UMAP: Mathematical Details (clearly explained!!!)

If you understand the main ideas of how UMAP works and want to dive in deeper, this 'Quest is for you!!! It also highlights some of the more subtle differences between UMAP and t-SNE. BAM!

NOTE: This StatQuest assumes that you are already familiar with the main ideas of how UMAP works...
   • UMAP Dimension Reduction, Main Ideas!!!  
...and with how Gradient Descent and Stochastic Gradient Descent work...
   • Gradient Descent, Step-by-Step  
   • Stochastic Gradient Descent, Clearly Expla...  

And if you're not already familiar with t-SNE and want to learn more, check out...
   • StatQuest: t-SNE, Clearly Explained  

ALSO NOTE: This StatQuest is based on the original UMAP manuscript...
https://arxiv.org/pdf/1802.03426.pdf
...specifically Appendix C, From t-SNE to UMAP, which is also here...
https://jlmelville.github.io/uwot/uma...
...and the UMAP user documentation...
https://umap-learn.readthedocs.io/en/...

For a complete index of all the StatQuest videos, check out:
https://statquest.org/video-index/

If you'd like to support StatQuest, please consider...

Patreon:   / statquest  
...or...
YouTube Membership:    / @statquest  

...buying one of my books, a study guide, a t-shirt or hoodie, or a song from the StatQuest store...
https://statquest.org/statquest-store/

...or just donating to StatQuest!
https://www.paypal.me/statquest

Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter:
  / joshuastarmer  

0:00 Awesome song and introduction
1:48 Calculating high-dimensional similarity scores
6:50 Making the scores symmetrical
8:47 Calculating low-dimensional similarity scores
10:41 Moving the low-dimensional points

#StatQuest #UMAP #DimensionReduction