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: [email protected] ▬▬ 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