A Validated Measurement System for Structural Preservation and Semantic-Spatial Correlation in Cognitive Research

Cognitive research on spatial memory, mental mapping, and dimensionality reduction requires quantitative measures of structural preservation and semantic-spatial alignment. However, existing metrics vary across studies, limiting cross-study comparability and reproducibility. We present a validated measurement system defining Structural Preservation (SP) and Semantic-Spatial Correlation (SSC) with operational clarity, systematic validation, and deterministic reproducibility. SP comprises adjacency preservation (k-NN Jaccard), order preservation (Kendall's τ), and cluster preservation (KMeans agreement). SSC quantifies rank correlation between semantic and spatial distance matrices (Spearman's ρ). Validation experiments demonstrated that SP reliably distinguished structured layouts (mean = 0.85) from random configurations (mean = 0.51). Adjacency rewiring produced smooth monotonic decrease (1.00 → 0.04). Topological disruptions reduced SP more than metric distortions (0.56 vs 0.77), generalizing across layouts. SP and SSC showed orthogonal behavior: coordinate noise reduced SP (0.85 → 0.54) while SSC remained near zero; semantic noise left SP unchanged. Properties remained stable across sample sizes (N = 16–100), layouts, and parameters. Real-world demonstration on MNIST showed that t-SNE preserved clusters (SP_clu = 0.50), UMAP preserved ordering (SP_ord = 0.58), while PCA achieved highest semantic-spatial alignment (SSC = 0.49) despite weak local structure, confirming SP-SSC orthogonality. This system provides validated, reproducible metrics for evaluating dimensionality reduction, spatial memory, and cognitive mapping. All code and data are openly available.