Consistent Estimation of Dimensionality for Data-Driven Methods in fMRI Analysis

Data-driven methods, such as principal component analysis and independent component analysis, have been successfully applied to functional magnetic resonance imaging (fMRI) data in particular and neuro-imaging data in general. A central issue of these methods is the importance of correctly selecting the number of components to be used in the factor model. This issue is often addressed using a model selection criterion, where the goodness-of-fit term is obtained from the log-likelihood function. In this paper, an alternative criterion is proposed for selecting the number of components. Unlike existing model selection criteria that use the log-likelihood function, the proposed goodness-of-fit term uses the sum of squares of the smallest eigenvalues of the sample covariance matrix. The proposed criterion is obtained from the asymptotic distribution of the goodness-of-fit term, for which consistency is established. This criterion has a straight-forward implementation and is shown to outperform conventional model selection criteria used in fMRI data analysis. Experiments are conducted using simulated and real fMRI data, in which improved performance is obtained by the proposed criterion, both in terms of accuracy and consistency under data variabilities.