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

• Published in: NeuroImage (Orlando, Fla.) Vol. 56; no. 2; pp. 531 - 543
• Main Authors: Yourganov, Grigori, Chen, Xu, Lukic, Ana S., Grady, Cheryl L., Small, Steven L., Wernick, Miles N., Strother, Stephen C.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 15.05.2011; Elsevier Limited
• Subjects: Activation; Adult; Aged; Algorithms; Area Under Curve; Brain - physiology; Brain Mapping - methods; Dimensionality estimation; Estimates; Failure; fMRI; Humans; Image Processing, Computer-Assisted - methods; Linear discriminant Analysis (LDA); Loci; Magnetic Resonance Imaging; Methods; Middle Aged; Model order selection; Multivariate analysis; Nerve Net - physiology; Networks; Noise; Optimization; Principal component analysis (PCA); Principal components analysis; Reproducibility; Reproducibility of Results; Risk; ROC Curve; Signal detection; Switching theory; Young Adult; Linear discriminant Analysis (LDA); fMRI; Model order selection; Dimensionality estimation; Principal component analysis (PCA); Signal detection
• ISSN: 1053-8119; 1095-9572; 1095-9572
• DOI: 10.1016/j.neuroimage.2010.09.034

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. ► We test multiple PCA-based dimensionality estimators for fMRI discriminant analysis. ► Spatial map reproducibility optimally detects covariance-based network signals. ► Only reproducibility detects dimensionality changes with stronger network signals. ► Other dimension estimates are unstable (eg, classification) or too big (eg, MDL). ► All results are demonstrated in simulations and multiple real fMRI data sets.