Run PCA and classical MDS on the same observations. PCA protects variance. MDS protects pairwise distances. The difference stops being theoretical when you can see and measure both.
label, group, feature 1, feature 2, feature 3
The representative sample is computed on load.
| Observation | PCA x | PCA y | MDS x | MDS y |
|---|
PCA rotates standardized features toward directions with the greatest spread. Classical MDS starts from every pairwise distance and searches for a lower-dimensional map that preserves those relationships. Compare the same labels across both panels: similar geometry means the dominant variance also carries most of the distance structure.
The first two PCA eigenvalues divided by all eigenvalues tell you how much standardized variance survives the projection. Higher is better, but it does not guarantee every local distance survives.
Normalized stress compares original distances with distances in the MDS map. Near zero means the 2D geometry faithfully preserves the original relationships.
Replace the sample with measurements from a real portfolio dataset. Keep labels and groups, add three numeric features, then export the two embeddings as analysis-ready evidence.