Creating a 2D map of objects given a sparse matrix of pairwise distances
This is known as "graph layout" or "graph drawing" (practical methods) or "graph embedding" (theoretical interest).  The relevant techniques are more closely associated with computational geometry and mathematical optimization, not machine learning.   See this Wikipedia article and Recovering a point embedding from a graph with edges weighted by point distance and Efficient algorithm to fulfil a set of coordinate constraints for an overview of some standard techniques.  Pairwise comparisons with confidence might also have some helpful techniques (it is focused on the 1D case, not the 2D case, but it might be possible to generalize Yuval's answer to the 2D case as well).