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https://github.com/tomfletcher/GeometryOfData

Last synced: 3 months ago
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Host: GitHub
URL: https://github.com/tomfletcher/GeometryOfData
Owner: tomfletcher
Created: 2019-08-20T19:38:17.000Z (almost 5 years ago)
Default Branch: master
Last Pushed: 2023-11-28T04:16:12.000Z (7 months ago)
Last Synced: 2024-01-16T14:34:47.750Z (5 months ago)
Language: Jupyter Notebook
Size: 57.1 MB
Stars: 4
Watchers: 3
Forks: 7
Open Issues: 0
Metadata Files:
- Readme: readme.md

Lists

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:** Thronton E316 / Zoom
* **Instructors:** [Tom Fletcher](https://engineering.virginia.edu/faculty/tom-fletcher) (ptf8v *AT* virginia *DOT* edu) and [Aman Shrivastava](https://4m4n5.github.io/) (as3ek *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:** Tom: Wednesdays, 3:00 - 4:00 pm in Rice 306 & Aman: Mondays, 3:00 - 4:00 pm in Rice 342

## 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)