  The main goal of this study is to extract a set of brain networks in multiple
time-resolutions to analyze the connectivity patterns among the anatomic
regions for a given cognitive task. We suggest a deep architecture which learns
the natural groupings of the connectivity patterns of human brain in multiple
time-resolutions. The suggested architecture is tested on task data set of
Human Connectome Project (HCP) where we extract multi-resolution networks, each
of which corresponds to a cognitive task. At the first level of this
architecture, we decompose the fMRI signal into multiple sub-bands using
wavelet decompositions. At the second level, for each sub-band, we estimate a
brain network extracted from short time windows of the fMRI signal. At the
third level, we feed the adjacency matrices of each mesh network at each
time-resolution into an unsupervised deep learning algorithm, namely, a Stacked
De- noising Auto-Encoder (SDAE). The outputs of the SDAE provide a compact
connectivity representation for each time window at each sub-band of the fMRI
signal. We concatenate the learned representations of all sub-bands at each
window and cluster them by a hierarchical algorithm to find the natural
groupings among the windows. We observe that each cluster represents a
cognitive task with a performance of 93% Rand Index and 71% Adjusted Rand
Index. We visualize the mean values and the precisions of the networks at each
component of the cluster mixture. The mean brain networks at cluster centers
show the variations among cognitive tasks and the precision of each cluster
shows the within cluster variability of networks, across the subjects.
