  The understanding of the convoluted evolution of infant brain networks during
the first postnatal year is pivotal for identifying the dynamics of early brain
connectivity development. Existing deep learning solutions suffer from three
major limitations. First, they cannot generalize to multi-trajectory prediction
tasks, where each graph trajectory corresponds to a particular imaging modality
or connectivity type (e.g., T1-w MRI). Second, existing models require
extensive training datasets to achieve satisfactory performance which are often
challenging to obtain. Third, they do not efficiently utilize incomplete time
series data. To address these limitations, we introduce FedGmTE-Net++, a
federated graph-based multi-trajectory evolution network. Using the power of
federation, we aggregate local learnings among diverse hospitals with limited
datasets. As a result, we enhance the performance of each hospital's local
generative model, while preserving data privacy. The three key innovations of
FedGmTE-Net++ are: (i) presenting the first federated learning framework
specifically designed for brain multi-trajectory evolution prediction in a
data-scarce environment, (ii) incorporating an auxiliary regularizer in the
local objective function to exploit all the longitudinal brain connectivity
within the evolution trajectory and maximize data utilization, (iii)
introducing a two-step imputation process, comprising a preliminary KNN-based
precompletion followed by an imputation refinement step that employs regressors
to improve similarity scores and refine imputations. Our comprehensive
experimental results showed the outperformance of FedGmTE-Net++ in brain
multi-trajectory prediction from a single baseline graph in comparison with
benchmark methods.
