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Multivariate Curve Resolution

Course Description

Multivariate Curve Resolution (MCR), also known as Self-Modeling Mixture Analysis (SMMA), is a powerful class of semi-quantitative methods used to elucidate the composition of a multivariate set of data taken on mixtures. Unlike standard quantification methods, MCR attempts to determine the composition of the mixtures without, or with incomplete prior knowledge of the components of the system or their response in the variables, i.e. pure-component spectra. The goal of MCR is to obtain a physically meaningful decomposition of the data. This course will discuss the relationship of MCR to Classical Least Squares (CLS) and Principal Component Analysis (PCA) and discuss various MCR methods. Central to this course’s objectives are an understanding of the challenges in MCR and how the different MCR approaches can be applied depending on the information that is known about the system under study. Examples from conventional spectroscopy will be considered along with hyper spectral images where MCR can be used to create “chemical maps” on surfaces. The course includes hands-on computer time for participants to work example problems using PLS_Toolbox and MIA_Toolbox or Solo+MIA.


Linear Algebra for Machine Learning and Chemometrics, Chemometrics I–PCA and Chemometrics II–Regression and PLS or equivalent experience.

Course Outline

  1. Introduction to Curve Resolution and Self-Modeling Mixture Analysis
  2. Evolving Factor Analysis / Evolving Window Factor Analysis
  3. Purity Based Approaches
  4. Alternating Least Squares MCR
  5. Constraints
  6. Handling Interferents
  7. Other Curve Resolution Methods