# Introduction to Matlab

Mathematical aspects of bilinear factor models (PCA and PLS)

# Frans van den Berg

University of Copenhagen, Faculty of Life Sciences
Department of Food Science, Quality & Technology group
Rolighedsvej 30
(Room T447)

DK-1958   Frederiksberg C
Denmark

# Introduction

Two titles = two aims: 1) to get a quick introduction to the computer program Matlab; 2) to get some insight into the bilinear factor models Principal Component Analysis (PCA) and Partial Least Squares (PLS) regression, focusing on the mathematics and numerical aspects rather than how's and why's of data analysis practice. For the latter part it is assumed (but not absolutely necessary) that the reader is already familiar with these methods. It also assumes you have had some preliminary experience with linear/matrix algebra.

This material is – amongst others - written as the introduction to the main part of the Advanced Chemometric Methods - Multi-way Analysis course at KVL, Denmark. The Matlab part is obligatory because all the exercises and project with multi-way models have to be performed in Matlab (there is no other program available!). The “maths” will hopefully assist in better understanding the concepts of N-way modeling: understanding things in flatland (the 2D data tables in PCA and PLS) make life “simple” in hyperspace (3D-and-up in multi-way models)!

This introduction is based on Matlab releases 6.1/12.1, 6.5/13, 7/14, 7.3/R2006b and 7.4/R2007a (differences between the releases are insignificant for the scope of this introductory; most exercises will work with any resent Matlab release). The computer exercise material can be found below as well.

# Documents and computer code

• IntroMatlab (PDF) ---------- Document with introductory material for Matlab and PCA/PLS bilinear factor modeling.
• GetStart (PDF) -------------- Official Matlab document with further introductory material.
• IntroMatlab_code (ZIP) --- Matlab code for the exercises.
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