Big data in multi-block data analysis: an approach to parallelizing partial least squares mode B algorithm

Partial Least Squares (PLS) Mode B is a multi-block method and a tightly coupled algorithm for estimating structural equation models (SEMs). Describing key aspects of parallel computing, we approach the parallelization of the PLS Mode B algorithm to operate on large distributed data. We show the scalability and performance of the algorithm at a very fine-grained level thanks to the versatility of pbdR, a R-project library for parallel computing. We vary several factors under different data distribution schemes in a supercomputing environment. Shorter elapsed times are obtained for the square-blocking factor 16 x 16 using a grid of processors as square as possible and non-square blocking factors 1000 x 4 and 10000 x 4 using an one-column grid of processors. Depending on the configuration, distributing data in a larger number of cores allows reaching speedups of up to 121 over the CPU implementation. Moreover, we show that SEMs can be estimated with big data sets using current state-of-the-art algorithms for multi-block data analysis.