A Validated Measurement System for Structural Preservation and Semantic-Spatial Correlation in Cognitive Research
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2025
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| author | HIDEKI |
| author_facet | HIDEKI |
| contents | <p>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.</p> <p>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 three components—adjacency preservation (k-NN Jaccard similarity), order preservation (Kendall's τ), and cluster preservation (KMeans agreement)—yielding a composite [0,1] score. SSC quantifies the rank correlation between semantic and spatial distance matrices (Spearman's ρ).</p> <p>We validated these metrics through systematic experiments: identity and isometry transformations (sp00), full destruction baselines (sp01), topological rewiring curves (sp02), layout robustness tests (sp03), topology-versus-metric comparisons (sp12-sp13), and independence tests under coordinate, semantic, and mixed noise (sp20-sp22). All experiments employed a deterministic execution contract ensuring bit-for-bit reproducibility.</p> <p>Results: SP reliably distinguished structured layouts (mean = 0.85) from random configurations (mean = 0.51). Adjacency rewiring produced a smooth monotonic decrease in SP (1.00 → 0.04). Topological disruptions reduced SP more strongly than metric distortions (SP = 0.56 vs 0.77 at disruption level 0.7), and this topology-dominance generalized across all layout types. SP and SSC demonstrated orthogonal behavior: coordinate noise reduced SP (0.85 → 0.54) while SSC remained near zero (|mean| ≈ 10⁻⁴); conversely, semantic noise left SP unchanged while SSC remained at baseline. Core measurement properties remained stable across sample sizes, layouts, and algorithmic parameters.</p> <p>This measurement system provides cognitive researchers with validated, reproducible metrics for quantifying structural preservation and semantic-spatial relationships. Immediate applications include evaluating dimensionality reduction algorithms, assessing spatial memory organization, and measuring cognitive map fidelity.</p> <p>Version: 1.0.0 (Initial preprint submission)<br>Repository: intelligence-relativity v2.0.0</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17674984 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Validated Measurement System for Structural Preservation and Semantic-Spatial Correlation in Cognitive Research HIDEKI structural preservation semantic-spatial correlation cognitive measurement spatial memory dimensionality reduction cognitive mapping reproducibility deterministic pipeline topology-sensitive metrics psychometrics <p>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.</p> <p>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 three components—adjacency preservation (k-NN Jaccard similarity), order preservation (Kendall's τ), and cluster preservation (KMeans agreement)—yielding a composite [0,1] score. SSC quantifies the rank correlation between semantic and spatial distance matrices (Spearman's ρ).</p> <p>We validated these metrics through systematic experiments: identity and isometry transformations (sp00), full destruction baselines (sp01), topological rewiring curves (sp02), layout robustness tests (sp03), topology-versus-metric comparisons (sp12-sp13), and independence tests under coordinate, semantic, and mixed noise (sp20-sp22). All experiments employed a deterministic execution contract ensuring bit-for-bit reproducibility.</p> <p>Results: SP reliably distinguished structured layouts (mean = 0.85) from random configurations (mean = 0.51). Adjacency rewiring produced a smooth monotonic decrease in SP (1.00 → 0.04). Topological disruptions reduced SP more strongly than metric distortions (SP = 0.56 vs 0.77 at disruption level 0.7), and this topology-dominance generalized across all layout types. SP and SSC demonstrated orthogonal behavior: coordinate noise reduced SP (0.85 → 0.54) while SSC remained near zero (|mean| ≈ 10⁻⁴); conversely, semantic noise left SP unchanged while SSC remained at baseline. Core measurement properties remained stable across sample sizes, layouts, and algorithmic parameters.</p> <p>This measurement system provides cognitive researchers with validated, reproducible metrics for quantifying structural preservation and semantic-spatial relationships. Immediate applications include evaluating dimensionality reduction algorithms, assessing spatial memory organization, and measuring cognitive map fidelity.</p> <p>Version: 1.0.0 (Initial preprint submission)<br>Repository: intelligence-relativity v2.0.0</p> |
| title | A Validated Measurement System for Structural Preservation and Semantic-Spatial Correlation in Cognitive Research |
| topic | structural preservation semantic-spatial correlation cognitive measurement spatial memory dimensionality reduction cognitive mapping reproducibility deterministic pipeline topology-sensitive metrics psychometrics |
| url | https://doi.org/10.5281/zenodo.17674984 |