Multivariate time-series forecasting plays a crucial role in many real-world applications. It is a challenging problem as one needs to consider both intra-series temporal correlations and inter-series correlations simultaneously. Recently, there have been multiple works trying to capture both correlations, but most, if not all of them only capture temporal correlations in the time domain and resort to predefined priors as inter-series relationships. In this paper, we propose Spectral Temporal Graph Neural Network (StemGNN) to further improve the accuracy of multivariate time-series forecasting. StemGNN captures inter-series correlations and temporal dependencies jointly in the spectral domain. It combines Graph Fourier Transform (GFT) which models inter-series correlations and Discrete Fourier Transform (DFT) which models temporal dependencies in an end-to-end framework. After passing through GFT and DFT, the spectral representations hold clear patterns and can be predicted effectively by convolution and sequential learning modules. Moreover, StemGNN learns inter-series correlations automatically from the data without using pre-defined priors. We conduct extensive experiments on ten real-world datasets to demonstrate the effectiveness of StemGNN. Code is available at https://github.com/microsoft/StemGNN/ * The work was done when the author did internship at Microsoft.
Anomaly detection on multivariate time-series is of great importance in both data mining research and industrial applications. Recent approaches have achieved significant progress in this topic, but there is remaining limitations. One major limitation is that they do not capture the relationships between different time-series explicitly, resulting in inevitable false alarms. In this paper, we propose a novel self-supervised framework for multivariate time-series anomaly detection to address this issue. Our framework considers each univariate time-series as an individual feature and includes two graph attention layers in parallel to learn the complex dependencies of multivariate time-series in both temporal and feature dimensions. In addition, our approach jointly optimizes a forecasting-based model and a reconstruction-based model, obtaining better time-series representations through a combination of single-timestamp prediction and reconstruction of the entire time-series. We demonstrate the efficacy of our model through extensive experiments. The proposed method outperforms other state-of-the-art models on three real-world datasets. Further analysis shows that our method has good interpretability and is useful for anomaly diagnosis.
An effective understanding of the contextual environment and accurate motion forecasting of surrounding agents is crucial for the development of autonomous vehicles and social mobile robots. This task is challenging since the behavior of an autonomous agent is not only affected by its own intention, but also by the static environment and surrounding dynamically interacting agents. Previous works focused on utilizing the spatial and temporal information in time domain while not sufficiently taking advantage of the cues in frequency domain. To this end, we propose a Spectral Temporal Graph Neural Network (SpecTGNN), which can capture inter-agent correlations and temporal dependency simultaneously in frequency domain in addition to time domain. SpecTGNN operates on both an agent graph with dynamic state information and an environment graph with the features extracted from context images in two streams. The model integrates graph Fourier transform, spectral graph convolution and temporal gated convolution to encode history information and forecast future trajectories. Moreover, we incorporate a multi-head spatio-temporal attention mechanism to mitigate the effect of error propagation in a long time horizon. We demonstrate the performance of SpecTGNN on two public trajectory prediction benchmark datasets, which achieves stateof-the-art performance in terms of prediction accuracy.
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