PSIRAGCN: Pattern-Spatial GCN for Traffic Forecasting

• PSIRAGCN is a spatio-temporal graph neural network that leverages K-means based pattern recognition and regional-aware convolution to model both global traffic regimes and local spatial dependencies.
• It combines efficient 1D CNNs (PEConv) and a Regional Awareness GCN to integrate dual-mode traffic patterns with region-specific message passing for improved forecasting accuracy.
• The architecture employs an encoder–decoder structure with multi-head self-attention and GRU to capture temporal dependencies while balancing computational cost on real-world highway data.

PSIRAGCN, short for Pattern-Spatial Interactive and Regional Awareness Graph Convolutional Network, is a spatio-temporal graph neural network designed specifically for traffic forecasting on sensor networks and road segments. It was introduced to address three deficits identified in prior spatial-temporal GNNs for traffic prediction: insufficient pattern-level modeling across perspectives, lack of interactive fusion between traffic patterns and spatial correlations, and neglect of regional heterogeneity during message-passing. Its central design combines a pattern-spatial interactive fusion framework with a Regional Awareness GCN (RAGCN), with the stated aim of capturing dependencies from global traffic regimes to local spatial propagation while maintaining balanced computational cost on real-world highway traffic datasets (Ji et al., 30 Aug 2025).

1. Problem setting and motivation

PSIRAGCN formulates traffic forecasting on an undirected graph

$$\boldsymbol{G} = (\boldsymbol{V}, \boldsymbol{E}, \mathbf{A}),$$

where $|\boldsymbol{V}| = N$ denotes the number of nodes and $\mathbf{A} \in \mathbb{R}^{N \times N}$ is the adjacency matrix. At time $t$, the traffic signal is written as

$\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$

and the forecasting task maps a historical sequence of length $T$,

$$\mathcal{X} = [\boldsymbol{X}^{(t-T+1)}, \ldots, \boldsymbol{X}^{(t)}],$$

to a future sequence of length $T'$,

$$Y = [\boldsymbol{Y}^{(t+1)}, \ldots, \boldsymbol{Y}^{(t+T')}].$$

In the reported experiments, the model performs multistep forecasting from the past 6 time steps to the next 6 time steps, with each step corresponding to 5 minutes (Ji et al., 30 Aug 2025).

The motivation is organized around three gaps. First, existing models are described as either coarse-grained—sequentially or in parallel applying temporal and spatial modules over the entire input sequence—or fine-grained—embedding GCNs into RNNs or vice versa per time step. The former can mix useful and noisy signals and ignore global traffic patterns, while the latter preserves local coupling but loses global pattern awareness such as daily peaks and trends. Second, prior methods typically learn temporal or pattern features and spatial features separately and fuse them once, for example by concatenation or summation, rather than allowing iterative mutual utilization with positive feedback. Third, dynamic graph methods are said to assume node homogeneity apart from traffic values, despite the practical importance of regional differences such as residential, CBD, or industrial structure, road type, width, POIs, and connectivity.

Within this framing, PSIRAGCN treats traffic forecasting not only as a spatial-temporal dependency problem but also as a regime-sensitive and region-sensitive propagation problem. This suggests a shift away from purely adjacency-centric spatial modeling toward graph learning that is conditioned by both traffic patterns and node-specific regional characteristics.

2. Architectural organization

PSIRAGCN follows an encoder–decoder structure with three principal stages: a Pattern-Spatial Interaction (PSI) Encoder, a Temporal Encoder, and a Decoder (Ji et al., 30 Aug 2025).

The PSI encoder takes the raw traffic sequence

$\mathcal{X} \in \mathbb{R}^{C \times N \times T}$

and comprises four components: K-means-based pattern recognition, pattern modules denoted PEConv, a spatial module denoted RAGCN, and an interactive fusion mechanism. Pattern recognition divides the sequence into two pattern subsequences, $|\boldsymbol{V}| = N$0 and $|\boldsymbol{V}| = N$1, corresponding to peak and off-peak modes. PEConv extracts temporal pattern features separately from these subsequences, while RAGCN operates on the full sequence to model regional-aware spatial correlations. Their fusion yields a pattern-spatial representation $|\boldsymbol{V}| = N$2, typically combined with the original input through a residual connection.

The temporal encoder then processes $|\boldsymbol{V}| = N$3 with Multi-Head Self-Attention (MHSelfAttention) to model global temporal dependencies and a GRU cell to refine temporal sequence features. The output is a sequence embedding denoted $|\boldsymbol{V}| = N$4. This arrangement places global temporal dependency modeling after pattern-spatial fusion rather than before it, so the temporal encoder operates on features that already encode both regime structure and regional-aware graph interactions.

The decoder integrates three streams:

$|\boldsymbol{V}| = N$5

It uses another RAGCN on the input $|\boldsymbol{V}| = N$6 with regional-aware adjacency $|\boldsymbol{V}| = N$7, a 1D convolution over $|\boldsymbol{V}| = N$8, and a fully connected output layer with $|\boldsymbol{V}| = N$9 activation. The decoder is explicitly non-autoregressive, directly outputting all future steps for all nodes rather than rolling predictions forward step by step.

A notable architectural implication is that PSIRAGCN does not isolate spatial modeling in a single encoder block. Spatial encoding reappears in the decoder, which indicates that regional-aware message passing functions both as a representation learner and as a prediction-time refinement operator.

3. Pattern-spatial interactive fusion

The PSI mechanism is the defining feature of PSIRAGCN. It is designed to capture traffic patterns and spatial correlations from a global to local perspective and to facilitate mutual utilization with positive feedback (Ji et al., 30 Aug 2025).

Pattern recognition

Traffic sequences are treated as multivariate time series with clear daily patterns. K-means clustering divides samples into $\mathbf{A} \in \mathbb{R}^{N \times N}$0 clusters $\mathbf{A} \in \mathbb{R}^{N \times N}$1, with centroid

$\mathbf{A} \in \mathbb{R}^{N \times N}$2

and objective

$\mathbf{A} \in \mathbb{R}^{N \times N}$3

The number of clusters is selected using the silhouette coefficient. Empirically, the average silhouette peaks at $\mathbf{A} \in \mathbb{R}^{N \times N}$4 across PEMS04, PEMS07, and PEMS08, so PSIRAGCN uses two patterns: $\mathbf{A} \in \mathbb{R}^{N \times N}$5 for high flow and $\mathbf{A} \in \mathbb{R}^{N \times N}$6 for low flow. These two modes are described as preserving periodicity and trend.

Pattern extraction convolution

For each pattern $\mathbf{A} \in \mathbb{R}^{N \times N}$7, where $\mathbf{A} \in \mathbb{R}^{N \times N}$8, the model applies a two-layer 1D CNN along the temporal dimension:

$\mathbf{A} \in \mathbb{R}^{N \times N}$9

The kernel sizes are $t$0 and $t$1, and the reported experimental setting uses $t$2. Sigmoid activation is used in both layers. This module is intended to capture local trends and short-term fluctuations efficiently and in parallel.

Interactive fusion

The first fusion round combines each pattern branch with the shared spatial representation from RAGCN:

$t$3

$t$4

Attention-like weights are then computed for the two pattern branches through a softmax over their transformed representations:

$t$5

The final fusion is

$t$6

After reshaping, this representation is fused with the original input through a residual connection to produce $t$7.

The intended interpretation is explicit: pattern recognition and PEConv supply a global perspective over peak and off-peak regimes, whereas RAGCN captures local spatial correlations conditioned on current traffic signals and regional structure. The model’s “positive feedback loop” refers to the claim that pattern features help refine spatial correlations and improved spatial features help reveal more subtle patterns. A plausible implication is that PSIRAGCN attempts to overcome the common decoupling between regime modeling and graph propagation found in many earlier spatio-temporal networks.

4. Regional awareness and message passing

The second distinctive component is the Regional Awareness GCN (RAGCN), which reconstructs message passing so that it reflects regional heterogeneity rather than treating all nodes as structurally equivalent (Ji et al., 30 Aug 2025).

Regional characteristics bank

Regional heterogeneity is encoded through a per-node scalar derived from the local clustering coefficient:

$t$8

where $t$9 is the number of edges among the neighbors of node $\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$0, and $\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$1 is the number of neighbors of node $\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$2. The regional weight is then defined as

$\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$3

Collecting these values yields the regional characteristics bank

$\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$4

Nodes with higher clustering coefficient therefore receive smaller $\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$5, and nodes with lower clustering coefficient receive larger values.

The bank is characterized as static with respect to topology but dynamically utilized during message passing because it affects every subsequent propagation step and interacts with the evolving input $\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$6. This distinction matters: PSIRAGCN is not simply learning a time-varying adjacency from data alone, but modulating spectral propagation with a topology-derived regional prior.

Chebyshev-based regional-aware propagation

Inspired by Defferrard et al. (Chabnet-style spectral GCN), RAGCN constructs higher-order message-passing weights via Chebyshev polynomials of the scaled normalized Laplacian. With adjacency $\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$7, degree matrix $\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$8, Laplacian $\boldsymbol{X}^{(t)} \in \mathbb{R}^{D \times N},$9, and scaled normalized Laplacian $T$0, the recursion is

$T$1

$T$2

$T$3

For each order $T$4, the regional-aware message-passing matrix is

$T$5

where $T$6 is trainable. The resulting graph convolution is

$T$7

With diffusion step $T$8 in the reported experiments, the model treats traffic propagation as diffusion on a region-aware dynamic graph.

The interpretation supplied for this construction is specific. At $T$9, message passing reduces to node-wise scaling by $$\mathcal{X} = [\boldsymbol{X}^{(t-T+1)}, \ldots, \boldsymbol{X}^{(t)}],$$0, representing self-region influence. For $$\mathcal{X} = [\boldsymbol{X}^{(t-T+1)}, \ldots, \boldsymbol{X}^{(t)}],$$1, influence spreads via the Laplacian so that neighbors are weighted by adjacency and by their own regional characteristics. Accordingly, RAGCN is intended to make graph convolution non-uniform across nodes and more sensitive to region-specific propagation strengths.

5. Training protocol, datasets, and empirical findings

PSIRAGCN is trained with Mean Absolute Error (MAE) loss:

$$\mathcal{X} = [\boldsymbol{X}^{(t-T+1)}, \ldots, \boldsymbol{X}^{(t)}],$$2

and is evaluated with MAE, RMSE, and MAPE. The optimizer is Adam, the initial learning rate is 0.001, the weight decay is 0.0001, and the batch size is 64. Inputs are Z-score normalized, and missing values are masked during training and testing as in Graph WaveNet. The optimization description reports 200 epochs with early stopping, while the hyperparameter summary reports max epochs 300 with early stopping (Ji et al., 30 Aug 2025).

The reported experiments focus on three highway traffic flow datasets:

Dataset	Nodes	Samples / time range
PEMS04	307	16992 / 2018-01-01 to 2018-02-28
PEMS07	883	28224 / 2017-05-01 to 2017-08-31
PEMS08	170	17856 / 2016-07-01 to 2016-08-31

All three use a 5-minute interval and a train/validation/test split of $$\mathcal{X} = [\boldsymbol{X}^{(t-T+1)}, \ldots, \boldsymbol{X}^{(t)}],$$3.

The baseline set includes traditional methods—HA, VAR, SVR, LSTM, and TCN—and graph-based spatial-temporal models—DCRNN, STGCN, ASTGCN, Graph WaveNet, AGCRN, and ASTGNN. These cover static graph models, adaptive graph constructions, attention-based architectures, and dynamic graph learning.

The quantitative results are summarized below:

Dataset	PSIRAGCN result	Comparative note
PEMS04	MAE 17.428, RMSE 28.040, MAPE 0.077	MAE and RMSE are 2nd best; best MAE is AGCRN with 17.416
PEMS07	MAE 18.045, RMSE 27.134, MAPE 0.041	MAE and RMSE are best; MAPE is equal to best
PEMS08	MAE 13.453, RMSE 20.502, MAPE 0.044	MAE and RMSE are best; MAPE is 2nd best

These results support a nuanced characterization. PSIRAGCN achieves SOTA or near-SOTA across the three datasets, but it does not uniformly dominate every metric on every benchmark: on PEMS04, AGCRN has a slightly better MAE. This is an important corrective to any simplified reading that the model strictly outperforms all baselines in all settings.

Ablation studies further identify the most consequential components. Removing RAGCN causes the largest performance drop; removing the regional characteristics bank also degrades performance; removing PEConv reduces the benefit of pattern feedback; and removing the whole PSI module is worse than keeping it. Hyperparameter sensitivity experiments indicate that performance improves as encoder feature channels $$\mathcal{X} = [\boldsymbol{X}^{(t-T+1)}, \ldots, \boldsymbol{X}^{(t)}],$$4 increase up to a point and then stabilizes or slightly declines, with $$\mathcal{X} = [\boldsymbol{X}^{(t-T+1)}, \ldots, \boldsymbol{X}^{(t)}],$$5 reported as optimal for PEMS04, PEMS07, and PEMS08.

6. Computational profile, limitations, and extensions

PSIRAGCN is explicitly described as balancing computational cost rather than being lightweight (Ji et al., 30 Aug 2025). Attention-heavy models such as ASTGNN incur high computational cost due to repeated attention operations, while PSIRAGCN keeps training time comparable and does not significantly exceed baselines. The reported explanation is architectural: PEConv is an efficient 1D CNN, and the spectral GCN with Chebyshev polynomials has linear complexity in edges. Because the temporal horizon in the experiments is short, with $$\mathcal{X} = [\boldsymbol{X}^{(t-T+1)}, \ldots, \boldsymbol{X}^{(t)}],$$6, the self-attention overhead remains modest relative to graph and convolutional operations.

At the same time, the model is not lightweight. Its Chebyshev-based spectral GCN with regional weighting, together with pattern splitting and attention, increases complexity, and deployment on very large traffic networks with tens of thousands of nodes may require substantial memory and compute. This limitation tempers the empirical efficiency claims: “balanced computational cost” in the reported experiments should not be conflated with low-resource deployment.

Several extensions are proposed. One direction is more efficient spatial-temporal interactive learning through lower-rank approximations of adjacency, more efficient attention mechanisms such as linear attention, and sparse or dynamic PSI stacking. Another is transfer to other spatial-temporal forecasting tasks, including demand prediction on grids, crowd flows, air quality, and energy consumption. A third is broader regional characterization, for example incorporating POIs, lane counts, and socioeconomic indicators, or learning node-specific region embeddings directly from data instead of relying only on clustering coefficient.

In conceptual terms, PSIRAGCN combines three commitments: explicit regime recognition through K-means and PEConv, regional-aware message passing through RAGCN and the regional characteristics bank, and mutual fusion between these two views through the PSI mechanism. The resulting system is positioned as a traffic forecaster in which pattern regimes and regional heterogeneity are first-class modeling objects rather than auxiliary signals.