The singular value decomposition (SVD) is one of the most powerful tools in all of data analysis. In this lecture we introduce the viewer to the basics of the method, including its existence, properties, and how it helps understand high-dimensional data. We further supplement the lecture with a coding demonstration where the SVD is applied to real data to see what we can find. The result is a complete lecture that stretches from theory to application of a method that will form the basis of much of the applications in the following lectures.
Coding demonstration in MATLAB comes Lecture 12 here: https://github.com/jbramburger/Data-Science-Methods/tree/main/Code
Get the book here: https://epubs.siam.org/doi/10.1137/1.9781611978162
Scripts and notebooks to reproduce all examples: https://github.com/jbramburger/DataDrivenDynSyst
This book provides readers with:
- methods not found in other texts as well as novel ones developed just for this book;
- an example-driven presentation that provides background material and descriptions of methods without getting bogged down in technicalities;
- examples that demonstrate the applicability of a method and introduce the features and drawbacks of their application; and
- a code repository in the online supplementary material that can be used to reproduce every example and that can be repurposed to fit a variety of applications not found in the book.
More information on the instructor: https://hybrid.concordia.ca/jbrambur/
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