Heterogeneous Multi-View Graph Masked Autoencoders

• The paper introduces STGMAE, a generative framework that leverages masked autoencoding and heterogeneous multi-view graph construction to learn robust spatio-temporal representations.
• It employs relation-aware GCN encoding to integrate diverse urban features, achieving lower prediction errors in tasks such as crime forecasting and traffic analysis.
• The model’s design, including node and edge masking with self-supervision, ensures efficient reconstruction and robustness against noise and label sparsity.

A Heterogeneous Multi-View Graph Masked Autoencoder (STGMAE) is an unsupervised generative framework for learning robust, contextually informed representations from spatio-temporal graph data characterized by multiple relational modalities, noise, and label sparsity. Designed for urban sensing tasks such as crime prediction, mobility forecasting, and house price estimation, STGMAE integrates heterogeneous multi-view graph construction, relation-aware graph convolutional encoding, and masked autoencoding principles to distill diverse spatial dependencies and augment temporal learning via self-supervision (Zhang et al., 2024).

1. Heterogeneous Spatio-Temporal Graph Construction

STGMAE employs an urban-region partitioning scheme, mapping a metropolitan area to a set of $I$ non-overlapping spatial regions $\{r_i\}_{i=1}^I$. The node set $V$ of the associated graph consists of these regions. Multi-view feature matrices $X^{(m)}$ are established to capture diverse urban attributes:

• POI View: $P \in \mathbb{R}^{I \times C}$, where $P_{i,c}$ records the count or TF–IDF of POIs of type $c$ in region $i$.
• Mobility View: $M \in \mathbb{R}^{I \times I}$, with $M_{i,j}$ representing aggregated people/taxi flows from $\{r_i\}_{i=1}^I$0 to $\{r_i\}_{i=1}^I$1 over time.
• Distance View: $\{r_i\}_{i=1}^I$2, given by pairwise centroidal geographical distances.

Heterogeneous edge relations are formalized:

Relation Symbol	Description	Edge Criterion
$\{r_i\}_{i=1}^I$3	POI-similarity	similarity$\{r_i\}_{i=1}^I$4
$\{r_i\}_{i=1}^I$5	Mobility link	$\{r_i\}_{i=1}^I$6 (weighted by flow)
$\{r_i\}_{i=1}^I$7	Distance proximity	$\{r_i\}_{i=1}^I$8
$\{r_i\}_{i=1}^I$9	Cross POI-mobility	link POI and mobility nodes
$V$0	Cross mob.-distance	link mobility and distance nodes

The overall adjacency is $V$1. This heterogeneous, multi-view schema is foundational for modeling diverse inter-region dependencies and cross-view dynamics.

2. Relation-Aware Spatio-Temporal Graph Neural Encoding

Encoding proceeds with a relation-sensitive message-passing scheme. For each GCN layer $V$2 and node $V$3:

$V$4

where $V$5 are neighbors under relation $V$6, $V$7 normalizes each relation, $V$8 are learnable weights, and $V$9ReLU.

To capture multi-order structural dependency, $X^{(m)}$0 stacked layers are summed:

$X^{(m)}$1

The encoder input $X^{(m)}$2 is constructed with a Skip-gram + MLP pipeline on $X^{(m)}$3, followed by region-wise multi-head self-attention:

$X^{(m)}$4

Temporal dependencies manifest through $X^{(m)}$5 (which is temporally aggregated) and stacking multi-day/-week snapshots; no explicit sequential modules (e.g., 1D Conv, Transformer) are deployed.

3. Masked Autoencoding: Node and Edge Denoising

STGMAE implements masking in both feature and structure domains to induce robust and non-trivial representations. A random subset $X^{(m)}$6 is selected at a masking ratio $X^{(m)}$7 (empirically optimal at 0.7):

• Node Feature Masking: For $X^{(m)}$8, $X^{(m)}$9 (learnable mask token).
• Edge Masking: Rows/columns in adjacency are replaced by $P \in \mathbb{R}^{I \times C}$0 (learnable), simulating missing edges.

The encoder operates on the masked $P \in \mathbb{R}^{I \times C}$1. Post-encoding, the hidden representation $P \in \mathbb{R}^{I \times C}$2 is again remasked:

$P \in \mathbb{R}^{I \times C}$3

A mirrored GCN decoder $P \in \mathbb{R}^{I \times C}$4 reconstructs node features $P \in \mathbb{R}^{I \times C}$5 and structure $P \in \mathbb{R}^{I \times C}$6. Optimization is driven by the reconstruction objective:

$P \in \mathbb{R}^{I \times C}$7

$P \in \mathbb{R}^{I \times C}$8

$P \in \mathbb{R}^{I \times C}$9

This design compels the model to "denoise"—reconstructing masked nodes/edges from local and relational context.

4. Encoder-Decoder Implementation, Training, and Hyperparameters

The overall autoencoding pipeline comprises symmetric stacks of L relation-aware GCNs for both encoding ($P_{i,c}$0) and decoding ($P_{i,c}$1). Parameter learning is performed over $P_{i,c}$2–$P_{i,c}$3 epochs with Adam (learning rate $P_{i,c}$4, weight decay $P_{i,c}$5), mini-batch masking (sample $P_{i,c}$6 nodes per batch), mask ratio $P_{i,c}$7, $P_{i,c}$8 GCN layers. Increasing $P_{i,c}$9 beyond $c$0 incurs over-smoothing and was found suboptimal.

Pre-training is fully generative; downstream fine-tuning leverages embeddings $c$1 for supervised tasks without retraining the encoder-decoder.

5. Robustness, Self-Supervision, and Ablation Findings

Masked autoencoding enforces resistance to data noise and label sparsity; masking disables trivial copying, compelling reconstruction from relational context. The design enables effective pre-training in unsupervised regimes—region representations emerge purely via graph reconstruction, independent of application-specific labels.

Ablation experiments confirmed:

• GCN encoders/decoders are necessary; replacing with MLP ("RP GCN") significantly degrades accuracy.
• Both node- and edge-masking are essential for optimal performance.
• Explicit edge-type masking further enhances performance, demonstrating the utility of modeling heterogeneous relations.

This suggests that generative denoising with multi-relation GCNs directly contributes to the robustness and efficacy of learned features in noisy, sparse, and heterogeneous urban data.

6. Empirical Evaluation and Results

Experiments were conducted on Chicago and NYC datasets:

Dataset	Regions	POIs	Tasks
Chicago	234	3.7M	Crime, taxi flow, house prices
Manhattan	180	20K	Crime, bike flow, house prices

Tasks included:

• Crime prediction: MAE, MAPE (against ST-SHN backbone)
• Traffic forecasting: MAE, RMSE (with ST-GCN backbone)
• House price prediction: MAE, MAPE (via Lasso on embeddings)

Benchmarked against baselines (Node2vec, GCN, GAT, GraphSage, GraphCL, RGCL, POI, HDGE, ZE-Mob, MV-PN, CGAL, MVURE, AutoST, MGFN), STGMAE attained lowest errors across all tasks:

• NYC crime MAE: $c$2 (AutoST: $c$3)
• Chicago taxi MAE: $c$4 (GCN: $c$5)
• NYC house price MAE: $c$6 (best baseline: $c$7)

Statistical significance: $c$8.

Efficiency: masking ratio $c$9 and 2-layer GCN yielded best results; training time ($i$0s) was notably lower relative to MGFN ($i$1s) and CGAL ($i$2s).

7. Applications and Implications

STGMAE supports spatio-temporal mining in urban domains under noise and label limitations. Its generative self-supervised design and explicit multi-view relational modeling make it broadly applicable to urban informatics and spatio-temporal data mining, facilitating transfer and fine-tuning of robust embeddings for diverse downstream analyses (Zhang et al., 2024). A plausible implication is that similar masked autoencoder paradigms could be generalized to other heterogeneous spatio-temporal systems, augmenting self-supervised representation learning beyond the urban context.