Unsupervised Clustering of fMRI Time Series with the Granger Causality Metric

INTRODUCTION Unsupervised clustering methods such as Self-Organizing Map (SOM) or Hierarchical Clustering (HC) are data-driven techniques, which have been used successfully in fMRI data analyses [Ngan, Peltier]. In conventional SOM or HC methods, the Euclidean distance is used as the similarity metric to compare signals [Kohonen]. However, Euclidean distance does not accurately delineate the interference of noise points in fMRI signals. In [Liao], a correlation-based spatio-temporal measure has been introduced that outperforms the Euclidean distance metric in fMRI data analysis. Both Euclidean distance and correlation metrics can distinguish data obtained from similar task paradigms (block-design or event-related) having large and discernible timing variability, of the order of a few seconds [Liao]. However, if the timing difference is small, of the order of a few tens of milliseconds, neither metric is very useful. We propose a new approach based upon Granger Causality to cluster fMRI data having small timing variability. High field fMRI provides high signal-to-noise ratio (SNR) measurements. A low TR during image acquisition at high field helps to detect small differences in latency of the blood oxygenation level-dependent (BOLD) response. In some cases, the temporal difference between signals may imply causal relationship which measures the directional influence (= effective connectivity) [Goebel]. In other cases, the timing difference indicates the presence of delayed signals from macrovasculatures. In any case, the temporal difference can be interpreted in terms of Granger Causality, which, in principle, gives the directional influence. We use this directional influence measure as a similarity metric in an Agglomerative Hierarchical Clustering method to cluster fMRI data into different latency groups. This metric also may segregate brain regions that have different patterns of effective connectivity.