Abstract
We tackle the problem of forecasting network-signal snapshots using past signal measurements acquired by a subset of network nodes. This task can be seen as a combination of multivariate time-series forecasting (temporal prediction) and graph-signal interpolation (spatial prediction). This is a fundamental problem for many applications wherein deploying a high granularity network is impractical. Our solution combines recurrent neural networks with frequency-analysis tools from graph signal processing, and assumes that data is sufficiently smooth with respect to the underlying graph. The proposed learning model outperforms state-of-the-art deep learning techniques, especially when predictions are made using a small subset of network nodes, considering two distinct real world datasets: temperatures in the US and speed flow in Seattle. The results also indicate that our method can handle noisy signals and missing data, making it suitable to many practical applications.
Highlights
S PATIOTEMPORAL (ST) prediction is a fundamental abstract problem featuring in many practical applications, including climate analyses [1], transportation management [2], neuroscience [3], electricity markets [4], and several geographical phenomenon analyses [5]
The gatedrecurrent unit (GRU) cell is composed of a hidden state ht, which allows the weights of the GRU to be shared across time, as well as by two gates qt and rt, which modulate the flow of information inside the cell unit
The graph signal (GS) in the SeattleLoop dataset, on the other hand, are not as smooth as the GSs in the Global Surface Summary of the Day Dataset (GSOD) dataset, leading to a larger reconstruction error. Even with this limitation on the prior smoothness assumption, the spectral graph GRU (SG-GRU) outperformed the ST graph convolution network (STGCN) combined with 1-hop interpolation and the TGCLSTM combined with graph signal processing (GSP) interpolation when the sampling set size is 25% or 50% of the total number of nodes
Summary
S PATIOTEMPORAL (ST) prediction is a fundamental abstract problem featuring in many practical applications, including climate analyses [1], transportation management [2], neuroscience [3], electricity markets [4], and several geographical phenomenon analyses [5]. Developing a predictive model capable of forecasting (temporal prediction) and interpolating (spatial prediction) time-varying signals defined on graph nodes can be of great applicability This problem can be regarded as a semi-supervised task, since only part of the nodes is available for training. A global interpolation approach is adopted as it provides accurate results when the signal is smooth in the GSP sense, whereas an RNN forecasting model is adopted given its prior success in network prediction. We consider that both the sampled GS and its spectral components — i.e., the Fourier coefficients, which carry spatial information on the underlying graph — work as inputs to a predictive model.
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