I'm facing a problem with mapping, I need mapping N dimensional vectors to one group/point, like [0,1....N-1] to 1 | [1,2....N-1] to 2.
The problem is that, right now I have one function where receive a dimensional vector and the return a point, that point is the result, I want avoid call the function, I already have all results stored in a table, the problem is, I'll remove the function and now I need mapping the new entry to a existing point.
There is some way to mapping the entry to a correct point?
There is some algorithm to mapping to the correct point?
Some help or advice?
I already saw this topic, but I'm not sure whether Hilbert Curve is the solution, I need study more about it. Mapping N-dimensional value to a point on Hilbert curve
I'll be grateful.
Mapping an n dimensional data to a one dimensional data is called projection. There are lots of ways to project an n dimensional data to a lower dimension the most well-known ones are PCA, SVD, or using radial basis functions. If you do not have your method of projection anymore, you probably can't project another point unless you have a hash-table of the previous projected points. If you happen to have exactly the same point, then you can map it to the same point. However, pay attention that the projection is not one-to-one meaning that there may exist two points that are mapped to the same point in the lower dimension. An example of such a case is the projection of 3D points on the screen on which many points may get mapped to exactly the same points on the screen. As a result, inverse projecting the points usually have ambiguities. About the link that you sent about Hilbert curve, this is a general approach to project a point in ND to a point on a space filling curve (SFC) such as Hilbert, Peano, etc. This website at MIT has interesting stuff about dimension reduction using SFC: http://people.csail.mit.edu/jaffer/Geometry/MDSFC