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Multi-way analysis - PhD course

Welcome to the homepage of “Multi-way Analysis”. On these pages you will find information about the course, its structure, the examination and other relevant aspects. If you have any comments or questions, just send an e-mail to


  • Practical details incl. how to sign up

  • What's learned

  • Course structure

  • The examination

  • Prepare for the course

  • Details in MATLAB



Practical details 

Official homepage:

Official home page

Course credit: 3 ECTS-points
Course responsible: Rasmus Bro
Course arrangements: One week
Period: Around May, right after Copenhagen School of Chemometrics
Place: Frederiksberg campus, Denmark
Language: English
Type of Evaluation: Written report
Software: PLS_Toolbox for Matlab is used throughout and must be installed before the course
Data: Please bring your own data to the course and make sure it is readily available in Matlab
Signup: See official page (link above)


What's learned?

After completing course the students will be able to apply advanced chemometric methods on real world problems. The course will focus on multi-way techniques such as multilinear-PLS, PARAFAC, and TUCKER as well as a review of classical chemometric methods including Principal Component Analysis, Principal Component Regression, and Partial Least Squares Regression. The methods treated will explicitly or implicitly cover the following application areas: classification, calibration, prediction, process optimization, spectral resolution, restrictions and interpretability of solutions. 

  • Introduction to two-way chemometrics
  • PARAFAC modeling
  • N-PLS modeling
  • Tucker3 modeling
  • Preprocessing of multi-way arrays
  • Validation
  • Advanced aspects





Every person analyze their own data and writes a report. The report must be short and concise. No basic multi-way theory should be given. A short description of the data and their background must be provided. A short description of aim of the present work must be provided. This aim is not necessarily the overall aim of the project from which the data stem (although this is of course nice). Rather the purpose should be chosen in order to test and evaluate the students ability to use the methods taught at the course. It is important to discuss in detail how the models have been critically used for the stated purposes. Preferably all methods should be used on a comparative level if possible.


Prepare for the course

The following literature should be read carefully before the course.

  1. Matlab introduction
  2. Chapter 1,3,4 in this
  3. Or chapter 1, 2, 3 and 5 in this
  4. Other stuff we will need


Details in MATLAB

Create a dataset object

>> Xnew = dataset(X);


Edit a dataset object (add labels, change individual values etc.)

>> editds(X);


Import e.g. an excel sheet

>> editds;


View model after you have closed the window

>> model = parafac(X,3);

>> modelviewer(model,X);

Could not access file: