PCA-GCA

This is a multivariate projection method for extracting common and distinctive components in data fusion

PCA-GCA can be used to extract common and distinctive components (or latent variables) from blocks of multivariate data. As the name suggests, it is a combination of Principal Component Analysis (PCA) and Generalized Canonical Correlation Analysis (GCA). The method can be used on data blocks where the common dimension is either the rows or columns.

The method starts by performing PCA on each data block individually, and then uses GCA to find canonical variates (common components) between the PCA scores (if rows are the common dimension) or loadings (if columns are the common dimension). Common components are identified by high canonical correlation coefficients at the same time as they explain a significant amount of variation in each of the data blocks. Distinct components are found by orthogonalizing the common components and applying Singular Value Decomposition (SVD) on the remainders.

The advantages of PCA-GCA are that it is invariant to between-block scaling, it can handle multiple data blocks effectively, and it is easy to implement and interpret.

The method is described in:

Smilde, A. K., Måge, I., Næs, T., Hankemeier, T., Lips, M. A., Kiers, H. A. L., Acar, E., & Bro, R. (2017). Common and Distinct Components in Data Fusion. Journal of Chemometrics, 31(7). https://doi.org/10.1002/cem.2900

Måge, I., Smilde, A. K., & van der Kloet, F. M. (2019). Performance of methods that separate common and distinct variation in multiple data blocks. Journal of Chemometrics, 33(1). https://doi.org/10.1002/cem.3085