Additive vs ultrametric: triangle inequality Additive vs ultrametric ...

Multidimensional scaling (MDS)
• Not an eigenanalysis method:
– Information in distance matrix is not decomposed.
• Points representing observations (taxa) are
‘squeezed’ into 1D, 2D, or 3D… space.
– Placed into space so that interpoint distances
reconstruct original distances as much as possible.
• Metric and nonmetric (monotonic) versions.
– Axes are arbitrary, and points can be arbitrarily rotated.
– Amount of distortion measured as ‘stress’.
• Observations (taxa) are projected onto the axes to
give projection scores, which can be plotted with
scattergrams.
Multidimensional scaling (MDS)
Stress = 0.27
Distance matrix
1 2 3 4 5
1 0.00 1.41 2.45 2.45 2.83
2 1.41 0.00 2.45 3.16 2.45
3 2.45 2.45 0.00 1.41 1.41
4 2.45 3.16 1.41 0.00 2.45
5 2.83 2.45 1.41 2.45 0.00
Dim2
1
0.5
0
-0.5
-1
2
1
3
4
Additive
4
-1.5 15
-1.5 -1 -0.5 0 0.5 1
Dim1
5
3
5
2
1
14