There Are No Patterns Before a Representation: What Unsupervised Learning Actually Sees

Abstract

Unsupervised learning is often described as discovering hidden structure in unlabeled data. That description omits the analytical object that makes discovery possible: a representation, a scale, a dissimilarity rule, and a neighborhood definition. Before an algorithm can identify groups, anomalies, manifolds, or latent factors, the analyst has already specified which differences matter and how they are aggregated. This paper audits that prior geometry using the 392 complete Auto MPG observations. The target variable, mpg, is excluded. Six numeric variables define four representations—raw, development-standardized, development-robust-scaled, and log-transformed plus standardized—combined with Euclidean, Manhattan, and cosine distance. Each of the resulting 12 configurations constructs a 10-nearest-neighbor graph. In raw Euclidean geometry, weight contributes 98.3% of total squared distance. After standardization, no feature contributes more than 26.2%. Mean cross-configuration neighborhood overlap is 0.414, with a minimum of 0.080. Under deterministic 1% perturbations, mean neighborhood stability is 0.910 and the minimum is 0.784. Origin is withheld from geometry construction and used only afterward as an external audit. Same-origin neighbor agreement exceeds its marginal baseline in every configuration, ranging from 0.644 to 0.744 against a baseline of 0.461. However, this does not identify a uniquely correct representation. Raw cosine geometry achieves the highest agreement while answering a different similarity question from standardized Euclidean distance. The findings support a representation-dependent account of unsupervised structure rather than the existence of one natural partition. The experiment audits the geometry supplied to downstream algorithms; it does not establish natural clusters, causal types, or a uniquely correct metric. The deposit includes the complete paper, source code, data, machine-readable outputs, generated figures, representation and distance audits, neighborhood-overlap analyses, perturbation-stability results, temporal diagnostics, a SHA-256 integrity manifest, and an automated reproduction verifier.