Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.
While deep convolutional neural networks (CNNs) have shown a great success in single-label image classification, it is important to note that real world images generally contain multiple labels, which could correspond to different objects, scenes, actions and attributes in an image. Traditional approaches to multi-label image classification learn independent classifiers for each category and employ ranking or thresholding on the classification results. These techniques, although working well, fail to explicitly exploit the label dependencies in an image. In this paper, we utilize recurrent neural networks (RNNs) to address this problem. Combined with CNNs, the proposed CNN-RNN framework learns a joint image-label embedding to characterize the semantic label dependency as well as the image-label relevance, and it can be trained end-to-end from scratch to integrate both information in a unified framework. Experimental results on public benchmark datasets demonstrate that the proposed architecture achieves better performance than the state-of-the-art multi-label classification model