A bridge between Tucker-1 and Carroll's generalized canonical analysis

A set of tools for analyzing relationships between and within multiple data matrices is presented. The starting point is a new, unified approach bridging two existing methods; Carroll's Generalized Canonical Analysis (GCA) with the Tucker-1 method for principal component analysis of multiple matrices. GCA and Tucker-1 are shown to correspond to particular choices of a ridge parameter. The unified method is then generalized to a larger space of methods.