Patterns › Dimension reduction

MDS (non-metric)

Non-metric (Kruskal) multi-dimensional scaling preserves only the rank order of distances, making it robust to non-linear distance scales.

What is MDS (non-metric)?

When the input distances are ordinal — you trust 'distance A < distance B' but not the magnitude difference — classical MDS over-fits the (unreliable) numeric values. Non-metric MDS preserves only the order: the embedding's distance matrix should have the same rank order as the input.

Kruskal's stress measures the rank-correlation between input and embedding distances. Lower stress = better fit; values below 0.1 indicate excellent representation, 0.2 = fair, 0.4+ = poor.

When should I use MDS (non-metric)?

  • Ordinal distance / similarity data (rated preferences, Q-sort results).
  • Robust alternative when the metric distances may have scale distortion.

What data does it need?

Same as classical MDS, treated as ordinal.

What does it report?

Coordinates + Kruskal stress.

How do I interpret the result?

Stress < 0.1 ⇒ excellent 2D representation, 0.1–0.2 ⇒ usable, > 0.2 ⇒ the configuration distorts the rank order materially; add dimensions or try a different distance.

See also

References

  • Kruskal (1964). Nonmetric multidimensional scaling: a numerical method. Psychometrika 29(2).