Distance Matrix to coordinates in Matlab?

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Nirmal
Nirmal 2013-5-17
回答： Victor Prohorov 2020-12-18
Hi I have a 6x6 distance matrix for which i have to find the coordinates. I have no clue of how to do it. Friends pls help me.. The distance matrix is [0 8 8 5 2 8; 8 0 6 3 9 3; 8 6 0 6 8 3; 5 3 6 0 6 4; 2 9 8 6 0 8; 8 3 3 4 8 0] This is going to be the input the traveling salesman code which i have to create. I find a lot of suggestions for converting coordinates to distance matrix but my case is the opposite, and I find it very difficult to crack this one.
  2 个评论
Roger Stafford
Roger Stafford 2013-5-17
Perhaps I have misunderstood your question, but are you trying to do something like the inverse of the 'pdist' function - you want to find the coordinates of six points (observations) for which your six-by-six matrix is the corresponding distance matrix (after conversion to vector form)?
In general, I judge that would require at least five dimensions (variables), but in any event a solution would certainly not be unique. There would exist an infinite continuum of them.
Please explain your question in far, far greater detail than you have.
Nirmal
Nirmal 2013-5-17
Yes it is the opposite of the pdist function i suppose, I understand from your comment that it is going to be difficult but i need to figure it out as this is the only data which i have, and i have to find the best possible route.

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回答（3 个）

Victor Prohorov
Victor Prohorov 2020-12-18
cmdscale
You are all stupid, and I am clever because I am russian
Jan
Jan 2013-5-17
There is no unique solution, because the final pattern can be rotated, translated and mirrored. So you can choose one solution by setting the first point to the origin and the 2nd point on the X-axis with the distance 8. Now there are two possible locations for the third point with the distances 8 from the 1st point and 6 from the 2nd point: One above and one below the X-axis. Choosing the positive Y-position is fair. Now you can construct the other points easily by further triangulations.
Roger Stafford
Roger Stafford 2013-5-17
This looks to be an impossible problem. Number the points according to the distance matrix rows or columns they correspond to. Points 2, 4, and 1 form a 3-5-8 triangle which must therefore be a straight line segment no matter how it is oriented or how many dimensions are used. Similarly points 2, 4, 5 make a 3-6-9 triangle which must therefore be a line colinear with the first line segment. That would force a distance of 1 between points 1 and 5 on the common line. Unfortunately the matrix says 2 for that distance!
The fact that points 2, 3, and 6 must also be in a straight line introduces even further difficulties.
Someone was playing games when they made up this distance matrix.

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