Linear Algebra v2: Regression and SVD
Date:
Speaker: Mohan Shankar
c/o 2024, Chemistry
Description:
Building off of my first talk, I will couple linear algebra and calculus to introduce the idea of the cost function along with the simple technique of linear regression. We’ll then revisit eigenvectors and values while briefly describing how to systematically find them. The Google Page Rank algorithm will also be shown again, this time with the numerical calculations of finding the eigenvector associated with $\lambda = 1$. From there, we’ll touch on the singular value decomposition (SVD), one of the most important linear algebraic tools given its utility for dimensionality reduction and look at image compression using the technique.
Note. This talk used a Jupyter Notebook as the mode of presentation, so the relevant “slides” file is linalg_talk.ipynb. In order for all of it to work, you’ll have to download the images in the folder and place them in the same directory as the .ipynb file so that it can run. The necessary one is tundy.jpeg while the others are used in Markdown cells instead meaning an error won’t occur if they aren’t present.