Tensor-based Multiple Canonical Correlation Analysis
R package for the multiple canonical correlation analysis (MCCA) of data tensors (multidimensional arrays) measured on the same individuals/objects. The goal is to find rank-1 tensors of canonical weights such that the sum of covariances or correlations between the associated canonical scores and across all pairs of datasets is maximal. Various scaling contraints and orthogonality constraints can be imposed on the canonical weights or scores during the optimization. The package implements several initialization methods (CCA, SVD, random) and optimization methods (block coordinate ascent, gradient-based with retraction by scaling, gradient-based with retraction by rotation). Permutation tests can be run to select the number of canonical components to retain. The package also features bootstrap methods, including basic-, percentile-, and normal bootstrap confidence intervals.
To install the R package:
library(devtools)
install_github("https://github.com/ddegras/tensorMCCA", subdir = "tensorMCCA")
Main functions:
- MCCA optimization:
mcca.cov,mcca.cor - Initialization:
mcca.init.cca,mcca.init.svd,mcca.init.random - Permutation tests:
permutation.test - Bootstrap confidence intervals:
mcca.boot,mcca.boot.ci - Model simulation:
simulate.factor.model