  To explain individual differences in development, behavior, and cognition,
most previous studies focused on projecting resting-state functional MRI (fMRI)
based functional connectivity (FC) data into a low-dimensional space via linear
dimensionality reduction techniques, followed by executing analysis operations.
However, linear dimensionality analysis techniques may fail to capture
nonlinearity of brain neuroactivity. Moreover, besides resting-state FC, FC
based on task fMRI can be expected to provide complementary information.
Motivated by these considerations, we nonlinearly fuse resting-state and
task-based FC networks (FCNs) to seek a better representation in this paper. We
propose a framework based on alternating diffusion map (ADM), which extracts
geometry-preserving low-dimensional embeddings that successfully parameterize
the intrinsic variables driving the phenomenon of interest. Specifically, we
first separately build resting-state and task-based FCNs by symmetric positive
definite matrices using sparse inverse covariance estimation for each subject,
and then utilize the ADM to fuse them in order to extract significant
low-dimensional embeddings, which are used as fingerprints to identify
individuals. The proposed framework is validated on the Philadelphia
Neurodevelopmental Cohort data, where we conduct extensive experimental study
on resting-state and fractal $n$-back task fMRI for the classification of
intelligence quotient (IQ). The fusion of resting-state and $n$-back task fMRI
by the proposed framework achieves better classification accuracy than any
single fMRI, and the proposed framework is shown to outperform several other
data fusion methods. To our knowledge, this paper is the first to demonstrate a
successful extension of the ADM to fuse resting-state and task-based fMRI data
for accurate prediction of IQ.
