https://github.com/tomfletcher/GeometryOfData

https://github.com/tomfletcher/GeometryOfData

Last synced: 10 days ago
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• Host: GitHub
• URL: https://github.com/tomfletcher/GeometryOfData
• Owner: tomfletcher
• Created: 2019-08-20T19:38:17.000Z (about 5 years ago)
• Default Branch: master
• Last Pushed: 2024-10-23T15:35:29.000Z (18 days ago)
• Last Synced: 2024-10-23T20:45:13.678Z (18 days ago)
• Language: Jupyter Notebook
• Size: 65.6 MB
• Stars: 7
• Watchers: 3
• Forks: 7
• Open Issues: 0
• Metadata Files:
  • Readme: readme.md

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• awesome-list - Shape Manifolds lecture slides - basics

README

        
## Description

Modern data are high-dimensional, multi-modal, and large-scale, for example, images with millions of pixels, text corpora with millions of words, gene sequences with billions of base pairs, etc. However, these data tend to concentrate on lower-dimensional, nonlinear subspaces known as manifolds. Learning and sampling from this real distribution, hence, is of tremendous value. This class covers the mathematical theory of

high-dimensional geometry and manifolds and how it applies to the latest advances in artificial intelligence.

## Logistics

* **Time:** Tue/Thu 2:00 - 3:15 PM

* **Location:** Thornton E303 / Zoom

* **Instructors:** [Tom Fletcher](https://engineering.virginia.edu/faculty/tom-fletcher) (ptf8v *AT* virginia *DOT* edu)

* **Prerequisites:** You should have basic (undergraduate level) knowledge of Probability, Linear Algebra, Multivariate Calculus, and be comfortable programming in Python

* **Software:** All homeworks will be done in [Jupyter](https://jupyter.org)

* **Office Hours:** Wednesdays, 1 - 2 pm, Rice 306

## Additional Reading

Manfredo do Carmo, *Riemannian Geometry*

Sigmundur Gudmundsson, [*Introduction to Riemannian Geometry*](http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf)

## Example Jupyter Notebooks

For those of you who are relatively new to Jupyter, here are a few notebooks that you might find useful (from my undergraduate course [Foundations of Data Analysis](https://tomfletcher.github.io/FoDA/).)

* [LaTeX math notation guide](https://tomfletcher.github.io/FoDA/examples/MathNotationGuide.ipynb)

* [Data plots in Python](https://tomfletcher.github.io/FoDA/examples/SimpleDataPlots.ipynb)

* [Singular value decomposition](https://tomfletcher.github.io/FoDA/examples/SVD.ipynb)

* [Multiple linear regression](https://tomfletcher.github.io/FoDA/examples/MultipleLinearRegression.ipynb)