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

▬▬ Papers / Resources ▬▬▬
Colab Notebook: https://colab.research.google.com/dri...

Sources:
TDA Introduction: https://www.frontiersin.org/articles/...
TDA Blogpost: https://chance.amstat.org/2021/04/top...
TDA Applications Blogpost: https://orbyta.it/tda-in-a-nutshell-h...
TDA Intro Paper: https://arxiv.org/pdf/2006.03173.pdf
Mathematical UMAP Blogpost: https://topos.site/blog/2024-04-05-un...
UMAP Author Talk:    • UMAP Uniform Manifold Approximation a...  
UMAP vs. t-SNE Global preservation paper: https://dkobak.github.io/pdfs/kobak20...
Fuzzy Topology Slidedeck: https://speakerdeck.com/lmcinnes/umap...
Short UMAP Tutorial: https://jyopari.github.io/umap.html


Image Sources:
Thumbnail Image: https://johncarlosbaez.wordpress.com/...
Persistent Homology: https://orbyta.it/tda-in-a-nutshell-h...


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▬▬ 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


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