Incremental Generalized Canonical Correlation Analysis

Generalized canonical correlation analysis (GCANO) is a versatile technique that allows the joint analysis of several sets of data matrices through data reduction. The method embraces a number of representative techniques of multivariate data analysis as special cases. The GCANO solution can be obtained noniteratively through an eigenequation and distributional assumptions are not required. The high computational and memory requirements of ordinary eigendecomposition makes its application impractical on massive or sequential data sets. The aim of the present contribution is twofold: (a) to extend the family of GCANO techniques to a split-apply-combine framework, that leads to an exact implementation; (b) to allow for incremental updates of existing solutions, which lead to approximate yet highly accurate solutions. For this purpose, an incremental SVD approach with desirable properties is revised and embedded in the context of GCANO, and extends its applicability to modern big data problems and data streams.