Autoregressive Tensor Factorization for Spatio-temporal Predictions

Analysis of spatio-temporal data is a common research topic that requires the interpolations of unknown locations and the predictions of feature observations by utilizing information about where and when the data were observed. One of the most difficult problems is to make predictions of unknown locations. Tensor factorization methods are popular in this field because of their capability of handling multiple types of spatio-temporal data, dealing with missing values, and providing computationally efficient parameter estimation procedures. However, unlike traditional approaches such as spatial autoregressive models, the existing tensor factorization methods have not tried to learn spatial autocorrelations. These methods employ previously inferred spatial dependencies, often resulting in poor performances on the problem of making interpolations and predictions of unknown locations. In this paper, we propose a new tensor factorization method that estimates low-rank latent factors by simultaneously learning the spatial and temporal autocorrelations. We introduce new spatial autoregressive regularizers based on existing spatial autoregressive models and provide an efficient estimation procedure. With experiments on publicly available traffic transporting data, we demonstrate that our proposed method significantly improves the predictive performances in our problems in comparison to the existing state-of-the-art spatio-temporal analysis methods.