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Linear algebra resources and links of interest

Online courses

Linear algebra

• Khan Academy: Linear Algebra

  • Not really a stand alone linear algebra class (more as a supplement), but contains lots of good information.

• Open Courseware: Linear Algebra

  • MIT’s introductory linear algebra course.Statistics for Applications (18.650/18.6501)

  • YouTube playlist

  • Principal Component Analysis

  • Principal Component Analysis (Lecture 19)

  Principal Component Analysis (cont.)(Lecture 20)

• Open Courseware: Matrix Methods i n in Data Analysis, Signal Processing, and Machine Learning

  • The follow-on course to the introduction linear algebra class. Matrix methods expands on the fundamental concepts discussed and introduces some additional ideas that are also very useful, such as positive-definite matrices, singular value decomposition, etc.

• edx.org: Linear Algebra Courses

  • Free (or paid, if you want a certificate), self-paced linear algebra courses from a number of institutions.

Singular Value Decomposition (SVD)

SVD is a fundamental factorization technique that is used a in wide variety of situations and fields that vary from statistics (e.g., principal component analysis) to fluid flow (e.g., dynamical systems).

• Steve Brunton

  • Singular Value Decomposition YouTube playlist

    • Book associated with lectures: Data Driven Science & Engineering: Machine Learning, Dynamical Systems, and Control

    • Book website

  • Notes

    • I (Jason) have been really enjoying this playlist. Great explanations of SVD with coding examples (Matlab and Python) and applications (e.g., image compression, fast approximations of fluid flow, PCA).

    • What may be of particular interest to some in this group is discussion of Robust Principal Component Analysis (RPCA), which is a means of dealing with matrices that are missing lots of data.

Principal Component Analysis (PCA)

A specific application of SVD focused on finding the rotation of a matrix that maximizes the most variation along a set of axes (columns) that have been standardized.

• MIT’s Open Courseware

  • Statistics for Applications (18.650/18.6501)

    • YouTube playlist

    • Principal Component Analysis

    • Principal Component Analysis (Lecture 19)

    • Principal Component Analysis (cont.)(Lecture 20)

Videos highlighting applications of linear algebra

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• Zach Star

  • Dear linear algebra students, This is what matrices (and matrix manipulation) really look like

  • The Applications of Matrices | What I wish my teachers told me way earlier

PCA

• Luis Serrano

  • Principal Component Analysis (PCA)

    • One of the better explanations of PCA I’ve seen.

• StatQuest with Josh Starmer (Genetics Dept., University of North Carolina at Chapel Hill)

  • Machine Learning playlist

    • PCA main ideas in only 5 minutes!!!

    • Principal Component Analysis (PCA) clearly explained (2015)

    • Principal Component Analysis (PCA), Step-by-Step

    • PCA - Practical Tips

      • Nice explanations of (among other things):

        • Scaling: so as not to artificially weight data measured at different scales.

        • Centering: SVD expects data at the origin, so PCA expects data to be centered at the origin.

    • PCA in R

      • Code used in the video

• STHDA

  • Principal Component Methods in R: Practical Guide

• Data4Bio

  • Data for Biologists

    • Dimensionality Reduction: High Dimensional Data, Part 1

• Julia Silge

  • Understanding PCA using Stack Overflow data

• Code Emporium

  • Principal Component Analysis (PCA) - The Math You Should Know!

    • A deep dive into the mathematical justification of PCA.

  Luis Serrano

  • Principal Component Analysis (PCA)

    • One of the best explanations of PCA I’ve seen.