Incremental singular value decomposition for some numerical aspects of multiblock redundancy analysis

Simultaneously processing several large blocks of streaming data is a computationally expensive problem. Based on the incremental singular value decomposition algorithm, we propose a new procedure for calculating the factorization of the multiblock redundancy matrix $${{\textbf {M}}}$$ M , which makes the multiblock method more fast and efficient when analyzing large streaming data and high-dimensional dense matrices. The procedure transforms a big data problem into a small one by processing small high-dimensional matrices where variables are in rows. Numerical experiments illustrate the accuracy and performance of the incremental solution for analyzing streaming multiblock redundancy data. The experiments demonstrate that the incremental algorithm may decompose a large matrix with a 75% reduction in execution time. It is more efficient to first partition the matrix $${{\textbf {M}}}$$ M and then decompose it with the incremental algorithm than to decompose the entire matrix $${{\textbf {M}}}$$ M using the standard singular value decomposition algorithm.