Fast algorithm for multiway regression
Flavio Camarrone, Marc M. Van Hulle · 2017
Higher-Order Partial Least Squares (HOPLS) regression is a powerful framework for dealing with ill-conditioned and multiway data. However, it relies on Higher-Order Orthogonal Iteration (HOOI) for extracting the latent factors which can be time consuming in case of large matrices. In this work, we propose an improved version of HOPLS, called fast Higher-Order Partial Least Squares (fHOPLS), which inherits the predictive property of HOPLS while demoting its time complexity by requiring less iterations for extracting the latent components. We compare fHOPLS and HOPLS on two sets of synthetic data and, for the sake of exposition, also unfolded partial least squared (PLS) and N-way PLS (NPLS). Results from the first data set confirms that the predictive performance of fHOPLS is comparable to HOPLS, and outperforms both PLS and NPLS, while results from the second data set confirm the faster computation of fHOPLS over HOPLS.