Figure 1.

Assessing the neighborhood size and the estimation of n _x(i) and n _y(i) in the k‐nearest neighbor‐based MI algorithm for k = 1. Left panel: The distance of the voxel i from other voxels in both validation time‐series space (d _y(y _i,y _j)) and training SPM space (d _x(x _i,x _j)) is calculated. The distance in the joint space (d _z) is defined as the maximum of the distance in the time‐series space (d _y) and the distance in the SPM statistic space (d _x). For voxel i rank d _z from smallest to largest. Then denote ε_z(i) as the distance from z _i to its kth neighbor where the kth neighbor is defined as the voxel with the kth smallest d _z(z _i,z _j) value in the list. The voxel l is the first nearest voxel to the voxel i, and for k = 1, its distance from the voxel i defines the neighborhood size; therefore, ε_z(i) = 1.7. Right panel: n _x(i) is defined as the number of voxels whose distances from voxel i in statistic space (X) is equal to or less than ε_z(i), which is n _x(i) = 3 in this example. n _y(i) is the number of voxels whose distances from voxel i in time‐series space (Y) is equal to or less thanε_z(i), which is n _y(i) = 5 in this example. For each voxel (i = 1, …, N), its kth nearest voxel is found, ε_z(i)is estimated, and using the calculated values of n _x(i) and n _y(i) the MI between the validation time‐series and SPM is estimated (see main text and Appendix for details).