I don't have sufficient mathematical background.
I am trying to get the absolute 2D coordinates from the pairwise comparison distances:
What I have distances between points: p1-p2 = 0.3 p1-p3 = 0.5...p1-p700 = 0.1 and the same for p2...pN. What I want to have - to plot them in 2D and have coordinates, like p1(0, 0) pN(10, 10), p2(2, 6) etc...
- I have already read/discovered/thought on the following things:
- My data may not be (most probably, cause there are 10K comparisons) in one plane, which could give me the 2D coordinates
- Data dimensionality can be reduced
- I thought I could use Pythagorean theory. I.e. I take two points (I am not sure, but I think the best decision would be to use two points with distance, equal to difference of 50%) and using the distances of any other point between those two (i.e. point3-point1 = 0.23, point3-point2 = 0.57 and point1-point2 = 0.5, which 'set up the space') I can calculate the absolute coordinate in 2D space. Is my assumption right or wrong?
If it's wrong what else should I use?