Exploring spatial patterns of immigrant settlement in Toronto using spatial Gaussian-Bernoulli DBN and GraphSAGE

Abstract

Traditional spatial analysis methods fail to capture the complex interactions shaping immigrant settlement patterns in metropolitan areas. This study introduces a novel deep learning framework combining Spatial Gaussian-Bernoulli DBN with GraphSAGE to analyze multi-ethnic settlement patterns. The proposed two-stage approach addresses GNN limitations with high-dimensional data by first extracting latent features through spatially constrained unsupervised learning, then applying graph-based prediction along street networks. Using Toronto data (2001–2021, 3,741 areas, 401 census features), the framework achieves exceptional accuracy for Iranian (R² = 0.953), Chinese (R² = 0.989), and Indian (R² = 0.987) communities—substantially outperforming traditional methods (R² = 0.382) and standard deep learning (R² = 0.885). The framework reveals three distinct settlement mechanisms: business-centered enclaves, education-transit corridors, and distributed multi-nuclear patterns. This study demonstrates that street network topology, not Euclidean distance, governs settlement diffusion, validating accessibility-based urban theory. Feature importance evolution shows how universal needs specialize into ethnic preferences—businesses for Iranians (0.15→0.30), education for Chinese (0.16→0.30), and growth dynamics for Indians (0.17→0.27). This interpretable, transferable framework establishes a new paradigm where domain knowledge amplifies machine learning for urban demographic modeling.

Introduction

Urban immigrant settlement patterns constitute complex spatial phenomena that fundamentally reshape metropolitan landscapes through intricate interactions between demographic flows, infrastructure networks, and socioeconomic dynamics. In major immigrant gateways like Toronto, where immigrants comprise nearly half of the metropolitan population (Statistics Canada, 2022), understanding these patterns has become critical for evidence-based urban planning, equitable resource allocation, and successful community integration policies (Drouhot and Nee, 2019; Kühn, 2021). The spatial concentration of immigrant communities influences housing markets, local economies, social service delivery, and community infrastructure development in ways that traditional analytical methods struggle to capture (Alba et al., 2000; Barajas, 2020). This complexity demands innovative approaches that can simultaneously model spatial dependencies, temporal dynamics, and the heterogeneous nature of urban data.

Recent advances in Graph Neural Networks (GNNs) have demonstrated transformative potential for analyzing complex spatial relationships across diverse geographical domains. Liu et al. (2020) successfully applied GraphSAGE to forecast traffic speeds in urban networks with sparse data, achieving significant improvements over traditional methods. Kong et al. (2025) combined morphological knowledge with graph neural networks for landform type recognition, achieving an F1-score of 87.40% and surpassing random forest and standard GCN methods by 5.24–12.50%. Similarly, Kong et al. (2024) achieved high accuracy in predicting building characteristics across diverse urban environments using graph-based approaches, while J. Wang et al. (2023) demonstrated over 80% accuracy in classifying urban functional zones by incorporating human mobility patterns. These successes highlight GNNs’ exceptional capability to capture spatial dependencies through explicit network structures that respect real-world connectivity patterns.

However, applying GNNs directly to immigrant settlement analysis faces a fundamental challenge: the high-dimensional, heterogeneous nature of census and urban infrastructure data. Unlike applications with well-defined, low-dimensional node features—such as traffic networks where nodes represent intersections with speed and flow attributes—settlement analysis requires processing hundreds of demographic, socioeconomic, and infrastructure variables that exhibit complex interdependencies. Standard GNNs assume that meaningful node features are readily available, but census data presents a different reality: 401-dimensional feature vectors containing disparate information ranging from age distributions and income levels to housing types and educational attainment. This dimensionality challenge is compounded by the need to capture temporal dynamics across multiple census periods (2001–2021) and integrate diverse data sources including immigration records, infrastructure databases, and ethnic business registries.

This critical gap motivates the proposed novel integration of Deep Belief Networks (DBNs) with GraphSAGE—a synergistic architecture that addresses the feature extraction challenge before applying graph-based analysis. DBNs have demonstrated exceptional capability in discovering hierarchical representations from complex urban data: Tan et al. (2016) successfully employed DBNs with Gaussian visible units for traffic flow prediction, while Y. Zhang et al. (2018) demonstrated their effectiveness in urban heat island analysis, highlighting their capacity to handle multi-dimensional spatial data. By introducing a Spatial Gaussian-Bernoulli DBN (SpatialDBN) that incorporates street network constraints directly into the energy function during unsupervised feature learning, we ensure that the extracted representations respect urban topology from the outset. This spatial constraint, implemented through network-based weights $S_{ij}=\mathit{exp}(-\frac{d_{ij}^{\mathit{2}}}{2{\gamma }^2})*A_{ij}$ where $A_{ij}$ represents street connectivity, fundamentally differs from traditional DBNs by enforcing that learned features maintain coherence among street-connected neighborhoods.

This study two-stage architecture represents a paradigm shift in settlement pattern analysis: the SpatialDBN first transforms the 401-dimensional census data into meaningful 64-dimensional representations that capture latent settlement patterns while respecting street network topology, then GraphSAGE leverages these learned features to perform settlement prediction through neighborhood aggregation along the same street network. This approach addresses multiple limitations simultaneously: (1) it handles the curse of dimensionality through hierarchical feature learning, (2) it incorporates urban infrastructure constraints at both feature extraction and prediction stages, (3) it captures both local and global spatial dependencies through the complementary strengths of DBNs and GNNs, and (4) it provides interpretable intermediate representations that reveal settlement preferences for different ethnic communities.

Using data from 3,741 Toronto dissemination areas connected through 12,150 street edges (2001–2021), proposed framework achieves exceptional accuracy: R² = 0.953 (Iranian), 0.989 (Chinese), and 0.987 (Indian)—substantially outperforming traditional methods (R² = 0.382) and standard deep learning (R² = 0.885)¹. Beyond quantitative improvements, the model reveals distinct settlement mechanisms: Iranian business clusters, Chinese education-transit corridors, and Indian multi-nuclear patterns, providing urban planners with actionable intelligence for inclusive city development.

Literature review

Evolution of settlement pattern analysis: From statistics to spatial intelligence

The analysis of immigrant settlement patterns has evolved from traditional spatial statistics using segregation indices (Poulsen et al., 2002; Walks and Bourne, 2006) and Moran’s I/LISA for identifying ethnic enclaves (Frank, 2003; Scardaccione et al., 2010), to machine learning approaches. However, these methods treated spatial units as independent entities, ignoring urban interconnectedness. Weber (2020) revealed their predictive limitations when conventional forecasting incorrectly predicted population decline in subsequently growing German municipalities.

Machine learning advanced the field but retained fundamental limitations. Weber (2020) achieved moderate success (R² > 0.5) for youth migration but struggled with family dynamics (R² = 0.25). Bogusz et al. (2024) improved accuracy using support vector regression for Warsaw suburbanization patterns. Copenhaver (2020) combined Random Forest with satellite imagery features, yet encountered systematic biases—overpredicting in commercial areas and underpredicting in dense settlements. These studies exposed a critical gap: treating spatial locations as isolated points ignores the network effects and spatial dependencies inherent in urban systems.

Graph neural networks: A paradigm shift in spatial analysis

The emergence of GNNs has revolutionized spatial analysis by explicitly modeling relationships between spatial entities. Recent applications demonstrate remarkable success across diverse geographical domains. In hydrology, Jia et al. (2021) developed physics-guided recurrent graph networks that achieved 33% improvement in streamflow prediction, while FloodGNN-GRU demonstrated 31% correlation improvement for flood forecasting by combining spatial graph convolutions with temporal dynamics (Kazadi et al., 2024). The computational efficiency gains are equally impressive, with GNN-based models providing predictions 100–1000 times faster than traditional physics-based models while maintaining reasonable accuracy.

Urban functional zone classification has witnessed particularly dramatic improvements through GNN applications. Ding et al. (2025) introduced a multi-temporal collaborative graph neural network model that achieved 8.5–16.1% accuracy improvements over traditional methods by incorporating dynamic human mobility patterns. The Marginalized Graph Autoencoder (MGAE) framework transforms Point of Interest data into geo-corpus representations while simultaneously processing remote sensing imagery, achieving 86.83% classification accuracy in Shenzhen’s Nanshan District (Yang et al., 2022). J. Wang et al. (2023) demonstrated that graph-based frameworks incorporating human mobility patterns could achieve over 80% accuracy in classifying urban functional zones, significantly outperforming methods that ignore spatial relationships.

Beyond urban environments, GNNs have transformed environmental and geological analysis. Kong et al. (2025) achieved an F1-score of 87.40% in landform type recognition by integrating morphological knowledge of contour data with graph neural networks, surpassing traditional methods by 5.24–12.50%. This work, published in the International Journal of Geographical Information Science, exemplifies how domain knowledge integration enhances GNN performance. The Multi-Scale Attention-based Graph Neural Network for Heavy Metal Prediction (MSA-GNN-HMP) achieved R² values of 0.841 for cadmium and 0.886 for lead prediction in the Pearl River Basin by constructing spatial graphs that consider parent material distribution and geographic relationships (Zha and Yang, 2024). Regional heatwave prediction using GNNs and weather station data demonstrated superior performance over grid-based methods by capturing non-local spatial dependencies (Li et al., 2023).

Deep learning architectures for urban feature extraction

While GNNs excel at modeling spatial relationships, they require meaningful node features as input—a challenge when dealing with high-dimensional, heterogeneous urban data. Deep Belief Networks (DBNs) have emerged as powerful tools for hierarchical feature extraction from complex urban datasets. Tan et al. (2016) successfully employed DBNs with Gaussian visible units for traffic flow prediction, demonstrating the model’s ability to extract meaningful patterns from multi-dimensional traffic data. Y. Zhang et al. (2018) further validated DBNs’ effectiveness in urban heat island analysis, achieving superior performance by maintaining spatial relationships while processing heterogeneous environmental variables.

The theoretical foundation of DBNs for spatial data lies in their ability to discover hierarchical representations through unsupervised learning. Unlike supervised methods that require labeled data for feature engineering, DBNs automatically discover latent patterns through layer-wise pretraining using Restricted Boltzmann Machines (RBMs). This capability proves particularly valuable for census data, where hundreds of variables interact in complex, non-linear ways. Recent advances have focused on incorporating spatial constraints: Dai et al. (2020) developed spatial regularization techniques for DBNs that preserve local spatial coherence during feature learning, while X. Wang et al. (2018) introduced attention mechanisms that weight features based on spatial proximity.

Hybrid architectures: Bridging feature learning and relational modeling

The integration of multiple deep learning architectures has emerged as a frontier in spatial analysis. A. Gao and Lin (2025) exemplifies this trend by combining CNN feature extraction with GNN neighborhood aggregation, achieving state-of-the-art spatial clustering performance with 10x parameter reduction. The success of hybrid models stems from their ability to leverage complementary strengths: CNNs excel at local feature extraction from grid-based data, RNNs capture temporal dependencies, while GNNs model explicit spatial relationships.

Recent innovations in spatio-temporal modeling demonstrate the power of architectural synergy. LSTM-GNN models for stock market prediction showed 10.6% MSE reduction by combining temporal dependency capture with inter-asset relationship modeling (Satishbhai Sonani, Badii and Moin, 2025). In traffic prediction, GCN-LSTM architectures model road network spatial dependencies through graph convolution while capturing historical speed changes through recurrent units, achieving superior performance over single-architecture approaches (Sharma et al., 2023). The Multi-Output Network combining GNN and CNN for remote sensing scene classification achieved over 90% accuracy while using significantly fewer parameters than pure CNN approaches (Peng et al., 2022).

Challenges in applying GNNs to high-dimensional heterogeneous data

Despite remarkable successes, standard GNNs face significant challenges when applied to settlement pattern analysis. The primary limitation concerns feature dimensionality: while traffic networks have well-defined node features (speed, flow, occupancy), census data presents hundreds of heterogeneous variables spanning demographics, economics, housing, and infrastructure. This challenge is compounded by data sparsity—immigrant populations often concentrate in specific areas, creating imbalanced datasets where most spatial units have zero or near-zero values for ethnic-specific variables.

Scalability emerges as another critical constraint. As noted in recent surveys (Sahili and Awad, 2023; Zhao et al., 2024), adjacency matrices scale quadratically with the number of spatial locations, rendering city-scale analysis computationally expensive. The heterogeneous nature of urban data poses additional challenges: standard GNNs assume homogeneous node types, but urban networks combine dissemination areas, infrastructure nodes, and service locations with fundamentally different characteristics. Multi-scale representation remains problematic as settlement patterns manifest differently at neighborhood, district, and city scales, requiring architectures that can capture patterns across spatial hierarchies simultaneously.

Research gaps and study contribution

Critical gaps persist in applying advanced deep learning architectures to immigrant settlement analysis. First, existing GNN applications in urban analysis typically assume well-defined, low-dimensional node features, whereas census data requires sophisticated feature extraction before graph-based processing. Second, while physics-informed GNNs have shown success in environmental applications (H. Gao et al., 2022; Ren et al., 2021), incorporating domain knowledge about urban infrastructure into settlement pattern analysis remains unexplored. Third, current methods fail to provide interpretable insights into settlement mechanisms—a crucial requirement for policy-relevant urban planning applications.

This study addresses these gaps through three key innovations: (1) This study introduces a spatially constrained DBN that discovers meaningful features from high-dimensional census data while respecting street network topology, solving the feature extraction challenge that limits direct GNN application; (2) We develop a unified framework where spatial constraints guide both unsupervised feature learning and supervised prediction, ensuring consistency throughout the modeling pipeline; and (3) We demonstrate that street network-based spatial relationships capture settlement dynamics more accurately than traditional distance-based or contiguity-based approaches, with proposed framework achieving R² scores exceeding 0.95 across different ethnic communities. By bridging the gap between hierarchical feature learning and graph-based spatial modeling, this study’s approach opens new possibilities for understanding complex urban demographic phenomena while providing actionable insights for evidence-based urban planning.

Methodology

Overview of the integrated framework

This study’s methodology consists of four interconnected components that transform raw census and urban infrastructure data into accurate settlement predictions (Figure 1). First, the data integration layer combines comprehensive census features (401 dimensions) from multiple time periods (2001–2021) with street network topology, creating a rich spatio-temporal representation of urban dynamics. Second, the preprocessing pipeline applies domain-specific transformations to four distinct feature categories—count features undergo logarithmic transformation to handle skewness, monetary features receive median imputation to address outliers, demographic features are normalized for scale consistency, and derived ratio features capture relative concentrations and temporal changes. This preprocessing ensures that heterogeneous urban data maintains its semantic meaning while achieving computational stability.

Figure 1.

Comprehensive framework of the proposed methodology.

Third, the Spatial Gaussian-Bernoulli DBN serves as an unsupervised feature extractor that discovers latent spatial patterns while respecting street network constraints. The architecture progressively reduces dimensionality from standardized input features through four hidden layers (256→128→96→64 units), with each layer incorporating spatial regularization that enforces consistency among street-connected areas. This novel spatial constraint, implemented through energy function modification (Equation (3)), ensures that learned representations reflect actual urban connectivity rather than arbitrary spatial proximity. Finally, the GraphSAGE model leverages the DBN’s extracted features to perform supervised settlement prediction through three layers of graph convolutions. The model aggregates information from street-connected neighborhoods using mean pooling, applies batch normalization for training stability, and incorporates dropout (p = 0.2) with gradient clipping to prevent overfitting. This two-stage architecture—unsupervised spatial feature learning followed by supervised graph-based prediction—enables the framework to capture both implicit settlement patterns and explicit infrastructure constraints.

Data sources and variable construction

The dataset encompasses 3,741 Toronto dissemination areas with 401 census features including demographics, housing, economics, education, and employment. Immigration variables track 46 origin countries, focusing on Iranian (dim_421), Chinese (dim_405), and Indian (dim_407) populations. Recent immigrant indicators (dims 456-497) distinguish established from emerging communities. Street network edges (12,150) encode actual urban connectivity rather than abstract proximity.

Spatial Gaussian-Bernoulli Deep Belief Network

The proposed model introduces a novel Spatial Gaussian-Bernoulli Deep Belief Network (SpatialDBN) that extends the traditional DBN architecture (Hinton et al., 2006; Hinton et al., 2006) by incorporating explicit spatial dependencies through urban street network connectivity. Building upon the Gaussian-Bernoulli RBM formulation (Cho et al., 2011), we develop a spatially aware variant specifically designed for urban pattern analysis (Figure 2 Panel A).

Figure 2.

Spatial DBN-GraphSAGE architecture for multi-ethnic settlement pattern analysis.

Drawing inspiration from spatial regularization techniques in deep learning (Jean et al., 2019; X. Wang et al., 2018; C. Zhang et al., 2019), we introduce several novel components to capture urban spatial relationships:

1. Street Network-Based Connectivity: Unlike traditional spatial models that rely on Euclidean distances, this study proposes a connectivity measure based on street network infrastructure. The adjacency relationship between two Dissemination Areas (DAs) is defined as:

$A_{ij}=\{\begin{array}{l}1\hspace{0.17em}if\hspace{0.17em}{DA}_i\cap {DA}_j\hspace{0.17em}shares\hspace{0.17em}a\hspace{0.17em}street\hspace{0.17em}segment\\ 0\hspace{0.17em}otherwise\end{array}$

(1)

• 2. Network-Constrained Spatial Weights: This study introduces a novel spatial weight computation that incorporates both network distance and connectivity:

$S_{ij}=\mathit{exp}\left(-\frac{d_{ij}^2}{2{\gamma }^2}\right)*\hspace{0.17em}{A}_{ij}$

(2)

where d_ij represents the shortest path distance through the street network between DA centroids and γ is a learnable bandwidth parameter. This formulation represents key contribution in adapting spatial relationships to urban infrastructure.

3. Spatially Aware Energy Function: This study extends the traditional GBRBM energy function by incorporating street network-based spatial structure:

$E\left(v,h,s\right)=-{\sum }_{ij}\frac{v_i{W}_{ij}{h}_j}{{\sigma }_i^2}-{\sum }_i\frac{{\left(v_i-b_i\right)}^2}{2{\sigma }_i^2}-{\sum }_j{c}_j{h}_j+\alpha {\sum }_{ij}{S}_{ij}{\left|\left|h_i-h_j\right|\right|}^2$

(3)

• 4. Network-Aware Spatial Attention: This study proposes a novel attention mechanism that respects street network connectivity:

${h\prime }_i=\left(1-\alpha \right)h_i+\alpha \left(A_i\circ {\sum }_j\in N\left(i\right)S_{ij}{h}_j\right)$

(4)

where N(i) represents the set of DAs connected to DA_i through the street network.

• 5. Street Network-Constrained Loss Function: This model introduces a specialized loss function that combines reconstruction accuracy with spatial consistency:

$L=Lrecon+\lambda Lspatial$

(5)

where $Lspatial={\sum }_{ij}{S}_{ij}{\left|\left|h_i-h_j\right|\right|}^2\hspace{0.17em}*\hspace{0.17em}{A}_{ij}$ enforces consistency between street-connected areas.

This novel architecture represents several key contributions to the field: (1) the integration of street network topology into deep belief networks, (2) a spatially aware energy function that respects urban infrastructure, and (3) a network-constrained regularization scheme that ensures learned representations align with actual urban connectivity patterns. These modifications enable the model to capture complex spatial dependencies in urban settlement patterns while maintaining the probabilistic learning capabilities of traditional DBNs.

GraphSAGE for settlement density prediction

The output features from the Spatial DBN were integrated into a graph structure where each Dissemination Area (DA) represents a node in the graph (Figure 2 Panel B). The graph preparation involved three components: node features (X ∈ ℝⁿ×^d) derived from the DBN’s 64-dimensional learned representations, edge connections (E ∈ ℤ²×^m) based on street network connectivity, and target variables representing ethnicity population density.

The edge structure encodes street network connectivity as:

$E=\left[\left[sourc{e}^1,sourc{e}^2,...,{source}^m\right],\left[targe{t}^1,targe{t}^2,...,{target}^m\right]\right]$

(6)

The target variable (y) for each node was computed as ethnicity population density:

$y_i=\{\begin{array}{l}\frac{{Ethnicit{y}_{Population}}_i}{{Tota{l}_{Population}}_i},if\hspace{0.17em}{Tota{l}_{Population}}_i\hspace{0.17em}>\hspace{0.17em}0\\ 0,otherwise\end{array}$

(7)

where i represents each DA. This normalized measure provides a standardized representation of ethnicity settlement patterns across DAs of varying sizes.

The final graph structure G = (X, E, y) was then partitioned into training (70%), validation (15%), and test (15%) sets using stratified sampling to ensure representative distribution of settlement patterns across all sets. The data was organized using PyTorch Geometric’s Data class, creating a cohesive graph structure that preserves both the spatial relationships and feature representations while maintaining the supervised learning framework for settlement pattern analysis.

Building upon the foundational GraphSAGE architecture introduced by Hamilton et al. (2017), this study developed a specialized variant, EthnicitySettlementSAGE, specifically designed for analyzing urban settlement patterns. The EthnicitySettlementSAGE architecture employs mean aggregation across three graph convolutional layers to capture multi-scale neighborhood effects along street networks. For each layer l, the aggregation operation combines a node’s own features with the mean of its street-connected neighbors:

$h_v^l=BN\left(\sigma \left(W_l\hspace{0.17em}·\hspace{0.17em}CONCAT\left(h_v^{l-1},\text{MEAN}\left(\left\{h_u^{l-1}:u\in N\left(v\right)\right\}\right)\right)\right)\right)$

(8)

where BN denotes batch normalization, σ is the ReLU activation function, MEAN computes the average of neighbor features, and N(v) represents the set of DAs connected to DA_v through the street network. This mean aggregation strategy ensures equal weighting of all street-connected neighbors, reflecting the assumption that accessibility through any connecting street segment contributes equally to settlement diffusion patterns.

The three-layer architecture (input → 256 → 256 → 256 dimensions) progressively expands the receptive field: Layer 1 aggregates immediate street neighbors (1-hop), Layer 2 captures 2-hop neighborhoods, and Layer 3 extends to 3-hop connectivity. This hierarchical aggregation enables the model to capture both local settlement clusters and broader metropolitan-scale patterns simultaneously.

The output transformation projects the final graph representations to settlement density predictions through a multi-layer perceptron:

${h\hspace{0.17em}}_{out}=MLP\left(h_v^L\right)=W_3·\hspace{0.17em}\sigma \left(BN\left(W_2\hspace{0.17em}·\hspace{0.17em}\sigma \left(BN\left(W_1\hspace{0.17em}·\hspace{0.17em}{h}_v^L+b_1\right)\right)+b_2\right)\right)+b_3$

(9)

where dropout (p = 0.2) is applied between layers to prevent overfitting.

The model predicts normalized ethnicity settlement density with robust outlier handling:

${\rho }_i=\mathit{min}\left(\frac{{{Ethnicity}_{Population}}_i}{\mathit{max}\left({Tota{l}_{Population}}_i,1\right)},q_{99}\right)$

(10)

where q₉₉ represents the 99th percentile of the density distribution, used for robust outlier handling. The final normalized density is obtained through min-max scaling:

${\widehat{\rho }}_i=\frac{{\rho }_i}{\mathit{max}\left(\left\{{\rho }_j:j\in V\right\}\right)}$

(11)

The model is trained using mean squared error loss with AdamW optimizer (weight decay λ = 1e-4), adaptive learning rate scheduling (ReduceLROnPlateau with factor 0.2, patience 5 epochs), and gradient clipping (max norm 0.5) for training stability. The final graph structure G = (X, E, y) was partitioned into training (70%), validation (15%), and test (15%) sets using stratified sampling to ensure representative distribution of settlement patterns. Implementation utilized PyTorch 2.1.0 and PyTorch Geometric on NVIDIA L4 GPUs.

Result

Spatial DBN feature extraction and pattern discovery

The Spatial Gaussian-Bernoulli DBN demonstrates remarkable capability in extracting hierarchical features capturing urban settlement interplay. Figure 3(A) reveals progressive spatial refinement through network layers, with spatial coherence increasing from 0.3 to 0.88 and 85% noise reduction, validating spatially aware energy function’s effectiveness in enforcing neighborhood consistency while preserving settlement signals.

Figure 3.

Spatial Gaussian-Bernoulli DBN reveals hierarchical settlement patterns through street network constraints.

The model’s ability to detect spatial dependencies surpasses conventional methods across all feature types (Figure 3(B)). The Spatial DBN consistently achieves Moran’s I values 0.2–0.4 points higher than traditional approaches, with the most substantial improvements observed for business-related features (Iranian) and educational infrastructure (Chinese). This enhancement stems from the network-constrained spatial weights (S_ij) that capture true urban connectivity rather than assuming Euclidean relationships. Street network integration proves particularly powerful for Chinese housing patterns, where spatial autocorrelation increases from 0.58 to 0.85, suggesting settlement decisions follow transportation corridors.

Perhaps most significantly, the DBN uncovers distinct hidden patterns in the learned representations that correspond to ethnic-specific settlement preferences (Figure 3(C)–(E)). The Iranian community exhibits business cluster formations in the hidden space, with two distinct concentrations emerging in the 64-dimensional representation. Chinese settlement patterns reveal education-housing coupling, where the hidden features form a clear corridor structure aligned with school accessibility. Indian communities demonstrate a unique multi-nuclear pattern with three distinct settlement cores, suggesting preference for distributed community centers rather than single ethnic enclaves. These patterns, invisible in the raw 401-dimensional input space, emerge through the DBN’s ability to learn non-linear transformations guided by spatial constraints.

Street network-based weights yield 20% average improvement over Euclidean approaches (Figure 3(F)), with Iranian predictions improving most dramatically (R² from 0.79 to 0.95). This validates that urban connectivity, not straight-line distance, governs settlement decisions. The discovered spatial clusters (Figure 3(G)–I) reveal fundamentally different settlement strategies across ethnic groups. Iranian clusters concentrate around business hubs in specific neighborhoods, forming tight, well-defined communities. Chinese settlements follow transit corridors, creating linear patterns that maximize access to educational facilities and public transportation. Indian communities exhibit a multi-nuclear structure with several medium-sized clusters rather than single large concentrations, suggesting a balance between community cohesion and integration with the broader urban fabric. These patterns, automatically discovered through unsupervised learning in the DBN’s hidden layers, align with sociological observations while providing quantitative validation.

The evolution of feature importance through the DBN layers (Figure 3(J)) demonstrates how the network progressively refines its understanding of settlement drivers. Initial layers treat all features relatively equally, but deeper layers amplify ethnic-specific preferences: business importance for Iranians increases from 0.15 to 0.30, education for Chinese rises from 0.16 to 0.30, and growth rate for Indians jumps from 0.17 to 0.27. This refinement process, guided by the spatial regularization term $\alpha \sum S\_ij{\Vert h\_i-h\_j\Vert }^{\mathit{2}},$ ensures that feature importance reflects not just statistical correlation but spatially coherent patterns. The opacity gradient in the visualization effectively illustrates how deeper layers crystallize these ethnic-specific preferences while maintaining spatial consistency across neighboring areas.

Settlement pattern by GraphSAGE

The integration of street network topology into GraphSAGE architecture represents a fundamental paradigm shift in modeling immigrant settlement patterns. Unlike conventional spatial autocorrelation methods that assume isotropic relationships, this study’s approach leverages the heterogeneous connectivity of Toronto’s urban infrastructure, where 3,741 dissemination areas are connected through 12,150 street-based edges with an average degree of 6.5 (Figure 4). This street-constrained graph structure captures the reality that settlement decisions propagate along transportation corridors and existing community networks rather than radiating uniformly through geographic space. The emergence of high-degree nodes as settlement hubs—with some areas maintaining up to 22 direct street connections—reveals critical urban junctions that act as information conduits for ethnic community formation. This topological insight, impossible to capture through traditional distance-based or contiguity-based models, explains why this model achieves substantially higher predictive accuracy (R² = 0.953) compared to conventional approaches that ignore the underlying urban fabric.

Figure 4.

Street network topology underlying the GraphSAGE architecture for immigrant settlement prediction.

The multi-scale aggregation mechanism through GraphSAGE introduces a novel conceptualization of how settlement information diffuses through urban networks. By implementing hierarchical message passing that respects street connectivity constraints, the model learns to weight neighborhood influences based on actual accessibility rather than Euclidean proximity (Figure 5). The aggregation function $h^{\prime }=\sigma \left(W·CONCAT\left(h,MEAN\left(\left\{h\_neighbors\right\}\right)\right)\right)$ operating on street-connected neighbors captures both direct influences from immediately accessible areas and indirect effects from 2-hop neighborhoods, mirroring how immigrant communities expand through word-of-mouth and social networks that follow transportation routes. This approach reveals that settlement patterns exhibit strong anisotropic characteristics—Iranian communities, for instance, show preferential expansion along specific transit corridors rather than uniform spatial diffusion. The ability to capture these directed flows through proposed graph-based architecture explains the model’s superior performance across all ethnic groups, as it aligns with the fundamental mechanisms of urban settlement: accessibility, community networks, and infrastructure-mediated social interactions.

Figure 5.

Multi-scale neighborhood aggregation mechanism in GraphSAGE for settlement pattern analysis.

The spatial predictions generated by proposed Spatial DBN + GraphSAGE framework reveal fundamentally distinct settlement strategies across ethnic communities, validating the exceptional quantitative performance metrics through qualitative pattern recognition (Figure 6, Panel A). The model successfully captures the polycentric nature of Iranian settlements, which manifest as discrete high-concentration clusters in North York and Richmond Hill with minimal spatial spillover—a pattern consistent with business-hub formation identified in DBN feature analysis. In contrast, Chinese settlements exhibit a more diffuse pattern with broader spatial coverage (1,827 settlement areas vs 724 for Iranians), creating continuous corridors of moderate concentration that align with educational infrastructure and transit networks. Indian settlements demonstrate an intermediate pattern with 1,707 active areas, forming multiple medium-density clusters that balance community cohesion with metropolitan integration. These divergent spatial configurations, accurately predicted by the model, explain why traditional regression approaches fail: each ethnic group follows unique settlement logics that require the adaptive learning capacity of graph neural networks to capture.

Figure 6.

Predicted immigrant settlement patterns and concentration distributions generated by the Spatial DBN + GraphSAGE framework.

The distribution analysis provides crucial validation of model’s ability to distinguish between concentration and dispersion dynamics, revealing why the achieved R² scores (0.953–0.989) represent genuine predictive power rather than overfitting (Figure 6, Panel B). Iranian settlements show a heavily right-skewed distribution with 90% of areas below 0.183 relative concentration, indicating a preference for intense clustering in select locations—a pattern street network-constrained model captures through high-degree node aggregation. Chinese settlements display a more gradual decay (90th percentile at 0.169) with substantial mid-range concentrations, reflecting their tendency to form extended community networks along transportation corridors. Indian settlements exhibit the most balanced distribution (median 0.030, 90th percentile 0.126), suggesting a dual strategy of maintaining cultural centers while achieving broader residential integration. This quantitative confirmation of qualitatively distinct settlement patterns demonstrates that proposed framework transcends simple density prediction to capture the underlying socio-spatial mechanisms of immigrant community formation. The model’s ability to simultaneously achieve high predictive accuracy while preserving these nuanced distributional characteristics validates initial hypothesis that street network topology, rather than abstract spatial proximity, governs urban settlement dynamics.

The performance of the proposed framework represents a fundamental advancement validated through comprehensive ablation studies and baseline comparisons (Supplementary Material S3.3-S3.4). Ablation experiments demonstrate that each component is essential: removing spatial constraints reduces performance by 37–78%, eliminating DBN feature extraction decreases accuracy by 15–20%, and replacing GraphSAGE with standard architectures causes complete failure (negative R²). Comparative evaluation against five baseline methods confirms superiority: while ensemble methods (XGBoost: R² = 0.927, Random Forest: R² = 0.905) show reasonable performance, they cannot match graph-based approaches explicitly modeling spatial dependencies, with performance gaps of 2.8–30.7%. Traditional approaches perform substantially worse (GWR: R² = 0.514–0.691, MLP: R² = 0.050–0.393), and even standard GCN fails catastrophically (R² = −1.79 to −7.28), confirming that successful spatial demographic modeling requires specifically the integration of spatially constrained feature learning with appropriate aggregation mechanisms.

Discussion

This study findings establish a new theoretical foundation for understanding immigrant settlement patterns through the lens of graph-based deep learning. The exceptional performance achieved across three distinct ethnic communities (R² = 0.953–0.989) transcends mere predictive accuracy to reveal fundamental principles governing urban demographic dynamics. The synergistic integration of Spatial DBN with GraphSAGE addresses a critical gap identified in recent literature: while GNNs excel at modeling spatial relationships, they assume well-defined node features—an assumption violated by the high-dimensional, heterogeneous nature of census data (Sahili and Awad, 2023; Zhao et al., 2024). Proposed two-stage architecture resolves this paradox by first discovering latent spatial patterns through constrained feature learning, then leveraging these representations for graph-based prediction.

The framework reveals three fundamental settlement strategies emerging through unsupervised discovery: enclave formation (Iranian business clusters), corridor development (Chinese education-transit alignments), and distributed integration (Indian multi-nuclear patterns). Feature importance evolution (Figure 3(J)) shows how universal needs progressively specialize into ethnic preferences—businesses for Iranians (0.15→0.30), education for Chinese (0.16→0.30), and growth dynamics for Indians (0.17→0.27). Transferability stems from modular architecture enabling: (1) universal graph construction from any digitized street network, (2) flexible feature extraction adaptable to local census variables, and (3) transfer learning reducing data requirements by 60–70%. These positions proposed framework as a calibratable methodology rather than a universal solution. For urban planning, the framework enables real-time scenario analysis (inference <0.5 seconds) and “what-if” evaluations. High-degree nodes identified as settlement hubs (Figure 4) suggest strategic infrastructure investment points. Understanding corridor versus enclave patterns directly informs housing policy and service allocation.

We acknowledge key limitations: data availability bias toward established communities, temporal lag in infrastructure responses, absence of policy variables like zoning, and aggregation masking household-level decisions. Performance may degrade for emerging groups or cities with different urban forms. These define boundary conditions rather than invalidating the approach.

The successful integration of unsupervised feature learning with supervised graph prediction offers a template for analyzing complex urban phenomena requiring both dimensionality reduction and spatial relationship preservation—demonstrating that sophisticated architectures need not sacrifice interpretability for accuracy.

Conclusion

This study presents a generalizable spatial deep learning framework combining Spatial Gaussian-Bernoulli DBN with GraphSAGE to analyze multi-ethnic settlement patterns. This study approach transforms 401-dimensional census data while respecting urban spatial relationships, achieving exceptional accuracy across Iranian (R² = 0.953), Chinese (R² = 0.989), and Indian (R² = 0.987) communities. Key innovations include hierarchical feature learning preserving spatial patterns, street network-based constraints capturing actual connectivity, and interpretable representations revealing distinct mechanisms—from business enclaves to education corridors to multi-nuclear distributions.

The framework’s modular architecture enables transferability across urban contexts, with transfer learning reducing data requirements by 60–70%. Combined with computational efficiency (inference <0.5 seconds), this makes proposed approach valuable for diverse cities monitoring demographic evolution. Future research should explore dynamic graph architectures for temporal evolution, multi-modal data fusion, and comparative cross-city studies. As cities face unprecedented migration flows, proposed framework provides theoretical insights and practical tools for evidence-based planning, demonstrating how domain knowledge amplifies machine learning for understanding complex social phenomena.

Supplemental material

Supplemental material - Exploring spatial patterns of immigrant settlement in Toronto using spatial Gaussian-Bernoulli DBN and GraphSAGE

Supplemental material for Exploring spatial patterns of immigrant settlement in Toronto using spatial Gaussian-Bernoulli DBN and GraphSAGE by Seyed Navid Mashhadi Moghaddam and Huhua Cao in Environment and Planning B: Urban Analytics and City Science.