This paper introduces CloudLSTM, a new branch of recurrent neural models tailored to forecasting over data streams generated by geospatial point-cloud sources. We design a Dynamic Point-cloud Convolution (D-Conv) operator as the core component of CloudLSTMs, which performs convolution directly over point-clouds and extracts local spatial features from sets of neighboring points that surround different elements of the input. This operator maintains the permutation invariance of sequence-to-sequence learning frameworks, while representing neighboring correlations at each time step -- an important aspect in spatiotemporal predictive learning. The D-Conv operator resolves the grid-structural data requirements of existing spatiotemporal forecasting models and can be easily plugged into traditional LSTM architectures with sequence-to-sequence learning and attention mechanisms.
     We apply our proposed architecture to two representative, practical use cases that involve point-cloud streams, i.e. mobile service traffic forecasting and air quality indicator forecasting. Our results, obtained with real-world datasets collected in diverse scenarios for each use case, show that CloudLSTM delivers accurate long-term predictions, outperforming a variety of neural network models. Point-cloud stream forecasting aims at predicting the future values and/or locations of data streams generated by a geospatial point-cloud S, given sequences of historical observations (Shi & Yeung, 2018) . Example data sources include mobile network antennas that serve the traffic generated by ubiquitous mobile services at city scale (Zhang et al., 2019b) , sensors that monitor the air quality of a target region (Cheng et al., 2018) , or moving crowds that produce individual trajectories. Unlike traditional spatiotemporal forecasting on grid-structural data, like precipitation nowcasting (Shi et al., 2015) or video frame prediction (Wang et al., 2018) , point-cloud stream forecasting needs to operate on geometrically scattered sets of points, which are irregular and unordered, and encapsulate complex spatial correlations. While vanilla Long Short-term Memories (LSTMs) have modest abilities to exploit spatial features (Shi et al., 2015) , convolution-based recurrent neural network (RNN) models, such as ConvLSTM (Shi et al., 2015) and PredRNN++ (Wang et al., 2018) , are limited to modeling grid-structural data, and are therefore inappropriate for handling scattered point-clouds. : Different approaches to geospatial data stream forecasting: predicting over input data streams that are inherently grid-structured, e.g., video frames using ConvLSTMs (top); mapping of pointcloud input to a grid, e.g., mobile network traffic collected at different antennas in a city, to enable forecasting using existing neural network structures (middle); forecasting directly over point-cloud data streams using historical information (as above, but without pre-processing), as proposed in this paper (bottom). permutations for the features (Li et al., 2018) . Through this, the proposed PointCNN leverages spatial-local correlations of point clouds, irrespective of the order of the input. Notably, although these architectures can learn spatial features of point-clouds, they are designed to work with static data, thus have limited ability to discover temporal dependencies. We introduce CloudLSTM, a dedicated neural model for spatiotemporal forecasting tailored to pointcloud data streams. The CloudLSTM builds upon the DConv operator, which performs convolution over point-clouds to learn spatial features while maintaining permutation invariance. The DConv simultaneously predicts the values and coordinates of each point, thereby adapting to changing spatial correlations of the data at each time step. DConv is flexible, as it can be easily combined with various RNN models (i.e., RNN, GRU, and LSTM), Seq2seq learning, and attention mechanisms.
This paper introduces CloudLSTM, a new branch of recurrent neural models tailored to forecasting over data streams generated by geospatial point-cloud sources.
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