Implementation of Line Search for Parafac Analysis of Fluorescence Excitation–Emission Matrix

Recovery of fluorophore groups in dissolved organic matter using the PARAFAC canonical tensor decomposition of fluorescence excitation–emission matrix (EEM) is widely used in the study of natural waters. However, fitting the PARAFAC model, especially for its validation, is very time consuming. Several strategies for accelerating the PARAFAC fitting to the EEM of sea waters were considered. It was shown that strategies with optimization of a large set of hyperparameters do not result in significant acceleration because of high time costs for this operation. It was proposed to perform optimization for one variable once for several iterations of the algorithm. This approach made it possible to achieve acceleration of calculations using line-search strategy. The maximum acceleration by 2.3 times was achieved for the line-search strategy using the extrapolation step in a power function of the iteration number although in this case sequential steps are collinear at some stages of the algorithm.