  Objective: Longitudinal neuroimaging studies have demonstrated that
adolescence is the crucial developmental epoch of continued brain growth and
change. A large number of researchers dedicate to uncovering the mechanisms
about brain maturity during adolescence. Motivated by both achievement in graph
signal processing and recent evidence that some brain areas act as hubs
connecting functionally specialized systems, we proposed an approach to detect
these regions from spectral analysis perspective. In particular, as human brain
undergoes substantial development throughout adolescence, we addressed the
challenge by evaluating the functional network difference among age groups from
functional magnetic resonance imaging (fMRI) observations. Methods: We treated
these observations as graph signals defined on the parcellated functional brain
regions and applied graph Laplacian learning based Fourier Transform (GLFT) to
transform the original graph signals into frequency domain. Eigen-analysis was
conducted afterwards to study the behavior of the corresponding brain regions,
which enables the characterization of brain maturation. Result: We first
evaluated our method on the synthetic data and further applied the method to
resting and task state fMRI imaging data from Philadelphia Neurodevelopmental
Cohort (PNC) dataset, comprised of normally developing adolescents from 8 to
22. The model provided a highest accuracy of 95.69% in distinguishing different
adolescence stages. Conclusion: We detected 13 hubs from resting state fMRI and
16 hubs from task state fMRI that are highly related to brain maturation
process. Significance: The proposed GLFT method is powerful in extracting the
brain connectivity patterns and identifying hub regions with a high prediction
power
