distribution that is invariant under rotation in the complex plane. While these assumptions are convenient because they simplify computations, there are many cases where proper and circular random signals are very poor models of the underlying physics. When taking impropriety and noncircularity into account, the right type of processing can provide significant performance gains. There are two key ingredients in the statistical signal processing of complex-valued data: 1) utilizing the complete statistical characterization of complex-valued random signals; and 2) the optimization of real-valued cost functions with respect to complex parameters. In this overview article, we review the necessary tools, among which are widely linear transformations, augmented statistical descriptions, and Wirtinger calculus. We also present some selected recent developments in the field of complex-valued signal processing, addressing the topics of model selection, filtering, and source separation.