Figure 1.

Schematic of the CJIVE decomposition for obtaining joint subject scores and loadings. Quantities specific to X₁ are shown in blue; those specific to X₂, orange. Gray boxes illustrate scores, with a green outline for joint scores. Checked and dotted boxes represent loadings. Steps are outlined in Algorithm 1. Separately, SVD is applied to each data block (far left) to obtain low-rank PC scores (all score matrices are shown as gray boxes). Next, CCA is applied to the PC scores with the number of components chosen using a permutation test. Joint subject scores are equivalent to a weighted average of the resultant canonical variables. Joint loadings result from the matrix product between joint subject scores and data blocks, i.e., regression of the data blocks onto joint subject scores.