The idm Package: Incremental Decomposition Methods in R

Abstract

In modern applications large amounts of data are produced at a high rate and are characterized by relationship structures changing over time. Principal component analysis (PCA) and multiple correspondence analysis (MCA) are well established dimension reduction methods to explore relationships within a set of variables. A critical step of the PCA and MCA algorithms is a singular value decomposition (SVD) or an eigenvalue decomposition (EVD) of a suitably transformed matrix. The high computational and memory requirements of ordinary SVD and EVD make their application impractical on massive or sequential data sets. A series of incremental SVD/EVD approaches are available to address these issues. The idm R package is introduced that implements two efficient incremental SVD approaches. The procedures in question share desirable properties that ease their embedding in PCA and MCA. The package also provides functions for producing animated visualizations of the obtained solutions. A comparison of online MCA implementations in terms of accuracy is also included.