Dimensionality estimation for optimal detection of functional networks in BOLD fMRI data

Abstract

Estimation of the intrinsic dimensionality of fMRI data is an important part of data analysis that helps to separate the signal of interest from noise. We have studied multiple methods of dimensionality estimation proposed in the literature and used these estimates to select a subset of principal components that was subsequently processed by linear discriminant analysis (LDA). Using simulated multivariate Gaussian data, we show that the dimensionality that optimizes signal detection (in terms of the receiver operating characteristic (ROC) metric) goes through a transition from many dimensions to a single dimension as a function of the signal-to-noise ratio. This transition happens when the loci of activation are organized into a spatial network and the variance of the networked, task-related signals is high enough for the signal to be easily detected in the data. We show that reproducibility of activation maps is a metric that captures this switch in intrinsic dimensionality. Except for reproducibility, all of the methods of dimensionality estimation we considered failed to capture this transition: optimization of Bayesian evidence, minimum description length, supervised and unsupervised LDA prediction, and Stein's unbiased risk estimator. This failure results in sub-optimal ROC performance of LDA in the presence of a spatially distributed network, and may have caused LDA to underperform in many of the reported comparisons in the literature. Using real fMRI data sets, including multi-subject group and within-subject longitudinal analysis we demonstrate the existence of these dimensionality transitions in real data.

Optimizing Preprocessing and Analysis Pipelines for Single-Subject fMRI: 2. Interactions with ICA, PCA, Task Contrast and Inter-Subject Heterogeneity

“…This is consistent with prior analyses of Yourganov et al [43], who found that ICA detection of brain networks underperforms, relative to linear discriminant methods. This may be partly due to the PCA-based dimensionality estimation method used in MELODIC.…”

Principal components of functional connectivity: A new approach to study dynamic brain connectivity during rest

“…The comparison of the eigenvalues to those obtained from surrogate data on the other hand provided a reasonable, rough estimate to guide the choice of dimensionality. Other dimensionality estimation approaches, such as those used in activation studies (Yourganov et al, 2011) or ICA (Varoquaux et al, 2010), could be adapted to dynamic FC and evaluated in future studies. The ten first eigenconnectivities used for further analysis did not use the full "signal space" and explained 34% of the variance in dynamic FC, but our results suggest that they captured important differences between the groups.…”

Increased insula coactivation with salience networks in insomnia

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