Find absolute position of objects when only distances are known.

Question

I have a set of objects u1, u2,..., un and an algorithm which gives a R(1000) [1000 dimensional] vector for each object.

Table 1
   t1  t2  ... t1000
u1 234 157 ... 92
u2 117 157 ... 39
...
un 234 157 ... 39

From this data, I'm calculating hamming distance between these objects:

Table 2
row col distance
u1  u2  200
u1  u3  500
u4  u2  200
u4  u3  900
...

I want to create a 2D plot in which each object is a point and distance between points comes from Table 2.

For that I need absolute positions of these objects in some 2D space. Is there a way to find or simulate absolute positions when only distances are known. If yes, how do I select what to put on x-axis and y-axis?

Answer 1

Figured out a way to this - Multidimensional Scaling https://en.wikipedia.org/wiki/Multidimensional_scaling

This may work accurately when "euclidean" distances are known. Not sure how much information does it compromise with hamming distances.