Multidimensional Scaling

distances between:

1 ↔ 2

0.3

1 ↔ 3

0.5

1 ↔ 4

0.5

2 ↔ 3

0.7

2 ↔ 4

0.5

3 ↔ 4

0.5

1

2

3

4

SSE: 0.72

Classical (metric) multidimensional scaling (MDS) tries to find points that have a given set of pairwise distances. When no set of points satisfies distance constraints, MDS finds the best solution in the least squares sense—sum of squared errors (SSE) is minimized. Sliders specify desired distances between the points, that is, a slider labelled

3↔4

gives the desired distance between points 3 and 4. The darkness of the line between each pair of points reflects how closely the actual distance meets the specified goal (lighter means better correspondence).