The singular value decomposition (SVD) is one of the most powerful tools in data analysis, providing deep insight into high-dimensional datasets. In this lecture, we introduce the fundamentals of SVD, covering its existence, key properties, and practical significance. We then bring theory to life with a hands-on coding demonstration, applying SVD to real data to uncover hidden patterns and structures. This lecture offers a complete journey from theory to application, laying the foundation for many of the advanced techniques and applications explored in the lectures that follow.
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/
Follow @jbramburger7 on Twitter for updates.
