Nonlinear kernel-based fMRI activation detection

Kernel Canonical Correlation Analysis (KCCA) is an effective method for globally detecting brain activation with reduced computational complexity. However, the current KCCA is limited to linear kernels, and the performance of more general types of kernels remains uncertain. This study aims to expand the current KCCA method to arbitrary nonlinear kernels. Our contributions are twofold: First, we propose an inverse mapping algorithm that works for general types of nonlinear kernels. Second, we demonstrate that nonlinear kernels yield improved performance, particularly when the true neural activation deviates from the hypothesized hemodynamic response function due to the complex nature of neural responses. Our results, based on a simulated fMRI dataset and two task-based fMRI datasets, indicate that nonlinear kernels outperform linear kernels and effectively reduce activation in undesired regions.