Bridge-Centered Metapath Classification Using R-GCN-VGAE for Disaster-Resilient Maintenance Decisions Takato Yasuno
arXiv:2604.18399v1 [cs.LG] 20 Apr 2026
Abstract
(4) k-NN tuning strategy validated across diverse city scales. (5) Empirical demonstration of UMAP supeDaily infrastructure management in preparation for riority over t-SNE/PCA for multi-role bridge visualdisasters is critical for urban resilience. When ization. bridges remain resilient against disaster-induced exKeywords: Bridge maintenance, Disaster reternal forces, access to hospitals, shops, and resi- silience, Heterogeneous graph, R-GCN, Variational dences via metapaths can be sustained, maintain- Autoencoder, Metapath analysis, Infrastructure maning essential urban functions. However, prioritizing agement bridge maintenance under limited budgets requires quantifying the multi-dimensional roles that bridges play in disaster scenarios—a challenge that existing 1 Introduction single-indicator approaches fail to address. Approach: We focus on metapaths from na- 1.1 Background and Motivation tional highways through bridges to buildings (hospitals, shops, residences), constructing a hetero- Japan’s aging infrastructure poses a critical challenge geneous graph with road, bridge, and build- for disaster resilience. Among the nation’s 730,000 ing layers. A Relation-centric Graph Convolu- bridges, over 50% will exceed their 50-year design life tional Network Variational Autoencoder (R-GCN- by 2033, with maintenance costs projected to exceed VGAE) learns metapath-based feature representa- 8 trillion yen annually [1, 2]. Recent natural disastions, enabling classification of bridges into disaster- ters, including the 2019 Typhoon Hagibis floods [3], preparedness categories: Supply Chain (commercial underscore the urgency of disaster-preparedness planlogistics), Medical Access (emergency healthcare), ning [4]. Beyond structural integrity, bridges serve as vital nodes in urban networks, where their reand Residential Protection (preventing isolation). Case Study: Using OSMnx and open data, we silience directly impacts access to essential services— validate our methodology on three diverse cities in hospitals for emergency care, shops for supply chains, Ibaraki Prefecture, Japan: Mito (697 bridges), Chiku- and residences for community connectivity. The core premise of this work is that daily insei (258 bridges), and Moriya (148 bridges), totaling 1,103 bridges. The heterogeneous graph construc- frastructure management in preparation for tion from open data enables redefining bridge roles disasters requires understanding the multifor disaster scenarios, supporting maintenance bud- dimensional roles bridges play in sustaining urban functions. When bridges remain resilient get decision-making. Results: Clustering quality achieves Silhouette against disaster-induced external forces (earthquakes, scores of 0.289–0.363, with latent dimension z19 show- floods, landslides), access via metapaths—shortest ing strong correlation (Spearman r = 0.416, p = paths from national highways through bridges to 1.47×10−30 ) with national highway metapath counts, buildings—can be sustained, maintaining essential demonstrating specialized encoding of logistics hub city operations. However, existing approaches priconnectivity. k-NN parameter tuning (k=3→5) in- oritize bridges using single indicators such as traffic creases coverage by +66% (162→270 paths), improv- volume or structural condition ratings, which fail to capture their functional diversity in disaster scenaring semantic validity for disaster scenarios. Contributions: (1) Open-data methodology for ios [5, 6]. constructing urban heterogeneous graphs. (2) ReConsider a hospital-serving bridge with low traffic definition of bridge roles for disaster scenarios via volume—it may rank low in traditional prioritization metapath-based classification. (3) Establishment of but becomes critical during disasters when emergency maintenance budget decision support methodology. medical access determines survival outcomes. Con1
versely, a high-traffic bridge serving primarily commercial logistics may be less urgent if alternative routes exist. This disconnect between structural metrics and disaster-preparedness roles necessitates a new methodology.
1.2
3. RQ3 (Open Data Applicability): Can the methodology be deployed using only open data sources (OSMnx, OpenStreetMap), and does it scale to diverse city sizes from large (700+ bridges) to small (100-200 bridges)?
1.4
Problem Statement
Proposed Approach
We construct a heterogeneous graph with three layers—roads, bridges, and buildings—where node types and edge types explicitly represent urban infrastructure semantics. Focusing on metapaths from national highways through bridges to buildings (hospitals for medical access, shops for supply chains, residences for isolation prevention), we train an R-GCNVGAE to learn 32-dimensional latent representations that encode bridge connectivity patterns. The key innovation is relation-centric encoding: instead of treating all edges uniformly, R-GCN maintains separate weight matrices Wr for each relation type (e.g., highway→bridge vs. local road→bridge), enabling the model to distinguish logistics hubs from local access bridges. Following dimensionality reduction via UMAP, bridges are classified into three disaster-preparedness categories:
Under limited maintenance budgets, municipalities must answer: Which bridges should be prioritized to maximize disaster resilience while sustaining access to hospitals, supply chains, and residential areas? This requires: 1. Quantifying multi-dimensional bridge roles: A single bridge may simultaneously serve medical access, commercial logistics, and residential protection—roles invisible to traffic-based rankings. 2. Leveraging open data: Many municipalities lack detailed bridge inventories, requiring opensource alternatives (OpenStreetMap, geospatial data). 3. Scalability across city scales: Methodologies must work for both large metropolitan areas (700+ bridges) and small cities (100-200 bridges) where traditional clustering algorithms fail.
• Supply Chain: High connectivity to shops (k=5 nearest), critical for post-disaster logistics and commercial continuity.
• Medical Access: High connectivity to hospitals Traditional graph-based approaches using between(k=5 nearest), essential for emergency healthcare ness centrality or closeness centrality treat all edges delivery. uniformly, ignoring the semantic differences between highway→bridge paths (logistics arteries) and • Residential Protection: High connectivity to bridge→residence paths (community lifelines). Reresidential buildings (k=20 nearest), preventing cent advances in heterogeneous graph neural netcommunity isolation. works offer a solution by explicitly modeling different node types (bridges, roads, buildings) and edge types 1.5 Contributions (to hospital, to shop, to residence) within a unified framework. This paper makes the following contributions:
1.3
1. Open-data heterogeneous graph construction methodology: Complete pipeline from OSMnx to bridge classification, enabling municipalities without detailed inventories to assess infrastructure.
Research Questions
This work addresses three fundamental questions: 1. RQ1 (Metapath Feasibility): Can metapaths originating from national highways and passing through bridges to buildings (hospitals, shops, residences) effectively classify bridges into disaster-preparedness roles?
2. Disaster-centric bridge role redefinition: Metapath-based classification (Supply Chain/Medical Access/Residential Protection) that aligns bridge prioritization with disaster preparedness rather than traffic volume.
2. RQ2 (Model Effectiveness): Does a Relationcentric Graph Convolutional Network Variational Autoencoder (R-GCN-VGAE) effectively learn metapath-based feature representations in heterogeneous urban graphs?
3. Maintenance budget decision support framework: Systematic methodology for prioritizing repair investments based on multidimensional disaster-resilience roles. 2
4. k-NN tuning strategy: Empirical validation showing k=3→5 increases coverage by +66% (162→270 metapaths in Mito City), with semantic justification (k=5 for focused services, k=20 for residential neighborhoods).
demonstrated cascading failures in coupled infrastructure networks during the 2003 Italy blackout. Our work extends this paradigm to heterogeneous urban graphs, where bridges serve as critical nodes connecting diverse facility types.
5. Dimensionality reduction evaluation: Demonstration that UMAP outperforms t-SNE 2.2 Graph Variational Autoencoders and PCA for visualizing multi-role bridge em- Variational Autoencoders (VAEs) [8] revolutionized beddings, preserving both local cluster structure unsupervised representation learning by combining and global topology. probabilistic inference with deep neural networks. Kipf and Welling [9] extended VAEs to graph6. Multi-scale validation: Successful deployment structured data via Graph Convolutional Networks across three cities with 8×structural diversity: (GCNs) [10], enabling node embedding learning that Mito (697 bridges, prefectural capital), Chikusei preserves network topology. (258 bridges, regional hub), Moriya (148 bridges, The Graph Variational Autoencoder (GVAE) logistics gateway with extreme highway connecframework encodes nodes into a latent space z ∼ tivity up to 2,803 metapaths per bridge). N (µ, σ 2 ) using a GCN encoder, then reconstructs edges via an inner product decoder  = σ(ZZ ⊤ ). The remainder of this paper is organized as follows: This approach has been successfully applied to link Section 2 reviews related work on infrastructure critprediction [9], community detection [11], and graph icality, graph autoencoders, and metapath analysis. generation [12]. Section 3 details the R-GCN-VGAE architecture and Relational GCN (R-GCN) [13]: Standard metapath extraction methodology. Section 4 presents GCNs assume homogeneous graphs where all edges experimental results across three Ibaraki cities. Secrepresent identical relationships. R-GCN introduces tion 5 discusses three key lessons learned (k-NN tunrelation-specific weight matrices to handle heterogeing, UMAP superiority, relation-centric vs. nodeneous edges, enabling modeling of knowledge graphs centric models) and practical implications. Section 6 and multi-relational networks. Our R-GCN-VGAE concludes with future research directions. architecture combines R-GCN’s edge-type awareness with VGAE’s generative modeling, specifically targeting bridge-centered metapath extraction. 2 Related Work Comparison to HetVGAE: Hamilton et al. [14] proposed heterogeneous GraphSAGE for inductive 2.1 Infrastructure Criticality and Disnode classification. Our previous work implemented aster Resilience HetVGAE (heterogeneous node-type embeddings) for Traditional bridge maintenance prioritization relies social impact prediction, achieving r = 0.56-0.68 coron structural health indicators such as crack width, relations. R-GCN-VGAE differs by encoding edgecorrosion depth, and load-bearing capacity [1]. While level semantics (street→bridge transitions) rather structural assessments remain essential, they fail to than node-level attributes, proving complementary capture network-level criticality—the role of individ- for disaster-preparedness classification. ual bridges in sustaining urban functionality during disasters. 2.3 Metapath-based Graph Analysis Graph-theoretic approaches have emerged to quantify infrastructure criticality via network centrality Metapaths—structured sequences of node types and metrics. Betweenness centrality, closeness central- edge types—capture semantic relationships in hetity, and eigenvector centrality identify bridges whose erogeneous networks. Sun et al. [15] introduced failure maximally disrupts network connectivity [7]. PathSim similarity for bibliographic networks, quanHowever, these topological metrics treat all edges uni- tifying author-paper-author co-authorship patterns. formly, ignoring semantic differences between com- Metapath2vec [16] extended node2vec to heterogeneous graphs by performing metapath-guided random mercial, medical, and residential connections. Recent disaster resilience research emphasizes walks, capturing semantic relationships across node multi-layer network analysis, modeling interdepen- types. dencies between transportation, power grids, and In urban infrastructure analysis, metapaths encode communication networks [5]. Buldyrev et al. [6] multi-hop connectivity: Bridge→Street→Shop repre3
sents supply chain access, Bridge→Street→Hospital represents emergency medical access, and Bridge→Street→Residence represents evacuation route potential. Unlike citation networks where metapaths follow predefined schemas (e.g., ”author-paper-venue”), urban graphs require distance-constrained metapaths—k-NN algorithms ensure bridges connect only to geographically proximate facilities (Section 3.4).
Methodology
3.1
Problem Formulation
Let G = (V, E, Tv , Te ) denote a heterogeneous graph where V is the set of nodes, E ⊆ V × V is the set of edges, Tv defines node types, and Te defines edge types (relations). In our urban infrastructure context:
Recent work on urban accessibility [17] uses shortest-path algorithms to measure facility reachability. Our metapath framework extends this by encoding multiple simultaneous connections (e.g., bridges near both hospitals and residences classified as Balanced Multi-Use) rather than single-target reachability.
2.4
3
V = Vbridge ∪ Vstreet ∪ Vbuilding
(1)
Tv = {bridge, street, building} Te = {to shop, to hospital, to residence,
(2)
street to street, street to bridge, . . .} (3) Each bridge b ∈ Vbridge is associated with a feature vector xb ∈ R21 comprising: - Structural attributes: span length, year built (if available) - Topological attributes: degree centrality, betweenness centrality Metapath counts: {highway metapath count, shop count, hospital count} - is highway: Binary indicator for highway proximity Disaster Resilience Formulation: We define bridge resilience Rb as the capacity to sustain access to critical urban functions under external forces F (earthquakes, floods). Formally, let Mb = {m1 , m2 , . . . , mk } denote the set of metapaths originating from national highways, passing through bridge b, and terminating at building nodes (hospitals, shops, residences). The disaster-preparedness role of bridge b is characterized by:
OpenStreetMap for Infrastructure Analysis
OpenStreetMap (OSM) has emerged as a critical open dataset for large-scale infrastructure studies. Boeing [18] introduced OSMnx, a Python library for downloading and analyzing street networks, enabling reproducible urban morphology research. OSMnxbased studies have quantified street network centrality [19], walkability [20], and disaster evacuation planning [21].
Bridge Extraction from OSM: OSM’s Role(b) = arg max P (c | Mb , zb ) (4) man made=bridge tag identifies standalone bridge c∈C structures, while bridge=yes on road segments where C = {Supply, Medical, Residential} are marks road-embedded bridges. We adopt the former disaster-preparedness categories, and zb ∈ R32 is a for municipal infrastructure focus, filtering unnamed latent representation learned via R-GCN-VGAE enbridges to exclude pedestrian footbridges. coding highway-origin connectivity patterns. Amenity Geocoding: OSM’s amenity Key Insight: A bridge’s disaster role is detertagging system (amenity=hospital, shop=*, mined not by traffic volume or structural condition, building=residential) provides detailed POI but by the types of buildings reachable via metapaths data. However, completeness varies: Mito’s 15,978 and the density of highway connections enabling loshops vs. 65 hospitals reflects both actual dis- gistics flow. tribution and volunteer mapper biases [22]. Our k-NN parameter tuning (Section 5.1) mitigates this 3.2 Heterogeneous Graph Construcimbalance.
tion
Quality Considerations: Haklay [23] reported 80% positional accuracy (within 6m of Ordnance Survey data in London). For disaster-preparedness classification, 80%+ accuracy suffices since metapath analysis operates at street-block granularity (∼100m) rather than centimeter-level precision. Our methodology’s open-data emphasis enables continuous improvement as OpenStreetMap volunteers enhance regional coverage.
3.2.1
Data Acquisition via OSMnx
We use OSMnx [18] to extract road networks, bridge locations, and building points of interest (POI) from OpenStreetMap [24] for three cities in Ibaraki Prefecture: 1. Road Network: able roads within 4
Download all city boundaries
drivusing
ox.graph from place(). National highways (highway=trunk) are identified via OSM tag filtering.
(ℓ+1)
hi
= σ
r∈R j∈Nr (i)
2. Bridges: Extract named bridges using Overpass API queries: (man made=bridge) AND (name!=None). Filter unnamed structures to focus on municipally managed infrastructure.
1 (ℓ) (ℓ) (ℓ) W (ℓ) h + W0 hi |Nr (i)| r j (5)
where: (ℓ)
• hi ∈ Rdℓ : Hidden representation of node i at layer ℓ
3. Buildings: Query amenity tags for {amenity=hospital, shop=*, building=residential} with spatial filtering (2km buffer around bridges).
• R: Set of relation types (street→street, street→bridge) • Nr (i): Neighbors of node i under relation r (ℓ)
3.2.2
X X
• Wr trix
Graph Topology
The heterogeneous graph G is constructed with the following node and edge types: Nodes:
∈ Rdℓ+1 ×dℓ : Relation-specific weight ma-
(ℓ)
• W0 : Self-loop transformation • σ: ReLU activation function Basis Decomposition: To reduce parameters, we use basis decomposition:
• bridge (|Vbridge | = 697 for Mito): Bridge centroids from OSM geometries • street (|Vstreet | = 31, 001 for Mito): Road segment nodes from OSMnx network
Wr(ℓ) =
B X (ℓ) (ℓ) arb Vb
(6)
b=1
• building (|Vbuilding | = 16, 791 for Mito): POI with B = 2 basis matrices, reducing parameters from nodes categorized as hospital, shop, or residence |R| × dℓ+1 × dℓ to B × dℓ+1 × dℓ + |R| × B. Architecture Configuration: Edges: R-GCN Layer 1: R21 −−−−−→ R128 (7) R-GCN • street to street: Road network connectivity Layer 2: R128 −−−−−→ R128 (8) (adjacency matrix) R-GCN Layer 3 (µ): R128 −−−−−→ R32 (9) • street to bridge: Spatial proximity (snapping R-GCN Layer 3 (log σ 2 ): R128 −−−−−→ R32 (10) bridges to nearest road segments) • to shop, to hospital, to residence: Bridge- 3.3.2 Variational AutoEncoder Framework to-building edges via k-NN algorithm (SecFollowing the VAE framework [8, 9], the encoder outtion 3.4) puts mean µ and log-variance log σ 2 for each node. The latent representation is sampled via reparame3.2.3 Coordinate System and Distance Calterization: culation zi = µi + σ i ⊙ ϵ,
All spatial coordinates are projected to EPSG:6677 (JGD2011 Plane Rectangular Coordinate System Zone 9) for metric distance calculations. Haversine distances are used for initial filtering, followed by planar distances for k-NN algorithms.
3.3
R-GCN-VGAE Architecture
3.3.1
Relational Graph Convolutional Encoder
ϵ ∼ N (0, I)
(11)
The decoder reconstructs edges via inner product: p(Aij = 1 | zi , zj ) = σ(z⊤ i zj )
(12)
The loss function combines reconstruction loss and KL divergence with β-annealing: L = Lrecon + βLKL Lrecon = −Eq(Z|X,A) [log p(A|Z)]
(13) (14)
LKL = KL[q(Z|X, A)∥p(Z)] (15) The encoder consists of three Relational Graph Convolutional Network (R-GCN) layers [13], each implewhere β anneals from 0.01 → 1.0 over the first 50 menting relation-specific message passing: epochs to prevent posterior collapse [8]. 5
3.4
Metapath Extraction and k-NN Tuning
3.4.1
Metapath Definition
• Medical Access (confidence > 0.7): |Mb,hospital | ≫ |Mb,shop |, |Mb,residence |. Essential for emergency healthcare delivery and ambulance routing.
A metapath m = ⟨vhighway , vbridge , vbuilding ⟩ represents a 3-hop path: (1) national highway node → (2) bridge node → (3) building node. We focus on three building types corresponding to disaster-preparedness roles:
• Residential Protection (confidence > 0.7): |Mb,residence | ≫ |Mb,hospital |, |Mb,shop |. Prevents community isolation and enables evacuation.
• mshop : Highway → Bridge → Shop (Supply Chain)
• Balanced Multi-Use (confidence < 0.3): Nearly uniform metapath distribution. Serves multiple roles with no clear specialization.
• mhospital : Highway → Bridge → Hospital (Medical Access)
3.6
Dimensionality Reduction
• mresidence : Highway → Bridge → Residence (Res- The 32-dimensional latent vectors zb are projected to 2D for visualization using UMAP [25] with the idential Protection) following configuration: Simplification: Rather than extracting full shortest paths from highways to bridges (30–85 segments on average), our approach focuses on direct bridge→building connections within a 2 km radius, using highway proximity as a binary node feature (is highway). 3.4.2
• n neighbors=15: Controls local vs. global structure balance • min dist=0.1: Minimum distance between points in embedding space • metric=’euclidean’: Distance metric in highdimensional space
k-NN Parameter Selection
For each bridge-building pair (b, c) with Haversine distance d(b, c) ≤ 2 km, we rank buildings by distance and select the top-k nearest neighbors. The choice of k balances semantic validity (meaningful service range) and computational efficiency: Empirical Validation (Mito City): Increasing shop k-NN from 3 to 5 increased Supply Chain metapath coverage by +66% (162 → 270 paths), capturing mid-tier commercial bridges previously classified as “Balanced Multi-Use.”
Comparison to Alternatives: Experiments with t-SNE (perplexity=30) and PCA (2 components) showed inferior performance: - PCA: Linear projection captures only 77% variance, failing to separate Supply Chain vs. Medical Access clusters. - t-SNE: While preserving local structure, global topology is distorted, making inter-cluster distances meaningless. - UMAP: Achieves both local cluster coherence and global structure preservation, critical for interpreting bridge role relationships (Section 5.2).
3.5
4
Experiments and Results
4.1
Dataset Description
Classification Strategy
Bridges are classified into disaster-preparedness categories based on dominant metapath counts and confidence scores derived from metapath proportions:
We evaluate our methodology on three cities in Ibaraki Prefecture, Japan, chosen to represent diverse |Mb,c | Confidence(b, c) = P (16) urban scales and functional characteristics: ′ c′ ∈C |Mb,c | Mito City: Prefectural capital with 279,126 popwhere |Mb,c | is the count of metapaths from bridge ulation, featuring diverse urban functions including government offices, universities, and major hospitals. b to category c. Represents a large-scale scenario with dense infrasCategory Definitions: tructure. • Supply Chain (confidence > 0.9): |Mb,shop | ≫ Chikusei City: Regional hub with 98,467 popu|Mb,hospital |, |Mb,residence |. Critical for post- lation, primarily agricultural and commercial. The shop-dominant metapath distribution (61 Supply disaster logistics and commercial continuity. 6
Table 1: k-NN Parameter Rationale for Disaster Scenarios Building Type
k
Rationale
Shop Hospital Residence
5 5 20
Focused commercial zones (e.g., downtown districts) Emergency medical facilities (typically 3-10 per city) Broader residential neighborhoods requiring evacuation access
• Training duration: dependent)
Table 2: Dataset Statistics Across Three Cities Attribute
Mito
Chikusei
Moriya
Bridges Street Nodes Buildings Total Shops Hospitals Residences
697 31,001 16,791 15,978 65 668
258 15,300 1,681 1,637 5 21
148 9,421 1,234 1,115 12 107
270 41 143
61 7 0
140 10 43
Capital
Regional hub
Logistics gateway
Metapath Counts Supply Chain Medical Access Residential City Type
4.3
(city-
Clustering Quality
We apply HDBSCAN clustering [28] to UMAPreduced embeddings with min cluster size = max(5, int(n*0.03)) to accommodate varying city scales: Table 3: Clustering Quality Metrics Metric Silhouette Score Clusters Found Noise Points (noise ratio)
Mito
Chikusei
Moriya
0.289 6 499 (71.6%)
0.363 2 162 (62.8%)
0.131 2 115 (77.7%)
Key Findings: 1. Mito (large scale): HDBSCAN identifies 6 clusters with Silhouette=0.289, indicating moderate cluster separation. High noise rate (71.6%) reflects diverse bridge roles not captured by metapath features alone.
Implementation Details
Framework: PyTorch 2.0.1 with PyTorch Geometric [26, 27] 2.3.1. Hyperparameters:
2. Chikusei (mid scale): Best Silhouette=0.363 (+25.6% vs. Mito) due to more homogeneous urban structure. Only 2 clusters reflect simpler functional division (commercial vs. local access).
• R-GCN layers: [21 → 128 → 128 → 32] • Number of relation types: street→bridge)
epochs
Convergence: Mito (100 epochs, loss=3.62), Chikusei (64 epochs, loss=3.34), Moriya (67 epochs, loss=3.62). Smaller cities converge faster due to fewer nodes.
Chain vs. 7 Medical Access) reflects limited healthcare infrastructure. Represents a mid-scale scenario. Moriya City: Residential suburb with 70,058 population, located 32 minutes from Tokyo via Tsukuba Express. Contains extreme logistics hub bridges with up to 2,803 highway metapaths (vs. Mito’s maximum of 1,943). Represents a small-scale scenario with high variability.
4.2
64-100
2 (street→street,
3. Moriya (small scale): HDBSCAN complete failure (100% noise), addressed via K-Means K=2 fallback (Silhouette=0.131). Successfully separates logistics hub bridges (33 bridges, avg 171.2 highway metapaths) from local access bridges (115 bridges, avg 9.7 metapaths).
• Number of bases: 2 (basis decomposition) • Learning rate: 0.001 (Adam optimizer) • β-annealing schedule: Linear 0.01 → 1.0 over 50 epochs • Negative sampling ratio: 1:1 (positive:negative edges)
4.4
Classification Results
Table 4 summarizes disaster-preparedness category distributions across the three cities:
• Early stopping patience: 10 epochs 7
Table 4: Bridge Classification by Disaster-Preparedness Category Category
Mito
Chikusei
Moriya
Total
Supply Chain Medical Access Residential Protection Balanced Multi-Use Mixed Variants
194 52 40 384 27
49 16 13 169 11
5 10 6 126 1
248 78 59 679 39
Total
697
258
148
1,103
4.6
Confidence Scores: Supply Chain bridges exhibit highest confidence (Mito: 0.966, Chikusei: 0.949, Moriya: 1.000), reflecting clear commercial dominance. Medical Access (Mito: 0.770) and Residential Protection (Mito: 0.793) show moderate confidence, indicating some overlap with other categories. City-Specific Patterns:
Dimensionality Reduction Comparison
Figure 1 visualizes PCA, t-SNE, and UMAP projections of the same 32-dimensional embeddings for Mito City, demonstrating the superiority of UMAP for heterogeneous graph representation learning. As shown in Figure 1, UMAP achieves clear cate• Mito: Balanced distribution reflects diverse pre- gory boundaries while preserving global inter-cluster fectural capital functions (27.8% Supply, 7.5% relationships. In contrast, t-SNE [30] preserves local structure but distorts global topology, while PCA Medical, 5.7% Residential). suffers from severe category overlap due to its linear• Chikusei: Commercial-skewed (19.0% Supply ity assumption (77% variance explained). A detailed vs. 6.2% Medical) due to limited hospital in- quantitative comparison is provided in Table 6 (Section 5.2). frastructure (only 5 hospitals vs. 1,637 shops).
• Moriya: Extreme logistics hub with only 5 Sup4.7 Visualize Bridges by Metapath ply Chain bridges but highest average shop metaCategory paths (7.2 per bridge). Zero residential bridges classified due to sparse residential POI data. To validate the generalizability of our metapath-based classification across diverse urban scales, we extend the UMAP visualization to Chikusei and Moriya cities 4.5 Metapath Correlation Analysis (Figure 2). Additionally, we overlay bridge classificaTo validate that R-GCN-VGAE learns meaningful tions onto OpenStreetMap geographical representametapath representations, we compute Spearman tions (Figure 3) to demonstrate the spatial distriburank correlations between latent dimensions zi and tion of disaster-preparedness categories. highway metapath count: Comparative Analysis: Comparison to Node-Centric HetVChikusei City (mid-scale): The UMAP embedding GAE: Previous node-centric approach achieved (Figure 2a) reveals a bimodal distribution reflecting r = 0.56-0.68 correlation with composite the commercial-agricultural urban structure. Supsocial impact score overall, indicating general ply Chain bridges cluster tightly (Silhouette=0.363), urban function learning. Alternative graph architec- while Medical Access bridges scatter due to sparse tures such as Graph Attention Networks [29] were not hospital infrastructure (only 5 hospitals). The OSM explored due to computational constraints for large- overlay (Figure 3b) shows bridge concentration along scale urban networks. R-GCN-VGAE’s r = 0.416 National Route 50, validating the logistics corridor with highway metapath count demonstrates spe- hypothesis. cialized encoding of logistics hub connectivity—a Moriya City (small-scale): UMAP visualization complementary role to HetVGAE. (Figure 2b) demonstrates extreme variability, with Interpretation: Dimension z19 acts as a “logis- logistics hub bridges (33 bridges, avg 171.2 hightics hub detector,” with high values for bridges in way metapaths) forming a distinct high-density clusthe Tsukuba Express corridor (Moriya) and Joban ter. K-Means K=2 fallback successfully separates Expressway junctions (Mito), while low values corre- these hubs from local access bridges (115 bridges, avg 9.7 metapaths). The OSM map (Figure 3c) respond to residential neighborhood bridges. 8
Table 5: Top Latent Dimensions Correlated with Highway Metapaths (Mito City) Latent Dim z19 z12 z18
(a) PCA (2 components)
Spearman r
p-value
Interpretation
0.416 0.333 0.258
−30
Logistics encoder Highway proximity Secondary connectivity
1.47 × 10 1.53 × 10−19 4.80 × 10−12
(b) t-SNE (perplexity=30)
(c) UMAP (n neighbors=15)
Figure 1: Dimensionality reduction comparison for Mito City bridge embeddings (697 bridges). (a) PCA shows severe category overlap, failing to distinguish disaster-preparedness roles. (b) t-SNE provides partial local cluster separation but loses global structure. (c) UMAP achieves clear category boundaries while preserving inter-cluster relationships, making it optimal for heterogeneous graph visualization. travel tolerance (5-minute walk radius, ∼400m) compared to immediate needs.
veals Tsukuba Express corridor dominance, with hub bridges positioned at interchange junctions. Spatial Validation: Comparing UMAP embeddings (latent space) with OSM overlays (geographical space) confirms that our learned representations capture both topological connectivity and spatial proximity [31]. Supply Chain bridges align with highway corridors, Medical Access bridges cluster near prefectural hospital complexes, and Residential Protection bridges distribute across neighborhood zones. Generalizability Assessment: The consistent category patterns across three diverse cities (697/258/148 bridges) demonstrate the robustness of R-GCN-VGAE for metapath-based classification. UMAP’s manifold preservation enables intuitive interpretability regardless of city scale, supporting the methodology’s applicability to other Japanese municipalities.
5
Discussion
5.1
k-NN Tuning for DisasterPreparedness Semantics
Hospital (k = 5) : Emergency medical access allows broader search radius given scarcity of critical care facilities (65 hospitals in Mito vs. 15,978 shops). Residence (k = 20) : Evacuation planning necessitates wider catchment areas to protect vulnerable populations (elderly, children) who may rely on specific bridges for access. Implication: Generic k-NN defaults (e.g., uniform k = 3 [32]) fail to capture disaster-preparedness semantics. Domain-informed parameter selection produces 66% denser metapath graphs while ensuring physically realistic connectivity (validated via OpenStreetMap driving distances). Trade-off: Higher k risks false positives (e.g., bridges far from actual supply routes). We mitigate this via confidence thresholding (Eq. 16) and post-hoc validation against Leaflet map overlays (htmlwidget visualization).
Finding: Increasing k-NN from 3 to 5 boosted Sup- 5.2 UMAP Superiority for Heterogeneous Graph Embeddings ply Chain metapath coverage by +66% in Mito City (from 162 to 270 metapaths), while maintaining seFinding: UMAP outperforms t-SNE and PCA for mantic validity. The rationale for category-specific k visualizing R-GCN-VGAE embeddings, preserving values is as follows: both local cluster separation and global inter-cluster Shop (k = 5) : Emergency supplies require longer relationships: 9
(a) Chikusei City (258 bridges)
(b) Moriya City (148 bridges)
Figure 2: UMAP visualization of bridge embeddings for mid-scale (Chikusei) and small-scale (Moriya) cities. (a) Chikusei shows clear commercial-residential separation with dominant Supply Chain cluster (49 bridges). (b) Moriya exhibits extreme variability with logistics hub bridges (high highway metapath counts) separated from local access bridges.
(a) Mito City
(b) Chikusei City
(c) Moriya City
Figure 3: Geographical distribution of bridge metapath categories overlaid on OpenStreetMap. Color-coding represents disaster-preparedness roles: Supply Chain (blue), Medical Access (red), Residential Protection (green), and Balanced Multi-Use (gray). (a) Mito shows dense urban network with distributed categories. (b) Chikusei exhibits commercial concentration along Route 50 corridor. (c) Moriya shows Tsukuba Express corridor dominance with extreme logistics hub bridges. Manifold Topology: UMAP’s Riemannian geometry optimization [25] aligns with heterogeneous graph structure, where Supply Chain, Medical Access, and Residential Protection categories form distinct manifold regions with smooth boundaries (Balanced Multi-Use). t-SNE’s over-dispersion breaks semantic proximity, while PCA’s linearity assumption fails to capture nonlinear metapath interactions.
5.3
R-GCN Relation-Centric vs. HetVGAE Node-Centric Learning
Finding: R-GCN-VGAE specializes in highway metapath encoding (z19 r = 0.416) compared to previous HetVGAE’s composite social impact correlation (z6 r = 0.56-0.68): R-GCN Architecture : Relation-specific weight matrices Wr allow targeted learning of edge type semantics (e.g., street-bridge transitions). Dimension z19 emerges as a logistics hub detector, strongly activating for Tsukuba Express and Joban Expressway bridges.
Practical Impact: UMAP visualizations enable non-expert stakeholders (e.g., municipal engineers) to HetVGAE Architecture : Node-type embeddings intuitively understand bridge prioritization without merge all metapath features into a holistic social examining raw 32-dimensional vectors. This humanimpact score. Achieves higher correlation with in-the-loop interpretability is critical for maintenance composite metrics but lacks fine-grained edgebudget decision-making. level interpretability. 10
Table 6: Dimensionality Reduction Comparison (Mito City) Criterion
UMAP
t-SNE
PCA
Cluster Separation Global Structure Computational Cost (s)
Yes (Clear) Yes (Preserved) 3.2
Partial No (Lost) 8.1
No (Overlap) Partial (77%) 0.1
Visual Interpretability
Best
Mediocre
Poor
Complementary Roles: R-GCN is preferable 5.5 Practical Implications for Disaster when edge connectivity patterns are the primary Preparedness disaster-preparedness signal (e.g., identifying traffic bottlenecks). HetVGAE is preferable for node-centric Maintenance Prioritization: Classification enattributes (e.g., building damage scores from popula- ables tiered inspection strategies: tion density). Hybrid architectures [33] warrant fu1. Priority 1 (Supply Chain): Annual inspecture exploration. tion to ensure post-disaster commercial logistics Code Efficiency: Removing the NetworkX deresilience pendency for shortest-path calculations reduced the codebase from 943 to 750 lines (−20%) while main2. Priority 2 (Medical Access + Residential): taining classification accuracy. Biannual inspection for emergency evacuation route integrity
5.4
Small City Challenges: HDBSCAN Failure and K-Means Fallback
3. Priority 3 (Balanced Multi-Use): Riskbased inspection using structural health scores
Return on Investment: Our methodology reChallenge: Moriya City (148 bridges) exhibits ex- duced bridge role annotation time from 138 mintreme metapath variability, causing HDBSCAN to utes (manual GIS inspection for Mito’s 697 bridges, mark 100% of bridges as noise. This stems from: 11.9s/bridge) to < 10 seconds (model inference + UMAP visualization), achieving 828× speedup. For 1. Sample Size Insufficiency: HDBSCAN’s minIbaraki Prefecture’s 14,000 bridges, this translates to imum cluster size constraint (5 bridges = 3.4% 32 person-days → 4 hours. of 148) requires at least 5 × 2 = 10 bridges for Policy Integration: Disaster resilience categories viable clustering. Moriya’s uneven distribution directly inform MLIT’s bridge health index (I–IV (126 Balanced vs. 10 Medical vs. 6 Residential) scoring [1]). Municipalities can allocate limited repair violates this assumption. budgets to bridges maximizing post-disaster connec2. Extreme Outliers: Single logistics hub bridge tivity (e.g., repairing one Medical Access bridge may with 2,803 highway metapaths (vs. city aver- protect access for 10 hospitals). age 21.6) creates density discontinuity that HDBSCAN interprets as noise. 5.6 Limitations and Future Work Solution: K-Means K=2 fallback successfully sep- Data Limitations: arates hub bridges (33 bridges, avg 171.2 metapaths) 1. OSM Completeness: OpenStreetMap coverfrom local access bridges (115 bridges, avg 9.7 metapage varies by region (Mito 95% complete vs. ruaths) with Silhouette=0.131. This binary separation ral areas 60% [18]). Missing amenity tags may suffices for small-city maintenance prioritization (”remisclassify critical bridges as Balanced Multipair hubs first”). Use. Generalization: For cities with < 150 bridges, we recommend: 2. Temporal Dynamics: Our snapshot analysis p (2023-11-24 OSM extraction) ignores seasonal • Use adaptive K-Means with K = ⌊ n/2⌋ (e.g., road closures, construction detours, and longK = 8 for Chikusei’s 258 bridges) term urban development. Longitudinal studies • Validate via domain expert review (post-hoc (quarterly OSM updates) would capture evolving infrastructure. htmlwidget map inspection) 11
Methodological Limitations:
1. Graph Neural Network for Infrastructure Analysis: R-GCN-VGAE successfully learned 32-dimensional embeddings capturing bridgecentered metapath topology. Dimension z19 emerged as a logistics hub detector with r = 0.416 correlation to highway metapath counts, enabling data-driven prioritization.
1. Earthquake/Flood Scenarios Absent: Current classification relies on peacetime metapath connectivity. Actual disasters may render high-metapath bridges unusable (e.g., liquefaction near rivers). Integration with geotechnical hazard maps is essential. 2. HDBSCAN Scalability: Small-city failure (Moriya 100% noise) requires adaptive clustering strategies. Hierarchical hybrid methods (HDBSCAN→K-Means fallback) need systematic validation across < 100 bridge scenarios.
2. Multi-City Validation: A case study across 1,103 bridges in three Ibaraki cities (Mito: 697, Chikusei: 258, Moriya: 148) validated scalability and generalizability, achieving moderate-togood clustering quality (Silhouette 0.289–0.363) despite OSM data heterogeneity.
3. Single-City Training: We train separate RGCN-VGAE models per city due to heterogeneous node distributions (Mito 31k nodes vs. Moriya 9k). Transfer learning approaches [14] could enable regional model reuse.
3. Open-Data Workflow: The end-to-end pipeline using OSMnx, PyTorch Geometric, and UMAP requires no proprietary infrastructure data, enabling reproducibility across Japanese municipalities and international contexts.
Future Directions:
• Multi-Hazard Scenarios: Incorporate seismic Three practical lessons emerged: (1) domainintensity, flood inundation, and landslide suscepinformed k-NN tuning (shop/hospital k = 5, resitibility layers to compute disaster-specific metadence k = 20) increased metapath coverage by 66% path accessibility. while maintaining physical realism; (2) UMAP out• Temporal Degradation Modeling: Integrate performed t-SNE and PCA for visualizing heterogebridge health inspection data (crack depth, ma- neous graph embeddings; and (3) R-GCN’s relationterial corrosion) into time-series R-GCN to pre- centric architecture complements node-centric HetVGAE by specializing in edge connectivity patterns. dict maintenance urgency. Our methodology achieves 828× speedup over man• Scalability Testing: Validate methodology on ual GIS annotation (138 minutes → 10 seconds for Tokyo Metropolitan Area (47,000 bridges) and 697 bridges), directly informing MLIT’s bridge health inter-city highway networks. index for evidence-based allocation of repair bud• Real-Time Monitoring: Deploy edge- gets. Future work will integrate multi-hazard scecomputing R-GCN inference on municipal IoT narios (seismic, flood, landslide), temporal degradainfrastructure for dynamic traffic rerouting tion modeling, and large-scale validation on the Tokyo Metropolitan Area (47,000 bridges). during disasters.
6
Conclusion
Acknowledgments
This paper introduced a novel bridge maintenance decision-making methodology centered on disasterpreparedness metapath classification using Relational Graph Convolutional Variational Autoencoder (R-GCN-VGAE). By integrating heterogeneous urban infrastructure networks—bridges, streets, shops, hospitals, and residences—extracted from OpenStreetMap, we demonstrated automated bridge role classification into four disaster-preparedness categories: Supply Chain, Medical Access, Residential Protection, and Balanced Multi-Use. Key Findings:
The author acknowledges OpenStreetMap contributors for providing the open geospatial data used in this study.
Data Availability The OpenStreetMap data used in this study is publicly available at https://www.openstreetmap. org/.
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