Uniform Manifold Approximation and Projection (UMAP) | Dimensionality Reduction Techniques (5/5)

▬▬ Papers / Resources ▬▬▬
Colab Notebook: https://colab.research.google.com/drive/1n_kdyXsA60djl-nTSUxLQTZuKcxkMA83?usp=sharing

Sources:
- TDA Introduction: https://www.frontiersin.org/articles/10.3389/frai.2021.667963/full
- TDA Blogpost: https://chance.amstat.org/2021/04/topological-data-analysis/
- TDA Applications Blogpost: https://orbyta.it/tda-in-a-nutshell-how-can-we-find-multidimensional-voids-and-explore-the-black-boxes-of-deep-learning/
- TDA Intro Paper: https://arxiv.org/pdf/2006.03173.pdf
- Mathematical UMAP Blogpost: https://topos.site/blog/2024-04-05-understanding-umap/
- UMAP Author Talk: https://www.youtube.com/watch?v=nq6iPZVUxZU&ab_channel=Enthought
- UMAP vs. t-SNE Global preservation paper: https://dkobak.github.io/pdfs/kobak2021initialization.pdf
- Fuzzy Topology Slidedeck: https://speakerdeck.com/lmcinnes/umap-uniform-manifold-approximation-and-projection-for-dimension-reduction?slide=39
- Short UMAP Tutorial: https://jyopari.github.io/umap.html


Image Sources:
- Thumbnail Image: https://johncarlosbaez.wordpress.com/2020/02/10/the-category-theory-behind-umap/
- Persistent Homology: https://orbyta.it/tda-in-a-nutshell-how-can-we-find-multidimensional-voids-and-explore-the-black-boxes-of-deep-learning/


▬▬ Support me if you like 🌟
►Link to this channel: https://bit.ly/3zEqL1W
►Support me on Patreon: https://bit.ly/2Wed242
►Buy me a coffee on Ko-Fi: https://bit.ly/3kJYEdl
►E-Mail: deepfindr@gmail.com

▬▬ Used Music ▬▬▬▬▬▬▬▬▬▬▬
Music from #Uppbeat (free for Creators!):
https://uppbeat.io/t/sulyya/weather-compass
License code: ZRGIWRHMLMZMAHQI

▬▬ Used Icons ▬▬▬▬▬▬▬▬▬▬
All Icons are from flaticon: https://www.flaticon.com/authors/freepik

▬▬ Timestamps ▬▬▬▬▬▬▬▬▬▬▬
00:00 Introduction
00:32 Local vs. Global Technqiues
1:25 Is UMAP better?
02:08 The Paper
02:40 Topological Data Analysis Primer
04:04 Simplices
05:04 Filtration
06:22 Persistent Homology
07:02 UMAP Overview
07:40 Step 1: Graph construction
08:25 Uniform distribution
09:44 Non-uniform real-world data
10:48 Enforcing uniformity
12:05 Exponential decay
12:43 Local connectivity constraint
14:24 Distance function
16:19 Local metric spaces
17:00 Fuzzy simplicial complex
18:38 The full picture of step 1
19:10 Step 2: Graph layout optimization
19:55 Comparing graphs
21:15 Cross entropy loss
22:14 Attractive and repulsive forces
22:56 More details
24:04 Code
26:28 t-SNE vs. UMAP
27:24 Outro


▬▬ My equipment 💻
- Microphone: https://amzn.to/3DVqB8H
- Microphone mount: https://amzn.to/3BWUcOJ
- Monitors: https://amzn.to/3G2Jjgr
- Monitor mount: https://amzn.to/3AWGIAY
- Height-adjustable table: https://amzn.to/3aUysXC
- Ergonomic chair: https://amzn.to/3phQg7r
- PC case: https://amzn.to/3jdlI2Y
- GPU: https://amzn.to/3AWyzwy
- Keyboard: https://amzn.to/2XskWHP
- Bluelight filter glasses: https://amzn.to/3pj0fK2