Nonlinear KCCA in fMRI activation analysis: Self-supervised optimization and robust back-reconstruction

Recent studies have extended nonlinear kernels to Kernel Canonical Correlation Analysis (KCCA), enabling more flexible modeling of complex relationships globally. Building on these developments, we propose three key enhancements to nonlinear KCCA. First, inspired by self-supervised learning in machine learning research, we refine the parameter optimization process by adopting a subject-wise criterion designed to mitigate overfitting. Second, we introduce an improved back-reconstruction (inverse mapping) method that achieves higher accuracy and robustness than existing voxel-importance estimation methods. Third, we further investigate the kernel selection strategy based on convergence behavior, and validate its effectiveness through activation accuracy, data augmentation robustness, and eigendecomposition. The proposed framework is evaluated on both simulated and task-based fMRI datasets, with results demonstrating consistent improvements across multiple performance metrics.