4 ms·
Euclidean distance calculations change based on number of dimensions, for example, in 3 dimensions it is sqrt(a^2+b^2+c^2).
by bick_nyers 5y ago
Euclidean distance calculations change based on number of dimensions, for example, in 3 dimensions it is sqrt(a^2+b^2+c^2).
- Retric 5y agoYes, that’s why it’s square root of 2. Consider the origin (0,0,0, …) to a random point on the sphere (~0, ~0, ~0, …). Distance = square root of ((X1 - X2) ^ 2 + (Y1 - Y2) ^2 + …). So D = square root of ((~0-0)^2 + (~0-0)^2 + (~0-0)^2 + … ), which is equal to 1 by definition of the unit high dimensional sphere. So distance from (1,0,0,0 …) to (~0, ~0, ~0, …) = square root of ((~0-1)^2 + (~0-0)^2 + (~0-0)^2 + … ) ~= square root of 2.
- bick_nyers 5y agoAhh ok, for some reason I was thinking (1,1,1) would be a valid point in this case