city2graph、OSMnx、PyTorch Geometricを用いた都市機能推論のための空間グラフニューラルネットワークの実装チュートリアル

In this tutorial, we build an end-to-end spatial graph learning pipeline using city2graph. We start by collecting real urban POI data and street network information from OpenStreetMap, with a synthetic fallback to ensure the workflow remains reliable. We then engineer spatial features, construct multiple proximity graph families, and compare how different graph-building strategies represent the same urban environment. After that, we create both heterogeneous and homogeneous graph structures, convert them into PyTorch Geometric format, and train a GraphSAGE model to predict POI categories from spatial structure. Through this process, we integrate geospatial data processing, graph construction, and GNN-based urban function inference into a single practical workflow.

Installing city2graph and Importing Geospatial and Graph Learning Libraries

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!pip -q install "city2graph[cpu]" osmnx contextily scikit-learn 2>/dev/null

import warnings, numpy as np, pandas as pd, geopandas as gpd

warnings.filterwarnings("ignore")

from shapely.geometry import Point

import matplotlib.pyplot as plt

import city2graph as c2g

print("city2graph version:", getattr(c2g, "__version__", "unknown"))

print("PyTorch / PyG available:", c2g.is_torch_available())

import torch

import torch.nn.functional as F

from torch_geometric.nn import SAGEConv, to_hetero

from torch_geometric.utils import to_undirected

from sklearn.preprocessing import StandardScaler

from sklearn.neighbors import NearestNeighbors

from sklearn.metrics import accuracy_score, f1_score

from sklearn.decomposition import PCA

SEED = 42

np.random.seed(SEED); torch.manual_seed(SEED)

We begin by installing the required libraries and importing the geospatial, graph learning, and machine learning tools used throughout the tutorial. We verify that city2graph and PyTorch Geometric are available so the rest of the workflow can run properly. We also set a fixed random seed to make the graph construction, training split, and model results more reproducible.

Collecting OpenStreetMap POI Data with a Synthetic Fallback

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CENTER = (35.6595, 139.7005)

DIST_M = 1100

TAG_QUERIES = {

"food": {"amenity": ["restaurant", "cafe", "fast_food", "bar", "pub"]},

"retail": {"shop": True},

"education": {"amenity": ["school", "university", "college", "kindergarten", "library"]},

"health": {"amenity": ["hospital", "clinic", "pharmacy", "doctors", "dentist"]},

}

def to_points(gdf):

g = gdf.copy()

g["geometry"] = g.geometry.representative_point()

return g

poi_gdf, segments_gdf = None, None

try:

import osmnx as ox

ox.settings.use_cache = True

ox.settings.log_console = False

frames = []

for label, tags in TAG_QUERIES.items():

try:

f = ox.features_from_point(CENTER, tags=tags, dist=DIST_M)

f = f[f.geometry.notna()]

if len(f):

f = to_points(f)[["geometry"]].copy()

f["category"] = label

frames.append(f)

except Exception as e:

print(f" (skip {label}: {e})")

if not frames:

raise RuntimeError("No POIs returned from Overpass.")

poi_gdf = gpd.GeoDataFrame(pd.concat(frames, ignore_index=True), crs="EPSG:4326")

G = ox.graph_from_point(CENTER, dist=DIST_M, network_type="walk")

segments_gdf = ox.graph_to_gdfs(G, nodes=False, edges=True).reset_index(drop=True)[["geometry"]]

print(f"OSM acquisition OK -> {len(poi_gdf)} POIs, {len(segments_gdf)} street segments")

except Exception as e:

print(f"OSM unavailable ({e}) -> generating synthetic clustered POIs.")

rng = np.random.default_rng(SEED)

cats = list(TAG_QUERIES.keys())

centers = rng.uniform(-0.01, 0.01, size=(8, 2)) + np.array(CENTER[::-1])

rows = []

for ci, c in enumerate(centers):

dom = cats[ci % len(cats)]

n = rng.integers(40, 90)

pts = c + rng.normal(0, 0.0016, size=(n, 2))

for (lon, lat) in pts:

cat = dom if rng.random() < 0.75 else rng.choice(cats)

rows.append({"geometry": Point(lon, lat), "category": cat})

poi_gdf = gpd.GeoDataFrame(rows, crs="EPSG:4326")

segments_gdf = None

print(f"Synthetic dataset -> {len(poi_gdf)} POIs")

if len(poi_gdf) > 700:

poi_gdf = poi_gdf.sample(700, random_state=SEED).reset_index(drop=True)

metric_crs = poi_gdf.estimate_utm_crs()

poi_gdf = poi_gdf.to_crs(metric_crs).reset_index(drop=True)

if segments_gdf is not None:

segments_gdf = segments_gdf.to_crs(metric_crs)

print("Class balance:\n", poi_gdf["category"].value_counts())

We collect real POI data from OpenStreetMap around Shibuya, Tokyo, and group the locations into broad urban function categories such as food, retail, education, and health. We also download the walkable street network so that the POIs can later be connected with urban-form features. If the OSM request fails, we generate a synthetic clustered dataset, which keeps the tutorial runnable even when online data access is unavailable.

Engineering Spatial Features and Building Proximity Graph Families

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poi_gdf["cx"] = poi_gdf.geometry.x

poi_gdf["cy"] = poi_gdf.geometry.y

coords = poi_gdf[["cx", "cy"]].to_numpy()

nn = NearestNeighbors(radius=150.0).fit(coords)

poi_gdf["local_density"] = [len(idx) - 1 for idx in nn.radius_neighbors(coords, return_distance=False)]

if segments_gdf is not None and len(segments_gdf):

try:

joined = gpd.sjoin_nearest(poi_gdf[["geometry"]], segments_gdf[["geometry"]],

distance_col="dist_street")

poi_gdf["dist_street"] = joined.groupby(level=0)["dist_street"].min().reindex(poi_gdf.index).fillna(0.0)

except Exception:

poi_gdf["dist_street"] = 0.0

else:

poi_gdf["dist_street"] = 0.0

poi_gdf["category"] = poi_gdf["category"].astype("category")

poi_gdf["label"] = poi_gdf["category"].cat.codes.astype(int)

CLASS_NAMES = list(poi_gdf["category"].cat.categories)

print("Classes:", CLASS_NAMES)

def graph_stats(name, builder):

try:

nodes, edges = builder()

deg = pd.Series(np.r_[edges.index.get_level_values(0),

edges.index.get_level_values(1)]).value_counts()

return name, len(edges), round(deg.mean(), 2), (nodes, edges)

except Exception as e:

return name, f"ERR: {e}", None, None

builders = {

"KNN (k=8)": lambda: c2g.knn_graph(poi_gdf, distance_metric="euclidean", k=8, as_nx=False),

"Delaunay": lambda: c2g.delaunay_graph(poi_gdf, as_nx=False),

"Gabriel": lambda: c2g.gabriel_graph(poi_gdf, as_nx=False),

"RNG": lambda: c2g.relative_neighborhood_graph(poi_gdf, as_nx=False),

"EMST": lambda: c2g.euclidean_minimum_spanning_tree(poi_gdf, as_nx=False),

"Waxman": lambda: c2g.waxman_graph(poi_gdf, distance_metric="euclidean", r0=150, beta=0.6),

}

print("\n--- Proximity graph comparison ---")

print(f"{'graph':<14}{'#edges':>10}{'avg_degree':>12}")

built = {}

for nm, b in builders.items():

name, ne, avgdeg, payload = graph_stats(nm, b)

print(f"{name:<14}{str(ne):>10}{str(avgdeg):>12}")

if payload: built[nm] = payload

fig, axes = plt.subplots(1, 3, figsize=(16, 5))

for ax, key in zip(axes, ["KNN (k=8)", "Delaunay", "EMST"]):

if key in built:

n_, e_ = built[key]

e_.plot(ax=ax, linewidth=0.4, color="#3b7dd8", alpha=0.6)

poi_gdf.plot(ax=ax, markersize=4, color="#d83b5c")

ax.set_title(key); ax.set_axis_off()

plt.suptitle("Spatial graph topologies on the same POI set", y=1.02)

plt.tight_layout(); plt.show()

We engineer spatial features for each POI by extracting its projected coordinates, calculating local density, and estimating distance to the nearest street segment. We then assign category labels and build several families of proximity graphs, including KNN, Delaunay, Gabriel, RNG, EMST, and Waxman. We compare their edge counts and average degrees, then visualize selected graph topologies to see how differently they connect the same set of POIs.

Constructing Heterogeneous and Homogeneous Graphs in PyTorch Geometric

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nodes_dict = {}

for cat in CLASS_NAMES:

sub = poi_gdf[poi_gdf["category"] == cat].copy().reset_index(drop=True)

nodes_dict[cat] = sub[["geometry", "cx", "cy", "local_density"]]

try:

_, bridge_edges = c2g.bridge_nodes(nodes_dict, proximity_method="knn", k=3,

distance_metric="euclidean")

hetero = c2g.gdf_to_pyg(

nodes_dict, bridge_edges,

node_feature_cols={cat: ["cx", "cy", "local_density"] for cat in CLASS_NAMES},

)

print("\nHeteroData node types:", hetero.node_types)

print("HeteroData edge types:")

for et in hetero.edge_types:

print(f" {et}: {hetero[et].edge_index.shape[1]} edges")

except Exception as e:

hetero = None

print("Heterogeneous build skipped:", e)

nodes, edges = c2g.knn_graph(poi_gdf, distance_metric="euclidean", k=8, as_nx=False)

deg = pd.Series(np.r_[edges.index.get_level_values(0),

edges.index.get_level_values(1)]).value_counts()

nodes["degree"] = deg.reindex(nodes.index).fillna(0).astype(float)

for col in ["cx", "cy", "local_density", "dist_street", "label"]:

if col not in nodes.columns:

nodes[col] = poi_gdf.loc[nodes.index, col].values

FEATS = ["cx", "cy", "local_density", "dist_street", "degree"]

nodes[FEATS] = StandardScaler().fit_transform(nodes[FEATS].astype(float))

data = c2g.gdf_to_pyg(nodes, edges, node_feature_cols=FEATS, node_label_cols=["label"])

data.edge_index = to_undirected(data.edge_index)

data.x = data.x.float()

y = data.y.long().view(-1)

N, num_classes = data.num_nodes, int(y.max()) + 1

print(f"\nHomogeneous Data: {N} nodes, {data.edge_index.shape[1]} directed-edges, "

f"{data.x.shape[1]} features, {num_classes} classes")

We construct a heterogeneous multi-layer graph by separating POIs into node types based on their urban function categories. We then use bridge edges to connect nearby nodes across different layers and convert the result into PyTorch Geometric HeteroData format. After that, we build a homogeneous KNN graph, attach degree and engineered features, standardize them, and prepare the final PyG Data object for GraphSAGE training.

Defining and Training a GraphSAGE Model for POI Classification

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perm = torch.randperm(N, generator=torch.Generator().manual_seed(SEED))

n_tr, n_va = int(0.6 * N), int(0.2 * N)

train_mask = torch.zeros(N, dtype=torch.bool); train_mask[perm[:n_tr]] = True

val_mask = torch.zeros(N, dtype=torch.bool); val_mask[perm[n_tr:n_tr + n_va]] = True

test_mask = torch.zeros(N, dtype=torch.bool); test_mask[perm[n_tr + n_va:]] = True

class GraphSAGE(torch.nn.Module):

def __init__(self, in_dim, hidden, out_dim, p=0.3):

super().__init__()

self.c1 = SAGEConv(in_dim, hidden)

self.c2 = SAGEConv(hidden, hidden)

self.lin = torch.nn.Linear(hidden, out_dim)

self.p = p

def forward(self, x, ei, return_emb=False):

h = F.relu(self.c1(x, ei))

h = F.dropout(h, p=self.p, training=self.training)

h = F.relu(self.c2(h, ei))

out = self.lin(h)

return (out, h) if return_emb else out

model = GraphSAGE(data.x.shape[1], 64, num_classes)

opt = torch.optim.Adam(model.parameters(), lr=0.01, weight_decay=5e-4)

def evaluate(mask):

model.eval()

with torch.no_grad():

pred = model(data.x, data.edge_index).argmax(1)

yt, yp = y[mask].numpy(), pred[mask].numpy()

return accuracy_score(yt, yp), f1_score(yt, yp, average="macro")

print("\n--- Training GraphSAGE ---")

best_val, best_state = 0.0, None

for epoch in range(1, 201):

model.train(); opt.zero_grad()

out = model(data.x, data.edge_index)

loss = F.cross_entropy(out[train_mask], y[train_mask])

loss.backward(); opt.step()

if epoch % 20 == 0:

va_acc, va_f1 = evaluate(val_mask)

if va_acc > best_val:

best_val, best_state = va_acc, {k: v.clone() for k, v in model.state_dict().items()}

print(f"epoch {epoch:3d} | loss {loss.item():.3f} | val_acc {va_acc:.3f} | val_f1 {va_f1:.3f}")

if best_state: model.load_state_dict(best_state)

te_acc, te_f1 = evaluate(test_mask)

print(f"\nTEST accuracy={te_acc:.3f} macro-F1={te_f1:.3f}")

We split the graph nodes into training, validation, and test masks so the model can learn and be evaluated properly. We define a two-layer GraphSAGE model that learns node representations from both node features and graph structure. We train the model for 200 epochs, monitor validation accuracy and macro-F1, save the best model state, and finally report test performance.

Visualizing Embeddings and Running a Heterogeneous GNN Forward Pass

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model.eval()

with torch.no_grad():

logits, emb = model(data.x, data.edge_index, return_emb=True)

pred = logits.argmax(1).numpy()

emb2d = PCA(n_components=2).fit_transform(emb.numpy())

fig, axes = plt.subplots(1, 2, figsize=(15, 6))

for cls in range(num_classes):

m = y.numpy() == cls

axes[0].scatter(emb2d[m, 0], emb2d[m, 1], s=10, label=CLASS_NAMES[cls], alpha=0.7)

axes[0].set_title("GraphSAGE node embeddings (PCA), coloured by TRUE class")

axes[0].legend(fontsize=8); axes[0].set_xticks([]); axes[0].set_yticks([])

plot_gdf = nodes.copy(); plot_gdf["pred"] = pred

plot_gdf["pred_name"] = [CLASS_NAMES[p] for p in pred]

plot_gdf.plot(ax=axes[1], column="pred_name", legend=True, markersize=12, cmap="tab10")

axes[1].set_title("Predicted urban function (mapped back to geography)")

axes[1].set_axis_off()

try:

import contextily as ctx

ctx.add_basemap(axes[1], crs=plot_gdf.crs, source=ctx.providers.CartoDB.Positron)

except Exception:

pass

plt.tight_layout(); plt.show()

if hetero is not None:

try:

for nt in hetero.node_types:

hetero[nt].x = hetero[nt].x.float()

class HGNN(torch.nn.Module):

def __init__(self, hid, out):

super().__init__()

self.c1 = SAGEConv((-1, -1), hid)

self.c2 = SAGEConv((-1, -1), out)

def forward(self, x, ei):

x = {k: F.relu(v) for k, v in self.c1(x, ei).items()}

return self.c2(x, ei)

hmodel = to_hetero(HGNN(32, 16), hetero.metadata(), aggr="sum")

out_dict = hmodel(hetero.x_dict, hetero.edge_index_dict)

print("\nHeterogeneous GNN output embedding shapes:")

for nt, t in out_dict.items():

print(f" {nt}: {tuple(t.shape)}")

except Exception as e:

print("Hetero GNN forward skipped:", e)

print("\nimage Done — proximity comparison, hetero construction, and a trained spatial GNN.")

We use the trained GraphSAGE model to extract node embeddings and predictions from the homogeneous graph. We reduce the learned embeddings with PCA and visualize them alongside a geographic prediction map to understand how the model separates urban functions. We also run a heterogeneous GNN forward pass with to_hetero, showing that the tutorial supports both homogeneous training and heterogeneous graph experimentation.

Key Takeaways

city2graph turns raw OpenStreetMap POI and street data into spatial graphs.

Six proximity graph families (KNN, Delaunay, Gabriel, RNG, EMST, Waxman) connect the same POIs differently.

A synthetic clustered fallback keeps the workflow runnable without OSM access.

A two-layer GraphSAGE model predicts urban function categories from spatial structure.

The pipeline supports both homogeneous training and heterogeneous graph experimentation via to_hetero.

Conclusion

In conclusion, we completed a full spatial GNN pipeline that transforms raw city data into graph-based learning and visualization. We compared several proximity graph methods, built a heterogeneous multi-layer graph, trained a homogeneous GraphSAGE classifier, and inspected the learned embeddings and geographic predictions. It gives us a practical understanding of how spatial relationships among POIs can be represented as graph structures and used to predict urban functions. It also shows how city2graph, GeoPandas, OSMnx, and PyTorch Geometric work together to support advanced geospatial machine learning experiments in a Colab-friendly setup.

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The post A Coding Implementation on Spatial Graph Neural Networks for Urban Function Inference Using city2graph, OSMnx, and PyTorch Geometric appeared first on MarkTechPost.