Traffic forecasting is the foundation for intelligent transportation systems.
Spatiotemporal graph neural networks have demonstrated state-of-the-art
performance in traffic forecasting. However, these methods do not explicitly
model some of the natural characteristics in traffic data, such as the
multiscale structure that encompasses spatial and temporal variations at
different levels of granularity or scale. To that end, we propose a
Wavelet-Inspired Graph Convolutional Recurrent Network (WavGCRN) which combines
multiscale analysis (MSA)-based method with Deep Learning (DL)-based method. In
WavGCRN, the traffic data is decomposed into time-frequency components with
Discrete Wavelet Transformation (DWT), constructing a multi-stream input
structure; then Graph Convolutional Recurrent networks (GCRNs) are employed as
encoders for each stream, extracting spatiotemporal features in different
scales; and finally the learnable Inversed DWT and GCRN are combined as the
decoder, fusing the information from all streams for traffic metrics
reconstruction and prediction. Furthermore, road-network-informed graphs and
data-driven graph learning are combined to accurately capture spatial
correlation. The proposed method can offer well-defined interpretability,
powerful learning capability, and competitive forecasting performance on
real-world traffic data sets.

提出了一种基于小波图卷积循环网络的多尺度分析方法和深度学习方法相结合的 Traffic 预测模型，能够准确捕捉交通数据的空间相关性和多尺度结构，并在真实交通数据集上展现出具有解释性、强大的学习能力和竞争性的预测性能。

基于小波灵感的多尺度图卷积循环网络用于交通预测

Wavelet-Inspired Multiscale Graph Convolutional Recurrent Network for  Traffic Forecasting

Cross-resolution image alignment is a key problem in multiscale gigapixel
photography, which requires to estimate homography matrix using images with
large resolution gap. Existing deep homography methods concatenate the input
images or features, neglecting the explicit formulation of correspondences
between them, which leads to degraded accuracy in cross-resolution challenges.
In this paper, we consider the cross-resolution homography estimation as a
multimodal problem, and propose a local transformer network embedded within a
multiscale structure to explicitly learn correspondences between the multimodal
inputs, namely, input images with different resolutions. The proposed local
transformer adopts a local attention map specifically for each position in the
feature. By combining the local transformer with the multiscale structure, the
network is able to capture long-short range correspondences efficiently and
accurately. Experiments on both the MS-COCO dataset and the real-captured
cross-resolution dataset show that the proposed network outperforms existing
state-of-the-art feature-based and deep-learning-based homography estimation
methods, and is able to accurately align images under $10\times$ resolution
gap.

本文提出了一种多模态的局部变换网络嵌入多尺度结构中，以显式学习分辨率不同的输入图像之间的对应关系，用于解决多尺度千亿像素摄影中的交叉分辨率匹配问题。实验证明，该方法在 MS-COCO 数据集和真实拍摄的交叉分辨率数据集上表现优于其他基于特征和深度学习的同类方法，能够在小于 10 倍的分辨率差异下精确地对齐图像。