The Copenhagen Chemometrics Group
5. ADVANCED MULTI-WAY REGRESSION
Contents
- Load data
- Preprocess data
- Fit three-way PLS regression model
- Compare to other calibration models
Data used
sugar.mat. Fluorescence spectra were measured on sugar dissolved in water. The according quality parameter color was determined in a sugar plant laboratory. In order to avoid the laborious determination of color in the laboratory it would be beneficial to be able to predict color, e.g. from on-line or at-line measured fluorescence spectra.
Purpose
Using different calibration tools and comparing their relative efficiency.
Information
R. Bro, Multi-way calibration.
Multi-linear PLS, J. Chemom., 1996, 10(1), 47-62.
Prerequisites
Be sure to understand the basics of handling multi-way arrays in MATLAB (Chapter 1).
You should know your two-way PLS and PCR
1. Load data
Get the data
load data (load sugar) and use whos to learn what files are there.
The files EmAx and ExAx are wavelengths for the respective modes in the two variable modes of the three-way array.
2. Prepare data for modeling
Divide the data set into a calibration and a validation set
(choose sizes yourself). Decide on appropriate preprocessing and preprocess the calibration as well as the validation set.
Use PCA or PARAFAC to investigate if there are any signs of outliers
(do not remove any, but bear them in mind in the subsequent calibration modeling step).
3. Fit three-way PLS regression model
Fit a three-way PLS regression model
and validate the model (outliers, number of components).
You can also use cross-validation to find the optimal number of components (ncrossreg)
4. Compare to other calibration models
Compare the results
of the three-way PLS regression model to the results obtained using two-way principal component and PLS regression as well as PARAFAC regression
