9  Method contrasts

Use after every method chapter. One page for closed-book comparisons.

9.1 Dimension reduction

Method	Input	What is preserved	Linearity	Output you read
PCA	Feature matrix	Variance / reconstruction in a linear subspace	Linear	Scores, loadings, scree
Classical MDS	Dissimilarity \delta_{ij}	Centred inner products / Euclidean map distances	Linear embedding	Map coordinates, eigenvalues
Non-metric MDS	Ranks of \delta_{ij}	Order of dissimilarities	Embedding of ranks	Map + stress
ISOMAP	Features → graph distances → classical MDS	Approximate geodesics	Non-linear distances, linear MDS step	Unfolded coordinates
SOM	Features	Topology on a discrete grid via prototypes	Local linear updates, non-linear map overall	Grid, component planes, U-matrix, QE/TE
Autoencoder	Features	Reconstruction through a bottleneck	Linear ≈ PCA; non-linear otherwise	Code, reconstruction error

9.2 Clustering

Method	Random?	Dissimilarity	Extra choice	Cut / K
K-means	Yes (nstart)	Squared Euclidean on features	Scale, K	Choose K then fit
Hierarchical	No (fixed D, linkage)	Any D	Linkage	Dendrogram cut / cutree

Shared judging tools: silhouette, negative counts, subsample stability, profiles, usefulness for the stated decision.

9.3 Quick traps

• PCA axis ≠ SOM grid direction.
• ISOMAP neighbourhood (data) ≠ SOM neighbourhood (grid).
• Elbow bend ≠ proof of clusters.
• Largest silhouette ≠ automatic override of purpose.
• Linear AE ≈ PCA subspace, not identical ordered components.
• nstart stability ≠ subsample stability.