Bit of a strange question but hope this is OK to ask here.
Has anyone heard of a '1-dimensional' projection of the world map - that is mapping all the points on the globe to a single line?
I was thinking of doing such a thing - trying to keep cities that are 'close' on the globe 'close' on the line.
Before I do this, I wondered what the state of the art might be in this area?
Answer
A general technique for mapping a collection of points (for which distances are given) into a Euclidean space (such as three-space, a plane, or even a line) with minimal distortion of the distances is called Multidimensional Scaling (MDS). There are several algorithms. Solutions are freely available in R and often are supplied with commercial statistics packages.
The largest 20 cities in the US are mapped here with Stata 11's default MDS settings. The ticks denote 100 km intervals.
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