Nonmetric multidimensional scaling reduces multidimensional data to fewer dimensions while preserving the ranked order of pairwise dissimilarities. It suits cases where distances come from subjective assessments or experiments and absolute values are not reliable. section 6.2.2 section 6.2
A practical interpretation follows this sequence:
- Calculate the pairwise distances or dissimilarities between observations. section 6.2.2
- Replace questionable absolute distances with their relative ranks. section 6.2.2
- Search for a lower-dimensional representation by optimizing a loss or cost function. section 6.2.2
- Inspect stress as a goodness-of-fit measure: 0.050 is described as good, 0.025 as excellent, and 0.000 as perfect. section 6.2.2
Ranking distances among four points
For points A, B, C, and D, the distances A–D, A–B, A–C, B–D, B–C, and C–D receive ranks 2, 3, 4, 5, 6, and 1 respectively. Nonmetric MDS uses this ordering instead of treating 95, 100, 105, 150, 205, and 55 as directly comparable magnitudes. section 6.2.2
Table 6.1 The respective distance between four points and the ranks of the distances
|
Pair of points
|
Distance
|
Ranks of the respective distances
|
|---|---|---|
|
A and B
|
100
|
3
|
|
A and C
|
105
|
4
|
|
A and D
|
95
|
2
|
|
B and C
|
205
|
6
|
|
B and D
|
150
|
5
|
|
C and D
|
55
|
1
|
Use the distance-and-rank table to inspect how nonmetric MDS converts pairwise measurements into an ordering. section 6.2.2
