I have a 100x100 square with each point having a node attached to it such that a node at point 0,99 is more similar to a node at point 0,0 than 0,95 lets say. The same can be said about the other axis.
I wish to feed that square into a machine learning algorithm, but before that I better convert the whole thing into something more interpretable by an algorithm that will know nothing about the nature of my data.
I was thinking of using the toroidal coordinate system for that, but I'm unsure how to proceed with conversion.
Edit: Basically, the distance function can only be euclidean, and space must be transformed into one higher dimension to make it mean something once more. 1D can be transformed into a 2D circle and still be monotonous (x becomes the angle of the circle such that x'=cosx, y'=sinx) I need to do something similar with a 2D space with the properties listed above.
I figured it out.
v1 = sin(x/100*2pi)
v2 = cos(x/100*2pi)
v3 = sin(y/100*2pi)
v4 = cos(y/100*2pi)
This will maintain the properly that something closest on the x,y surface (in the sense previously described) will remain closest in the v1..4 euclidean system, however the scale will of course be altered.