An Empirical Comparison of Information-Theoretic Criteria in Estimating the Number of Independent Components of fMRI Data

BACKGROUND: Independent Component Analysis (ICA) has been widely applied to the analysis of fMRI data. Accurate estimation of the number of independent components of fMRI data is critical to reduce over/under fitting. Although various methods based on Information Theoretic Criteria (ITC) have been used to estimate the intrinsic dimension of fMRI data, the relative performance of different ITC in the context of the ICA model hasn't been fully investigated, especially considering the properties of fMRI data. The present study explores and evaluates the performance of various ITC for the fMRI data with varied white noise levels, colored noise levels, temporal data sizes and spatial smoothness degrees. METHODOLOGY: Both simulated data and real fMRI data with varied Gaussian white noise levels, first-order auto-regressive (AR(1)) noise levels, temporal data sizes and spatial smoothness degrees were carried out to deeply explore and evaluate the performance of different traditional ITC. PRINCIPAL FINDINGS: Results indicate that the performance of ITCs depends on the noise level, temporal data size and spatial smoothness of fMRI data. 1) High white noise levels may lead to underestimation of all criteria and MDL/BIC has the severest underestimation at the higher Gaussian white noise level. 2) Colored noise may result in overestimation that can be intensified by the increase of AR(1) coefficient rather than the SD of AR(1) noise and MDL/BIC shows the least overestimation. 3) Larger temporal data size will be better for estimation for the model of white noise but tends to cause severer overestimation for the model of AR(1) noise. 4) Spatial smoothing will result in overestimation in both noise models. CONCLUSIONS: 1) None of ITC is perfect for all fMRI data due to its complicated noise structure. 2) If there is only white noise in data, AIC is preferred when the noise level is high and otherwise, Laplace approximation is a better choice. 3) When colored noise exists in data, MDL/BIC outperforms the other criteria

Estimating intrinsic dimensionality of fMRI dataset incorporating an AR(1) noise model with cubic spline interpolation

Estimating the true dimensionality of the data to determine what is essential in the data is an important but a difficult problem in fMRI dataset. In this paper, cubic spline interpolation is introduced to detect the number of essential components in fMRI dataset. By constructing proper interpolation variable, more reasonable estimation of the coefficient of an autoregressive noise model of order I can be made. Simulation data and real fMRI dataset of resting-state in human brains are used to compare the performance of the new method incorporating an autoregressive noise model of order 1 with cubic spline interpolation (AR1CSI) with that of the method based only on an autoregressive noise model of order 1 (AR1). The results show the AR1CSI method leads to more accurate estimate of the model order at many circumstances, as illustrated in simulated datasets and real fMRI datasets of resting-state human brain.Estimating the true dimensionality of the data to determine what is essential in the data is an important but a difficult problem in fMRI dataset. In this paper, cubic spline interpolation is introduced to detect the number of essential components in fMRI dataset. By constructing proper interpolation variable, more reasonable estimation of the coefficient of an autoregressive noise model of order I can be made. Simulation data and real fMRI dataset of resting-state in human brains are used to compare the performance of the new method incorporating an autoregressive noise model of order 1 with cubic spline interpolation (AR1CSI) with that of the method based only on an autoregressive noise model of order 1 (AR1). The results show the AR1CSI method leads to more accurate estimate of the model order at many circumstances, as illustrated in simulated datasets and real fMRI datasets of resting-state human brain. (C) 2008 Elsevier B.V. All rights reserved

A tiny glimpse into the human brain using model-free analysis for resting-state fMRI data

Resting-state functional Magnetic Resonance Imaging (fMRI) acquires four dimensional data that indirectly depicts human brain activity. Within these four dimensional datasets reside resting-state functional connectivity networks (RFNs), depicting how the human brain is organized functionally. This series of studies delve into the use of data-driven analysis methods for resting-state fMRI data. Their strengths were explored and their weaknesses tackled, both in their methodologies and applications, all in hope to gain a better understanding of the data, and thereby how the brain function. The journey begins through the usage of one of the most common data-driven analysis methods in use today: Independent Component Analysis (ICA). ICA requires no user input parameter apart from the input dataset and the number of output Independent Components (NIC). The requirement of the NIC, a priori, is troubling as the inherent number of Independent Components (ICs) that exists within non-simulated datasets is unknown, due to the existence of various noise and artefact sources to differing degrees. Furthermore, comparing datasets using ICA is problematic because of the inherently different dimensionality of different datasets. To investigate the effects of NIC on the ICA output results, a classification framework based on Support Vector Machines (SVM) was implemented to automatically classify ICs as either potential RFNs, or noise/artefact signal. This feature-optimized classification of ICs with SVM, or FOCIS, framework uses features derived from verbal instructions for manual visual inspection of ICs. With only few significant features selected through iterative feature-selection and a small training set, the classification framework performed well with over 98% in overall accuracy for group ICA output results. Analysis of different resting-state fMRI datasets using FOCIS indicated that the specification of NIC can critically affect the ICA results on restingstate fMRI data. These changes are complex and are individually different from one another, irrespective whether the IC is a potential RFN or artefact/noise signals. Applying this knowledge on group comparison studies, ICA was used to study migraine patients undergo kinetic oscillation stimulation treatment. The immediate effects of the treatment allows direct correlation of a patient’s pain levels with changes in their RFNs. Differences in RFNs that include areas in the midbrain and limbic system regulating the central nervous system were discovered in migraine patients compared to healthy control group. Overlapping areas were also shown to be affected by the treatment. These results provide supporting evidence for the hypothesis that the treatment affects and regulates the parasympathetic autonomic reflex, alleviating migraine symptoms. Hierarchical clustering is another data-driven analysis method that is almost devoid of all userinput parameters. The algorithm naturally stratifies data into a hierarchical structure. It is believed that brain function is hierarchically organized, so an algorithm which reflects this aspect is a seemingly excellent choice to use for analyzing the resting-state fMRI data. A hierarchical clustering analysis framework was developed to extract RFNs from resting-state fMRI data with full brain coverage at voxel level. The RFNs identified using hierarchical clustering conforms to those identified previously using other data processing techniques, such as ICA. An innate ability of the clustering algorithm is to naturally organize data into a hierarchical tree (dendrogram). This was fully utilized though extensions in the framework for cluster evaluation. Extending the hierarchical clustering framework with the cluster evaluation pipeline allowed extraction of functional subdivisions of known RFNs. This demonstrated that not only can hierarchical clustering be used to extract the modular organization at the scale of large systems for entire RFNs, but can also be used to derive the functional subdivision of RFNs and provide a consistent method of analysis at different levels of detail. The subnetworks extracted using hierarchical clustering reveals the intrinsic functional connectivity amongst the subnetworks within RFNs and provide clues for further exploring the potential for currently unknown functional junctions within RFNs