Fig. 3

Visual representation of variable importance. Vectors are the projection on the two leading KPCA axes of the vectors in the kernel feature space pointing to the direction of maximum locally growth of the represented variables. In this scheme, the reference variable is in red and original variables are in black. Each sample point anchors a vector representing the direction of maximum locally growth. a When an original variable is associated with the reference variable, the angle between both vectors, averaged across all samples, is close to zero radians. b In contrast, when an original variable is negatively associated with the reference variable, the angle between both vectors, averaged across all samples, is close to π radians. c When an original variable does not show any association with the reference variable, the angle changes non-consistently among the samples. In noisy data, behavior (c) is expected to occur in most variables, so the variable with average angle closest to the overall angle after accounting for all variables is assumed to be the least relevant