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Rumor source detection has long been an important but difficult problem. Due to the complexity of the underlying propagation model, most existing methods only rely on the limit observation of a single batch of single snapshot during the propagation process in the spatial graph networks, which neglects temporal dependency and temporal features of the rumor propagation process. Taking multiple batches of multiple snapshots as input can reveal the temporal dependency. Inspired by the traditional spatial-temporal graph convolution network (STGCN), which is a model that can combine spatial and temporal features. In this paper, we propose a STGCN based model called Spatio-Temporal Approximate Personalized Propagation of Neural Predictions (STAPPNP), which firstly learns both the spatial and temporal features automatically from multiple batches of multiple snapshots to locate the rumor source. As there are no input algorithms that are suitable for multiple batches of multiple snapshots to capture the feature of nodes’ connectivity in STAPPNP, we develop an input algorithm to generate a 4-dimensional input matrix from the multiple batches of multiple snapshots to feed the proposed model. Nonetheless, for deep learning models, such input of multiple batches of multiple snapshots requires multiple convolutional layers to extract spatial features. Too many convolutional layers can lead to over-smoothing and long training time. To address these issues, we improve the Spatio-Temporal-Convolutional(ST-Conv) block, in which we adopt the approximate personalized propagation of neural predictions in the spatial convolutional layer of STAPPNP. Our experimental results show that the accuracy of the rumor source detection is improved by using STAPPNP, and the speed of the training process of STAPPNP outperforms state-of-the-art deep learning approaches under the popular epidemic susceptible-infected (SI) and susceptible-infected-recovery (SIR) models in social networks. [ABSTRACT FROM AUTHOR]