Interactive introduction to multi-way analysis in MATLAB
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CHAPTER 5

ADVANCED MULTI-WAY REGRESSION



 
 
 
Contents
  1. Load data
  2. Preprocess data
  3. Fit three-way PLS regression model
  4. Compare to other calibration models
  5. Comments
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

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.

how to do it

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).

how to do it
 

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)

how to do it

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

how to do it

5. Comments please

Please comment here if the above exercises help in understanding the basics of multi-way data, or give suggestions to improvements


Next Chapter: Preprocessing Previous Chapter: Multi-way calibration First Chapter: Contents

The N-way tutorial
Copyright © 1998
R. Bro