AI 中文总结
该研究提出尺度调整的图拉普拉斯描述符，通过光谱指纹编码街道网络形态，推导网格指数等读数，可区分形态类型并关联活动多样性，补充空间句法且适配图学习。
AI 中文摘要
数十年的空间句法研究已证实，街道网络的拓扑结构会影响人流、共存现象及城市活动。该领域的标准术语——整合度、选择度与连接度——将每条街道的位置概括为标量中心性，但两条中心性相同的街道可能处于截然不同的形态结构中。我们提出一种紧凑、可比较、可用于机器学习的局部结构编码：光谱指纹，它是基于街道网络的COINS对偶图计算得到的每个节点k跳自我子图的图拉普拉斯特征值分布的固定维度核密度表示。从中我们推导得到两个可解释的标量读数：网格指数（Mesh Index, MI，一种归一化的光谱熵）和连通性弹性指数（Connectivity Resilience Index, CRI，即代数连通性，又称Fiedler值）。两者均针对主导原始光谱统计的自我子图大小混杂因素进行了校正。将该描述符应用于波兰波兹南的完整街道网络（1908条基于连续性的街道段）时，其对编码超参数（光谱分辨率和核带宽）具有鲁棒性（斯皮尔曼相关系数ρ≥0.98），同时在邻域半径上保持尺度依赖性。尺度调整使网格指数与整合度接近正交（相关系数r=0.06），承载了经典中心性所不具备的信息。光谱指纹可在无监督情况下区分形态组织类型，且网格指数与邻域尺度下街道相邻活动的功能多样性相关（基于开放街图数据，r≈0.19）。我们明确了该方法的适用范围：它表征街道位置能提供何种类型的活动，而非该活动的价值。它提供了一种信息论形态描述符，可补充空间句法，并可直接用于现代图学习管道。
英文摘要
Decades of space-syntax research have established that the topology of the street network conditions movement, co-presence and urban activity. The standard vocabulary for this -- integration, choice and connectivity -- summarises each street's position as a scalar centrality, yet two streets with identical centrality can sit in radically different morphological fabric. We introduce a compact, comparable, machine-learning-ready encoding of that local fabric: the spectral fingerprint, a fixed-dimensional kernel-density representation of the graph-Laplacian eigenvalue distribution of each node's k-hop ego subgraph, computed on the COINS dual graph of the street network. From it we derive two interpretable scalar readouts: the Mesh Index (MI), a normalised spectral entropy, and the Connectivity Resilience Index (CRI), the algebraic connectivity (Fiedler value). Both are corrected for an ego-subgraph-size confound that dominates raw spectral statistics. Applied to the full street network of Poznan, Poland (1,908 continuity-based strokes), the descriptor is robust to its encoding hyperparameters (spectral resolution and kernel bandwidth; Spearman rho >= 0.98) while remaining scale-dependent in its neighbourhood radius. The size adjustment leaves the Mesh Index near-orthogonal to integration (r = 0.06), carrying information classical centrality does not. The fingerprint separates morphological tissue types without supervision, and the Mesh Index is associated with the functional diversity of street-adjacent activity at the neighbourhood scale (r ~ 0.19, on open OpenStreetMap data). We delineate the method's scope honestly: it characterises what kind of activity a street's position affords, not the price that activity commands. It offers an information-theoretic morphological descriptor that complements space syntax and is directly consumable by modern graph-learning pipelines.
Comments18 pages, 7 figures. Under review at Journal of Complex Networks (Oxford University Press)
