子空间稳定、轴语义易位与连续谱:跨城市路网形态主成分表征的测量条件审计 (Stable Subspaces, Variable Axes, and the Morphological Continuum: Auditing Measurement Conditions in Cross-City Street-Network PCA)

Abstract

【目的】 跨城市路网形态比较常依赖开放地理空间数据(OSM)与主成分分析(PCA)构建低维表征,但既有研究多预设离散分类范式,且普遍忽视数据质量异质性、空间尺度推移与特征共线性对主成分轴语义的构造性干扰。本文旨在检验跨城市路网形态主成分表征的前提假设是否成立,对数据适用性、空间尺度与特征共线性等关键测量条件实施系统审计,评估低维形态空间的代数稳定性与解释边界。 【方法】 选取42个城市(含31个中国内地直辖市与省会首府、香港及10个国际基准城市)的126个嵌套OSM窗口(5×8 km、2×与4×面积),提取5项道路级形态描述符(蜿蜒度、归一化曲率、方向一致性、平面交叉度、邻接类型熵)执行PCA降维。建立面向描述符的三级数据适用性分类(参考适用13城、支持受限21城、表征受限8城);采用旋转不变经典RV系数与轴锚定余弦分别度量子空间代数稳定性与轴语义方向;通过Procrustes对齐合成城市形态空间;实施2几何对2拓扑的对称特征消融以剥离共线特征造成的方差虚假集中;并结合SRTM 30 m DEM与OSM三维层差代理(p3d),检验宏观地形与立体交通对拓扑份额的线性解释力。 【结果】 ① 在全部126个窗口中,49%(62个)触发至少一项质量风险标记,证实开放数据跨城形态推断需要前置分层;在低维空间中,城市路网形态呈现为平滑过渡的几何–拓扑连续谱而非离散群落,PC2在39/42个城市中一致承载拓扑轴,初评标记的“反相位类型”在参考类复核下未能独立成簇(载荷幅值极低且与几何组共簇),现有数据不支持离散划分。② 载荷子空间跨尺度表现出高代数稳定性(参考类经典RV中位数0.997),但轴语义在特定尺度易受特征值排序扰动(重庆5×8↔4×轴锚定余弦仅0.228对经典RV 0.983);且拓扑极点读数(重庆0.675、贵阳0.657)高度依赖长尾极端弯路,剔除单条道路即骤降至0.130与0.255。③ 对称特征消融表明:剔除方向一致性后,92.9%的窗口(117/126)与92.9%的城市(39/42)中PC1转为拓扑主导(37座城市发生主导轴角色易位),城际拓扑排序完全解耦(Spearman ρ = -0.142,p = 0.370)。④ 机制假说检验表明,宏观地形与城市拓扑份额无统计关联(ρ = +0.063,p = 0.690),3D连接代理在参考类中虽呈名义弱相关(ρ = 0.569,p = 0.042)但未通过Benjamini–Hochberg校正,局部环境属性无法线性解释全局网络结构。 【结论】 基线分析中主成分PC1的“几何主导”受制于共线几何变量方差聚集的测量协议构造。对称消融表明其轴语义具有框架依赖性。在本文道路级表征框架与适用性复核下,现有数据不支持普适性离散形态划分假设,城市路网形态更接近低维连续谱分布;城市在轴上的相对位次仍由真实形态数据驱动。基于开放数据的跨城市形态比较,需将数据适用性分层、空间尺度外推、轴语义易位与尾部极端样本敏感性纳入前置边界条件,以防范将测量构造误读为城市空间规律。 ================================ Stable Subspaces, Variable Axes, and the Morphological Continuum: Auditing Measurement Conditions in Cross-City Street-Network PCAAuthor: Wenhao WANG*Affiliation: School of Geography and Urban-Rural Planning, Longdong University, Qingyang 745000, ChinaCorresponding Author: Wenhao WANG, E-mail: gew500781@gmail.com [Objectives] Cross-city comparative analyses of urban street networks frequently employ OpenStreetMap (OSM) data and principal component analysis (PCA) to extract low-dimensional morphological representations. However, existing studies commonly presuppose discrete typologies while overlooking how data quality heterogeneity, spatial scale shifts, and descriptor collinearity structurally distort low-dimensional representations. This study systematically audits the measurement conditions and foundational assumptions underlying PCA-derived street network spaces, evaluating the algebraic stability of subspaces, the semantic consistency of dominant axes, and their empirical interpretive boundaries across spatial scales.[Methods] Using 126 nested OSM windows (5×8 km, 2× area, and 4× area) across 42 global cities (31 Chinese provincial capitals and municipalities, Hong Kong, and 10 international benchmarks), we extracted five road-level descriptors (sinuosity, normalized curvature, directional consistency, planar degree, and adjacency-type entropy) to perform PCA. We instituted a three-tier descriptor-specific fitness-for-use classification (reference: 13 cities; support-limited: 21; representation-limited: 8) and decoupled cross-scale structural stability into two analytical tiers: the rotation-invariant classical RV coefficient for loading subspaces and the axis-anchored cosine for directional semantic fidelity. City-level morphology spaces were synthesized via Procrustes alignment. To diagnose measurement framework artifacts, we conducted a symmetric feature ablation (two geometric versus two topological descriptors) by removing collinear directional consistency. Finally, we evaluated macro-terrain (SRTM 30 m DEM) and vertical connectivity (OSM 3D layer-difference proxy p3d) hypotheses to assess whether local environmental attributes linearly explain city-level topology share.[Results] (1) Across all 126 windows, 49% (62 windows) trigger data quality risk flags, demonstrating that open-data cross-city morphological inference requires systematic upfront sample conditioning. In the low-dimensional space, urban street networks occupy a smooth geometric–topological continuum rather than forming discrete clusters; PC2 consistently serves as the primary topological axis across 39 of 42 cities, while a hypothesized "counter-phase" typology fails to form an independent cluster upon reference-class re-examination (manifesting low loading magnitude and co-clustering with the geometric group), rejecting discrete clustering. (2) Loading subspaces exhibit high cross-scale algebraic stability (median classical RV 0.997 among reference-class pairs), yet axis semantics remain vulnerable to eigenvalue reordering (e.g., Chongqing 5×8↔4× exhibits an axis-anchored cosine of only 0.228 alongside classical RV 0.983). Furthermore, topological pole scores (Chongqing 0.675, Guiyang 0.657) are governed by extreme descriptor tails, collapsing to 0.130 and 0.255 upon removing a single most sinuous road. (3) In symmetric feature ablation, removing directional consistency caused PC1 to flip to topological dominance in 92.9% of windows (117/126) and 92.9% of cities (39/42; 37 cities underwent dominant-axis role reversals), completely decoupling inter-city topological rankings (Spearman ρ = -0.142, p = 0.370). (4) Macro-terrain exhibits no statistical association with topology share (ρ = +0.063, p = 0.690), and the 3D proxy's nominal correlation in the reference class (ρ = 0.569, p = 0.042) fails Benjamini–Hochberg false-discovery-rate control, demonstrating that macro-terrain does not drive city-level topology share; furthermore, road-level environmental attributes fail to explain city-level morphology linearly (mean regression R² < 0.163).[Conclusions] The apparent geometric dominance of PC1 in baseline street-network representations is constrained by the measurement protocol through collinear variance concentration; symmetric ablation demonstrates that axis semantics are framework-dependent, while relative city positions along these axes remain driven by empirical morphological data. Under this road-level PCA framework and fitness-for-use re-examination, the data provide no empirical support for universal discrete typological classifications, with street networks instead following a low-dimensional continuum. Cross-city morphological comparisons using open data must treat fitness-for-use, spatial scale, axis instability, and descriptor-tail sensitivity as indispensable boundary conditions, to prevent observational artifacts from being mistaken for universal urban regularities. Key words: street network / OpenStreetMap / principal component analysis / subspace stability / axis semantics / cross-city comparison / spatial scale / measurement uncertainty基金项目: 无作者简介: 王文浩,陇东学院地理与城乡规划学院。E-mail: gew500781@gmail.com —— v1.0.1(2026-09-12):表3消融列三处数字经复核后修正并由落盘产物锚定:基线行 PC1 几何主导 123/126→120/126 (95.2%);剔除 E_entropy 行 123/126→126/126、城级 40/42→42/42、ρ +0.676→+0.675;§4.3 主导判据(123/126,例外为海口三尺度)与幅度阈值判据(124/126 即 98.4%)拆分陈述。—— v1.0.2(2026-09-16):二轮修改稿,新增三组经落盘产物锚定的内容:①固定队列对照(126 对 RV 中位 0.999、最低 0.881,9 对轴锚定余弦 <0.9,重庆 2×↔4× −0.9985);②重庆 5×8 窗口命名走廊实际跨度 7.3×11.4 km(约 2.08 倍名义面积);③道路分段制图粒度检验(ρ=+0.624/+0.535/参考类 +0.069)。—— v1.0.3(2026-09-17):三轮修改稿——全文语言精修、标题升版、表3 消融对照移入 §4.3;复现脚本口径与 AI 工具声明规范化;数值零改动。 —— v1.0.4(2026-09-20):版本升版发布;英文摘要 (4) 句新增量化上限——局部环境对几何形态的平均回归 R² < 0.163(正文 §4.5 同行印 0.163,产物锚定城级最大值 0.1625)。 The full standalone reproduction package (816 files, verified via metric contracts and ledger assertions) is bundled in limit-sense-repro-v1.0.4.tar.gz (SHA-256: 9d4efb0ca8641692d2f1fb9b5b2c905a78f5dd7e03a7253ae56bc762b53e2d25).