What do numbers look like ?▻https://johnhw.github.io/umap_primes/index.md.html
This is the first million integers, represented as binary vectors indicating their prime factors, and laid out using the UMAP dimensionality reduction algorithm by Leland Mcinnes.
A very pretty structure emerges; this might be spurious in that it captures more about the layout algorithm than any “true” structure of numbers. However, the visual effect is very appealling and requires no tricky manipulation to create.
Et d’où proviennent les structures à 1 dimension ?
(qui ressortent particulièrement fortement dans le graphique coloré en fonction de la parité)
Une belle application d’UMAP à des données génétiques :
▻https://www.biorxiv.org/content/early/2018/09/23/423632
Un tutorial assez simple sur la réduction de dimensionalité
▻https://idyll.pub/post/dimensionality-reduction-293e465c2a3443e8941b016d
nouvelles slides de Leland McIness
▻https://speakerdeck.com/lmcinnes/learning-topology-topological-methods-for-unsupervised-learning
Un exemple très complet d’analyses génomiques avec UMAP
▻https://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1008432
Et encore un exemple (interactif et tout)
▻https://pair-code.github.io/understanding-umap
Ooops! Du nouveau sur cette carte des nombres premiers
▻https://twitter.com/hippopedoid/status/1318917878364672001
Et d’où proviennent les structures à 1 dimension ?
Turns out, the swirly and spaghetti UMAP structures were artifacts
