Joint and Individual Variation Explained (JIVE) is a method for decomposing multiple datasets obtained on the same subjects into
shared structure, structure unique to each dataset, and noise. The two most common implementations are R.JIVE, an iterative
approach, and AJIVE, which uses principal angle analysis. JIVE estimates subspaces but interpreting these subspaces can be
challenging with AJIVE or R.JIVE. We expand upon insights into AJIVE as a canonical correlation analysis (CCA) of principal component
scores. This reformulation, which we call CJIVE, 1) provides an ordering of joint components by the degree of correlation between
corresponding canonical variables; 2) uses a computationally efficient permutation test for the number of joint components, which
provides a p-value for each component; and 3) can be used to predict subject scores for out-of-sample observations.
Please cite the following article when utilizing this package:
Murden, R., Zhang, Z., Guo, Y., & Risk, B. (2022)
Joint and Individual Variation Explained via Canonical Correlation (or CJIVE) searches for directions of joint variance within two data sets. CJIVE analysis allows extraction of "joint subject scores", which act as a summary of the joint information found across data blocks, and "joint variable loadings", which exhibit the strength with which a variable contributes to the joint variability. CJIVE also allows for extraction of individual scores/loadings. These quantities are based on directions of variance that are unique (not shared) to a dataset.
The file "CheckAJIVE_v_CJIVE_Simulations" provides an example of how to implement CJIVE and compares it to AJIVE, which is closely related to CJIVE. Both analyses use "toy data." The toy data are constrcuted in a manner similar to the simulations in our CJIVE manuscript: Interperative JIVE: Connections with CCA and an Application to Brain Connectivity (10.3389/fnins.2022.969510). The manuscript has been accepted for publication in Frontiers in Neuroscience - Brain Imaging Methods.