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Classical Least Squares (CLS) Methods

March 2, 2021

Eigenvector Research, Inc. is pleased to bring you Classical Least Squares (CLS) Methods, an online instructor-led live short course. Complete information about the course can be found by following the links below.

Course Description

Inverse Least Squares (ILS) methods such as Principal Components Regression (PCR) and Partial Least Squares (PLS) are ubiquitous in data science and chemometrics. However, Classical Least Squares (CLS or forward least squares) techniques are seeing a resurgence in popularity. The two major reasons for this are 1) better interpretability due to their relationship with first principles models, and 2) the ability to more closely control aspects of the regression modeling. As with ILS, CLS methods can be used for exploratory analysis, detection, classification and quantification.

This half-day course will start by covering CLS regression methods including classical, extended, weighted and generalized least squares. It will be shown how these methods can be used to account for interferents (i.e. analytes other than the one of interest) in spectroscopic systems. CLS also provides a natural framework for the development of popular de-cluttering methods such as External Parameter Orthogonalization (EPO) and Generalized Least Squares (GLS) weighting. It will also be shown how constraints can be easily employed with these methods to allow greater control over the modeling. Hands-on exercises will be done using PLS_Toolbox/Solo.


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

Course Outline

  1. Introduction to Classical Least Squares Methods
    1. The CLS Model
    2. Inherent Challenges
  2. Practical use of CLS Models
    1. Model identification
    2. Model application
    3. Examples
  3. Extended CLS
    1. Why?
    2. Creating extended factors
    3. Application
    4. Examples
  4. Weighted CLS
    1. Introduction
    2. Suitable scenarios
    3. Application
    4. Examples
  5. Generalized Least Squares
    1. Origins
    2. Applications
  6. Conclusions

Course Fee

Prices include instruction, course materials (provided in advance in .pdf format), a certificate of completion and access to the recorded class sessions. Prices shown are shown below. Payment must be received by 5pm PST, Monday, March 1, 2021.

Linear Algebra for Chemometricians

Note: Payment must be received by 5pm PST, Monday, March 1, 2021. Credit card orders are strongly encouraged. Acceptable forms of payment include MasterCard, VISA, American Express, and checks drawn on a US bank. Wire transfers can also be arranged.

Academic discount: University students and faculty are eligible for the academic rate. Verification of University affiliation is required by providing valid university mailing and e-mail address. Note that we define academic as “degree granting institution.”

How to Register, Deadlines and Cancellations

To register, login to your Eigenvector account, or create an account, then select the class you would like to attend under the “Purchase” tab. You can pay directly with your MasterCard, VISA or American Express using our secure credit card processing. You may ask to be invoiced, however, Payments must be received by 5pm PST, Monday, March 1, 2021.

Complete refunds will be made for cancellations prior to Friday, February 26, 2021. No refunds will be made for cancellations after that date, however, substitutions are gladly accepted.


Classical Least Squares (CLS) Methods will be taught in a single session of 3.5 hours on Tuesday, March 2. The schedule will be as follows.

Daily Schedule, Pacific Standard Time (PDT)
06:45 – 07:00 WebEx available for login*
07:00 – 08:00 Instruction
08:00 – 08:10 Coffee Break
08:10 – 09:10 Instruction
09:10 – 09:20 Coffee Break
09:20 – 10:20 Instruction
10:20 – 10:30 Wrap-up and questions

* 7:00 am PST is 10:00am in New York, 15:00 in London and 16:00 in Paris.

Can’t make it at this time? The sessions will be recorded and made available to course participants for their use for one year after the event.