The Map Changes What Looks Like a Group: What Dimensionality Reduction Actually Preserves

Dimensionality reduction is often treated as a neutral route from many variables to a readable plane. A projection, however, is an optimization result: it preserves some relations, distorts others, and can create visually separated regions that do not correspond to the original high-dimensional partition. This paper evaluates 76 two-dimensional embeddings of the 307 development vehicles in the complete-case Auto MPG data. Four representations are combined with principal component analysis (PCA), Isomap, and t-distributed stochastic neighbor embedding (t-SNE). Isomap uses 5, 10, or 20 neighbors; t-SNE uses perplexities of 5, 30, or 50; and Euclidean, Manhattan, and cosine dissimilarities are audited where supported. A later population of 85 vehicles from 1980–1982 remains reserved for temporal diagnosis, while origin is withheld until post-fit external audit. Across the four PCA maps, two-component explained variance ranges from 0.842 to 1.000. Among 12 prespecified primary maps, mean cross-projection 10-nearest-neighbor Jaccard agreement is 0.279, with a minimum of 0.077. The most visually separated two-group map reaches a silhouette of 0.949, yet its adjusted Rand agreement with the corresponding high-dimensional partition is −0.001. Mean primary perturbation stability is 0.828, with a minimum of 0.628. Across the 40 candidates with a native out-of-sample transform, mean temporal neighbor agreement is 0.383. The 36 t-SNE candidates receive no temporal transport score because the fitted estimator has no native transform for later observations. Refitting on the combined populations would change the reference map and violate the frozen temporal boundary. The results show that explained variance, neighborhood fidelity, global distance fidelity, visual separation, perturbation stability, and temporal transport are distinct properties. A clear picture is not necessarily a faithful map, and no projection alone establishes natural groups, causal types, or a uniquely correct view of the data. The deposit includes the complete paper and a reproducibility package containing source code, data, machine-readable results, five generated figures, 50-path perturbation audits, a 12 × 12 cross-projection neighborhood-agreement matrix, a SHA-256 integrity manifest, and an automated verifier.