Continuous Spatio-Temporal Data Reconstruction
5.1 Introduction
Spatio-temporal data widely exists in real-world applications. For instance, in the traffic flow forecasting task, each roadside sensor records several traffic mea- surements such as vehicle speed, volume, etc., at different times. To analyze the spatio-temporal data, most recent studies exploit deep learning approaches, such as spatio-temporal graph neural networks, to capture the spatial and temporal features hidden in the highly non-linear real-world data [53, 142, 171]. These models represent the data by a temporal graph with sensor stations as nodes.
Travel distance is often used to weigh the edge between sensor stations to retain spatial proximity. The measurements of the sensors at a station (i.e., node), are regarded as node features, which change over time.
Existing spatio-temporal graph neural networks model the temporal aspect of the data as a sequence of discrete time steps [79, 147, 145, 59, 86]. As such, the prediction granularity of these models greatly depends on the interval of the input data. To be specific, if the traffic measurements are collected every 5 minutes, then these models can only predict the traffics in the next 5, 10, 15 minutes, etc., and they cannot infer the next 2 or 3 minutes’ traffic conditions. The limitation of these methods is caused by the intrinsic discreteness of neural networks and the discrete data collection process. Specifically, sequence models, such as RNN,
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LSTM, GRU [153, 111, 31], or Transformer [135] are often employed to capture the temporal correlation of the data. Yet, both sequence models and Transformers take discrete-time sequences as input. Meanwhile, many real-world sensors such as meteorology, aerography, and environmental sensors collect data in fixed time intervals (e.g., per minute, per hour, per day) due to practical constraints such as energy consumption and storage limitation [91, 61].
Figure 5.1: Difference between imputation and continuous reconstruction. Im- putation aims to replace the missing value (shaded circle) in the given dataset with a rigid data shape. Continuous reconstruction tries to learn the underlying continuous temporal pattern and be able to infer data for any timestamp (arrow).
Nevertheless, sensors are deployed to help humans perceive and understand the continuously changing world in a discrete way. We believe that the recon- struction of the continuous world from the observed discrete data is essential for making precise spatio-temporal data analysis. In this work, we propose a new research problem calledContinuous Spatio-Temporal Data Reconstruction. The goal is to estimate the data atany given timestampwithin the period of interest as illustrated in Figure 5.1. It is worth noting that this task differs from imputation, which aims to refill the missing data at pre-defined timestamps [33]. For example, a weather station sensor often records the nearby temperature hourly. When the reading of 2 pm is missing, imputation methods try to fill the missing data for 2 pm according to the adjacent time steps (i.e., 1 pm and 3 pm) and nearby sensors. Unlike imputation, in the continuous reconstruction problem, we aim to reconstruct the temperature value at any query timestamp, e.g., 2:35:28 pm.
Introduction 115
A straightforward idea to solve the proposed continuous reconstruction prob- lem is to model the temporal features by regression. For example, one can fit a function that takes a timestamptas input and outputs the corresponding value attfor each measurement at each sensor station. However, this approach has three limitations: First, spatio-temporal data often exhibit strongspatio-temporal corre- lations. For example, measurements observed at nearby locations and adjacent timestamps tend to be similar. Such spatio-temporal correlations have proved to be effective in spatio-temporal data mining [79, 147, 145, 59, 86]. However, they are not utilized in the straightforward method. Second, due to the high non-linearity of spatio-temporal data, it is hard to learn a function that fits the entire time dimension and adapts to abrupt changes at a specific time. Third, do- main knowledge is often used for defining the form of the function. For example, the cubic spline method assumes the time series data can be fit by a third-order polynomial function.
To address the above challenges, we propose a Spatio-Temporal Representation Learning (STRL) framework, motivated by the successful ofrepresentation learningin spatio-temporal data mining tasks [152, 141]. For ease of presentation, measurements observed at a station and a timestamp are referred to as a spacetime event in this paper. In a nutshell, the main technical novelty of STRL is to infer the latent representation of the query timestamp from its local spatio-temporal context, which is then passed to a decoder for predicting the measurement at the query timestamp. Specifically, we address the first limitation of the straightforward solution by designing a spacetime encoder using graph con- volution networks (GCNs) and bidirectional long short-term memory (Bi-LSTM) as building blocks. The spacetime encoder is able to learn the representations of spacetime events by capturing their spatio-temporal correlations.STRLaddresses the second and the third limitations with a novel representation construction module. Given a query timestamp, the representation construction module infers the representation of the query timestamp by combining the representations of spacetime events in the local spatio-temporal context, weighted by the time differences of these spacetime events to the query. Note thatSTRLdoes not fit a function of specific forms for the entire time dimension. Instead, it concentrates on the local spatio-temporal context of the query timestamp, and thus adapts to abrupt local changes.
In short, the contribution of this work is three-fold:
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1. We propose a new task, which aims to rebuild the underlying continuous patterns from the discretely sampled data.
2. We propose a novel framework for the new task. Our framework learns the representations of spacetime events and infers the representation of the query timestamp from the learned representations of spacetime events within a local spatio-temporal context.
3. We conduct experiments on real-world spatio-temporal time series datasets and show that the proposed framework is effective in the continuous recon- struction problem.