Multi-way partial least squares modeling of water quality data

A 10 years surface water quality data set pertaining to a polluted river was analyzed using partial least squares (PLS) regression models. Both the unfold-PLS and N-PLS (tri-PLS and quadri-PLS) models were calibrated through leave-one out cross-validation method. These were applied to the multivariate, multi-way data array with a view to assess and compare their predictive capabilities for biochemical oxygen demand (BOD) of river water in terms of their relative mean squares error of cross-validation, prediction and variance captured. The sum of squares of residuals and leverages were computed and analyzed to identify the sites, variables, years and months which may have influence on the constructed model. Both the tri- and quadri-PLS models yielded relatively low validation error as compared to unfold-PLS and captured high variance in model. Moreover, both of these methods produced acceptable model precision and accuracy. In case of tri-PLS the root mean squares errors were 1.65 and 2.17 for calibration and prediction, respectively; whereas these were 2.58 and 1.09 for quadri-PLS. At a preliminary level it seems that BOD can be predicted but a different data arrangement is needed. Moreover, analysis of the scores and loadings plots of the N-PLS models could provide information on time evolution of the river water quality.