# Visual Analysis of Spatiotemporal Data Predictions with Deep Learning Models
## 2 Related Work
[36] provided a visual tool to improve the performance of LSTM models with the exploration and summarization of long-term dependencies in time series and sequence data. Since our data have temporal features, we employ LSTM and GRU for deep learning modeling. Spatial interpolation estimates the unobserved data inside the sampled area with the observed data [37]. Spatial interpolation is generally applied for visualization, mainly by computing the pixel values from pixel-based data [38]. Many algorithms were developed for interpolation, including nearest-neighbor interpolation, bilinear interpolation, and bicubic interpolation [39]. Inverse distance weighted interpolation (IDW) is assumed to have similar values as the data become closer to each other [40]. IDW interpolation estimates the value of an unknown point by weighting it inversely with distance [41]. IDW interpolation assigns consecutive weights, while nearest-neighbor interpolation weights only 1 to the nearest data. Linear interpolation is a simple interpolation that estimates data linearly. We can use cubic interpolation to reduce the discontinuities caused by linear interpolation. Cubic interpolation produces more smooth data than linear interpolation or nearest-neighbor interpolation. As a high-order interpolation, radial basis function (RBF) is employed for more accurate interpolation of unstructured data. The RBF interpolation can be constructed in an artificial neural network by using RBFs as activation functions [42]. In this work, we apply cubic, linear RBF, and nearest-neighbor techniques for spatial interpolation. Prediction of spatiotemporal data is generally performed considering both the temporal and spatial feature points. Deep learning algorithms that are mainly used for space-time data prediction include LCRN [43] and convolutional LSTM (ConvLSTM) [8]. LCRN has a structure in which CNN and LSTM are sequentially connected. In the LCRN structure, the spatiotemporal data inputs are trained for the spatial feature points with the CNN and the temporal feature points with the LSTM. [PERSON] et al. [44] presented PVNet, usingthe LCRN structure. PVNet predicts photovoltaic power by training numerical weather information, including irradiance, cloud, temperature, the clear sky model and a power model, calculated with the persistence model. LCRN contains a sequential connection structure between CNN and LSTM, while ConvLSTM includes convolution operations within the cells of LSTM. ConvLSTM trains spatiotemporal data by performing convolution operations as soon as input data are inserted into LSTM cells. ConvLSTM has faster computational speed and has higher performance than LCRN in many studies. [PERSON] et al. (2020) conducted a study on the traffic accident prediction problem, using the ConvLSTM model. They predicted data by applying a spatial ensemble to the results predicted by ConvLSTM. The proposed model shows a much higher prediction accuracy than the conventional method. [PERSON] et al. (2019) proposed STCNN using ConvLSTM for long-term traffic predictions. The proposed model combines the weekly ConvLSTM prediction result and the daily Skip-ConvLSTM prediction result for CNN training to identify the periodic pattern of traffic. [PERSON] et al. (2019) proposed a ConvLSTM-based spatiotemporal temperature deviation prediction model (PredTemp). They compared the predictions with ConvLSTM, using temperature deviation data, and with ConvLSTM, using both precipitation and temperature deviation data. To utilize spatiotemporal features, we also include ConvLSTM for deep learning modeling.