Accurate PM_2.5 prediction is essential for effective urban air quality management. However, existing methods often struggle to capture the complex, nonlinear, and coupled spatiotemporal dynamics in long-term air pollution evolution. Most existing models rely on short-term observations and overlook long-range temporal trends and inter-station dependencies, which limit their ability to capture the spatiotemporal evolution of air pollution. To address these challenges, we propose a novel dynamic global–local spatiotemporal graph framework for PM_2.5 long-term forecasting across multiple cities. Specifically, we introduce a Multi-Station iTransformer (MS-iTransformer) module to capture long-term temporal dependencies from station-specific historical sequences. To globally model evolving inter-city relationships, we design a bilinear spatiotemporal attention (BSTA) module to adaptively build dynamic spatiotemporal graphs using bilinear spatial and temporal attention. Furthermore, we propose a Graph-Enhanced Spatiotemporal Module (GESM) to capture localized spatiotemporal dependencies through graph convolution and recurrent modeling. The experimental results demonstrate that our model has significant improvements across PM_2.5 forecasting tasks on three real-world air quality datasets, outperforming widely adopted baseline approaches. The MAE and RMSE are decreased by 1.7665 and 1.8578, respectively. The FAR is reduced by 0.0312. The CSI and R² are improved by 0.0194 and 0.0260, respectively. Therefore, the proposed method achieves accurate air quality forecasting by effectively capturing long-term temporal trends, dynamic spatial dependencies, and localized spatiotemporal interactions.

The field of multi-source remote sensing observation is becoming increasingly dynamic through the integration of various remote sensing data sources. However, existing deep learning methods face challenges in differentiating between internal and external relationships and capturing fine spatial features. These models often struggle to effectively capture comprehensive information across remote sensing data bands, and they have inherent differences in the size, structure, and physical properties of different remote sensing datasets. To address these challenges, this paper proposes a novel geometric-algebra-based spectral–spatial hierarchical fusion network (GASSF-Net), which uses geometric algebra for the first time to process multi-source remote sensing images, enabling a more holistic approach to handling these images by simultaneously leveraging the real and imaginary components of geometric algebra to express structural information. This method captures the internal and external relationships between remote sensing image features and spatial information, effectively fusing the features of different remote sensing data to improve classification accuracy. GASSF-Net uses geometric algebra (GA) to represent pixels from different bands as multivectors, thus capturing the intrinsic relationships between spectral bands while preserving spatial information. The network begins by deeply mining the spectral–spatial features of a hyperspectral image (HSI) using pairwise covariance operators. These features are then extracted through two branches: a geometric-algebra-based branch and a real-valued network branch. Additionally, the geometric-algebra-based network extracts spatial information from light detection and ranging (LiDAR) to complement the elevation data lacking in the HSI. Finally, a genetic-algorithm-based cross-fusion module is introduced to fuse the HSI and LiDAR data for improved classification. Experiments conducted on three well-known datasets, Trento, MUUFL, and Houston, demonstrate that GASSF-Net significantly outperforms traditional methods in terms of classification accuracy and model efficiency.

Hyperspectral anomaly detection (HAD) is of great significance in remote sensing by identifying spectrally distinct pixels as anomalies without prior information, while the majority of pixels with similar spectral characteristics are classified as background. While existing approaches combine the strengths of deep learning (DL) in feature extraction and background suppression with the effectiveness of low-rank representation (LRR) in background modeling, they fail to fully exploit rich spatial information and long-range spectral dependencies due to the limitations of conventional convolutional operations. To address this issue, we propose a geometric algebra (GA)-based deep neural network for HAD, named GA-HAD. The network constructs an encoder-decoder architecture using GA convolutional layers to extract spectral-spatial features, capturing multidimensional spatial information while preserving the intricate spectral characteristics of hyperspectral images (HSIs). A specialized reconstruction error is designed to train the GA feature extraction network with high efficiency and accuracy. The encoder features are integrated with the LRR algorithm and a Gaussian mixture model (GMM)-based dictionary to improve background modeling and robustness. Finally, the detection maps output by the low-rank detection module are refined through an edge-preserving filter to produce the final detection result. Extensive experiments on four datasets demonstrate the superiority of our proposed GA-HAD framework in overall detection effect compared to thirteen representative baselines, implying our potential application in the field of HAD.