Overview of distance-induced Kernel Canonical Correlation Analysis (KCCA) technique in the context of β-amyloid and tau PET datasets. For each dataset, all of the images are first stacked as a large dimensional vector to allow for the computation of an inter-distance matrix, which results from calculating the Euclidean distance between each pair individual images. These inter-distance matrices are readily transformed to normalized kernels that are combined into a classical KCCA to produce individual scores that are maximally distance-correlated in an underlying latent space.
The diagram illustrates the main component of our Canonical Distance-Correlation Analysis, which is simply a Kernel Canonical Correlation technique with distance-induced kernels.
First, for each PET modality, a matrix of inter-Euclidean distances between each pair of images must be computed. Then, distance-induced kernels are computed as one minus the normalized matrix of the corresponding Euclidean inter-distances.
The nonlinear kernels are then subjected to a classical Kernel Canonical Correlation Analysis to obtain a set of individual tau and β-amyloid scores. These individual scores are then maximally distance-correlated in the underlying latent space.