Learning from Procrustes analysis to improve multivariate calibration
For the multivariate calibration model y = Xb + e, y and X are typically mean centered to respective column means to remove offsets before estimating b. Often X is obtained under different experimental conditions (temperature, days, etc.). In this case, mean centering across all the conditions (global mean centering) assumes a common offset for the different conditions. Additionally, after a calibration model has been developed for process analysis, it is often necessary to update the model later in time to new conditions. In this case, new measurements are made. These new X and y values can be augmented to the original X and y arrays; mean centered to new column means, that is global mean centering; and a new calibration model is then obtained. The established method of Procrustes analysis (PA) is used in many spectral preprocessing and calibration transfer methods and local mean centering is a key processing element in PA. Rather than global mean centering in multivariate calibration, this paper looks at local mean centering where X and y are locally mean centered relative to respective experimental conditions, that is mean centering data groups with common offsets. When this approach is used, improved results are possible as demonstrated with two spectroscopic data sets where prediction errors and uncertainties reduce. Other regression diagnostics are also shown to improve. Copyright (c) 2008 John Wiley & Sons, Ltd.
procrustes analysis multivariate calibration mean center calibration transfer