Multivariate Data Analysis Course Outline

The course is offered over three days and will cover topics on multivariate applications as presented by Professor John F. MacGregor and ProSensus staff. ProSensus, Inc. is a world leader in the development and use of multivariate data analysis methods for the analysis, monitoring and control of batch processes. Professor John F. MacGregor (Distinguished University Professor, McMaster University and President of ProSensus) is the developer of most of the modern multivariate data analysis methods for industrial processes.

If you require information about the materials provided, software used, target audience and the course instructors, then please visit this page instead.

Day 1

Registration and breakfast

Introduction
	Objectives and overview of the course
	Nature of multivariate process data and data tables
	Why use multivariate methods and the concept of latent variables
	Some process examples
Coffee break
Principal Component Analysis (PCA)
	Geometric and algebraic interpretations
	Score and loading plots and their interpretation
	Analysis of an example data set
	Hotelling's T² and confidence ellipse on the score plot
Lunch
Software Introduction
	Demonstration of the software by repeating the analysis of the example data set
	Interactive session with class on using the software
PCA : continued
	Analysis of residuals
	Determining goodness of fit : introducing Q²
	How the principal components are calculated
	Outliers and clusters
	Interrogating the PCA model: contribution plots
Coffee break
Use of PCA for inspection of historical databases
	What plots are available and how to interpret them score plots loading plots score and loading bi-plots Hotelling's T² and SPE plots Contributions plots: in SPE and t-score plots

Day 2

Breakfast

Projection to Latent Structures Partial Least Squares (PLS)
	The two names for PLS: two interpretations
	Quick review of ordinary least squares (OLS) and multiple linear regression (MLR)
	Moving to principal component regression (PCR)
Coffee break
	PLS: how the model parameters are calculated
	Geometric interpretation
	Relationship of PLS to MLR and PCR
	Example: how to interpret and use the PLS plots
Software session
	Demonstration of the software for PLS analysis
Lunch
	Exercises to help understand PLS analysis

Coffee break
Multivariate statistical process control (MSPC)
	Recap of traditional SPC charts and some of their shortcoming
	Use of online measurements for MSPC: the latent variable approach
	Building an online monitoring system What is required? How to build the monitoring model Work-flow: how each new observation is handled
	Key point of monitoring: detection and diagnosis
	Two industrial case studies
Coffee Break
Interpretation of empirical models and soft sensor applications	Problems with all empirical models: OLS, stepwise regression, PLS, and neural networks Some cautions: Correlation vs. causation Effects of feedback control Building soft sensor applications: Using empirical and theoretical models Implementing models on-line Incorporating process dynamics into the models

Day 3

Breakfast

Classification
	Where classification can be used, and the data required
	Unsupervised classification: PCA
	Supervised classification: SIMCA and PLS-DA
Coffee break
Analysis, monitoring and control of batch processes
	Analysis of historical batch data
	Unfolding batch data for PCA and PLS vs. feature extraction
	Alignment of trajectory data
	Two industrial case studies on batch analysis
	On-line monitoring and control of batch processes
Lunch
Multivariate Image Analysis (MIA)
	Imaging basics: grayscale, colour and multivariate images
	What can be done with images: segmentation class decisions predictions (soft-sensors)
	Introduction to further topics: dealing with multiple sets of images colour segmentation
	Two examples of industrial monitoring from image data
Coffee break
Closing workshop
	Participants will have the opportunity to raise further questions on all course topics, and to interact with the instructors at their computers.

ProSensus, Inc.