5 ms·

Can someone explain to me like I am 5 ?

Jtsummers 4y ago
Convert numbers to a vector space represented by their prime factors: 2 => [1 0 0 0...] 3 => [0 1 0 0...] 4 => [1 0 0 0...] And map that high dimensional space back down to two dimensions (using some technique I haven't dug into yet). Colors are assigned by some scheme, later images help to illustrate how the particular clusterings happen like one where primes are rendered in white.
- LanceH 4y ago
  The whole thing seemed elaborately overly-formally-described and that just lessened the value of the cool graph.
  - alanbernstein 4y ago
    "I have a friend who’s an artist and has sometimes taken a view which I don’t agree with very well. He’ll hold up a flower and say “look how beautiful it is,” and I’ll agree. Then he says “I as an artist can see how beautiful this is but you as a scientist take this all apart and it becomes a dull thing,” and I think that he’s kind of nutty. First of all, the beauty that he sees is available to other people and to me too, I believe. Although I may not be quite as refined aesthetically as he is … I can appreciate the beauty of a flower. At the same time, I see much more about the flower than he sees. I could imagine the cells in there, the complicated actions inside, which also have a beauty." - Richard Feynman
    - tunnuz 4y ago
      https://www.youtube.com/watch?v=ZbFM3rn4ldo https://www.youtube.com/watch?v=ZbFM3rn4ldo
  - teo_zero 4y ago
    I dissent. The list of ingredients of the cake I'm eating doesn't lessen its exquisite taste.
- alanbernstein 4y ago
  other umap examples: https://umap-learn.readthedocs.io/en/latest/interactive_viz.html#umap-zoo https://umap-learn.readthedocs.io/en/latest/interactive_viz....
- O_H_E 4y ago
  ahem .... explain like I am 0.5
  - jerpint 4y ago
    Numbers are placed in an image according to their prime numbers
  - sidlls 4y ago
    This isn’t exactly it, but roughly: Make a vector space with primes as a basis (instead of “x, y, z,…” use “2, 3, 5, …”). For a number, find its prime factors. Make a vector and set elements corresponding to the prime factors of the number equal to 1. Apply some algorithm to map a high-dimensional (more than 2 elements) vector into a two dimensional image where color has some significance.
- 2-718-281-828 4y ago
  2 and 4 are mapped to the same vector?
  - _nalply 4y ago
    Yes. I wondered about that, too.
    - nerdponx 4y ago
      Yes, 4 and 2 have the same set of prime factors: 2.
- nerdponx 4y ago
  The UMAP and tSNE algorithms both use fancy math to find a 2-dimensional representation of the data that tries to preserve local structure as much as possible. So blobs in the original space should be represented as blobs in the reduced space, but the relative positions of any two blobs in the reduced space is not meaningful.
chrisshroba 4y ago
Numbers that have similar prime factors are closer together.

Convert numbers to a vector space represented by their prime factors: 2 => [1 0 0 0...] 3 => [0 1 0 0...] 4 => [1 0 0 0...] And map that high dimensional space back down to two dimensions (using some technique I haven't dug into yet). Colors are assigned by some scheme, later images help to illustrate how the particular clusterings happen like one where primes are rendered in white.

LanceH 4y ago
The whole thing seemed elaborately overly-formally-described and that just lessened the value of the cool graph.
- alanbernstein 4y ago
  "I have a friend who’s an artist and has sometimes taken a view which I don’t agree with very well. He’ll hold up a flower and say “look how beautiful it is,” and I’ll agree. Then he says “I as an artist can see how beautiful this is but you as a scientist take this all apart and it becomes a dull thing,” and I think that he’s kind of nutty. First of all, the beauty that he sees is available to other people and to me too, I believe. Although I may not be quite as refined aesthetically as he is … I can appreciate the beauty of a flower. At the same time, I see much more about the flower than he sees. I could imagine the cells in there, the complicated actions inside, which also have a beauty." - Richard Feynman
  - tunnuz 4y ago
    https://www.youtube.com/watch?v=ZbFM3rn4ldo https://www.youtube.com/watch?v=ZbFM3rn4ldo
- teo_zero 4y ago
  I dissent. The list of ingredients of the cake I'm eating doesn't lessen its exquisite taste.
alanbernstein 4y ago
other umap examples: https://umap-learn.readthedocs.io/en/latest/interactive_viz.html#umap-zoo https://umap-learn.readthedocs.io/en/latest/interactive_viz....
O_H_E 4y ago
ahem .... explain like I am 0.5
- jerpint 4y ago
  Numbers are placed in an image according to their prime numbers
- sidlls 4y ago
  This isn’t exactly it, but roughly: Make a vector space with primes as a basis (instead of “x, y, z,…” use “2, 3, 5, …”). For a number, find its prime factors. Make a vector and set elements corresponding to the prime factors of the number equal to 1. Apply some algorithm to map a high-dimensional (more than 2 elements) vector into a two dimensional image where color has some significance.
2-718-281-828 4y ago
2 and 4 are mapped to the same vector?
- _nalply 4y ago
  Yes. I wondered about that, too.
  - nerdponx 4y ago
    Yes, 4 and 2 have the same set of prime factors: 2.
nerdponx 4y ago
The UMAP and tSNE algorithms both use fancy math to find a 2-dimensional representation of the data that tries to preserve local structure as much as possible. So blobs in the original space should be represented as blobs in the reduced space, but the relative positions of any two blobs in the reduced space is not meaningful.

chrisshroba 4y ago

Numbers that have similar prime factors are closer together.