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The use of hyperbolic space to encode hierarchies is absolutely genius (in not small part because it should be obvious), given the properties of hyperbolic spac
by darkmighty 7y ago
The use of hyperbolic space to encode hierarchies is absolutely genius (in not small part because it should be obvious), given the properties of hyperbolic space to "expand" around fixed points exponentially, exactly like trees do* . It seems like a continuous generalization of trees essentially. Beautiful.
*: https://en.wikipedia.org/wiki/Hyperbolic_space https://en.wikipedia.org/wiki/Hyperbolic_space
"Another distinctive property is the amount of space covered by the n-ball in hyperbolic n-space: it increases exponentially with respect to the radius of the ball for large radii, rather than polynomially. (...)"
- zenorogue 7y agoGenius because it should be obvious? Yes, it should be obvious for people familiar with both areas, and it is actually known for quite a long time. Hyperbolic geometry is used for visualizing hierarchical data since Lamping-Rao 1995 and Munzner 1998, then there were papers about hyperbolic SOMs (2001 IIRC) and lots of papers about the Hyperbolic Random Graph model for scale-free networks. I would say that the paper linked above introducing "Poincare embeddings" (a rather poor name IMO, BTW) does not feel as impressive if you know the details and the earlier work.