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UMAP: Mathematical Details (clearly explained!!!)

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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... https://youtu.be/eN0wFzBA4Sc ...and with how Gradient Descent and Stochastic Gradient Descent work... https://youtu.be/sDv4f4s2SB8 https://youtu.be/vMh0zPT0tLI And if you're not already familiar with t-SNE and want to learn more, check out... https://youtu.be/NEaUSP4YerM 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/umap-for-tsne.html ...and the UMAP user documentation... https://umap-learn.readthedocs.io/en/latest/parameters.html For a complete index of all the StatQuest videos, check out... https://app.learney.me/maps/StatQuest ...or... https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...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: https://twitter.com/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

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