Many real-world applications involve multivariate, geo-tagged time series data: at each location, multiple sensors record corresponding measurements. For example, air quality monitoring system records PM2.5, CO, etc. The resulting time-series data often has missing values due to device outages or communication errors. In order to impute the missing values, state-of-the-art methods are built on Recurrent Neural Networks (RNN), which process each time stamp sequentially, prohibiting the direct modeling of the relationship between distant time stamps. Recently, the self-attention mechanism has been proposed for sequence modeling tasks such as machine translation, significantly outperforming RNN because the relationship between each two time stamps can be modeled explicitly. In this paper, we are the first to adapt the self-attention mechanism for multivariate, geo-tagged time series data. In order to jointly capture the self-attention across different dimensions (i.e. time, location and sensor measurements) while keep the size of attention maps reasonable, we propose a novel approach called Cross-Dimensional Self-Attention (CDSA) to process each dimension sequentially, yet in an order-independent manner. On three real-world datasets, including one our newly collected NYC-traffic dataset, extensive experiments demonstrate the superiority of our approach compared to state-of-the-art methods for both imputation and forecasting tasks. 

A novel self-attention mechanism for multivariate, geo-tagged time series imputation. This paper proposes the problem of applying the transformer network to spatiotemporal data in a compuationally efficient way, and investigates ways of implementing 3D attention. This paper empirically studies the effectiveness of transformer models for time series data imputation across dimensions of the input.