Graph Learning Techniques Using Structured Data for IoT Air Pollution Monitoring Platforms

Abstract

Existing air pollution monitoring networks use reference stations as the main nodes. The addition of low-cost sensors calibrated in-situ with machine learning techniques allows the creation of heterogeneous air pollution monitoring networks. However, current monitoring networks or calibration techniques have limitations in estimating missing data, adding virtual sensors or recalibrating sensors. The use of graphs to represent structured data is an emerging area of research that allows the use of powerful techniques to process and analyze data for air pollution monitoring networks. In this paper, we compare two techniques that rely on structured data, one based on statistical methods and the other on signal smoothness, with a baseline technique based on the distance between nodes and that does not rely on the measured signal data. To compare these techniques, the sensor signal is reconstructed with a supervised method based on linear regression and a semi-supervised method based on Laplacian interpolation, which allows reconstruction even when data is missing. The results, on data sets measuring O3, NO2 and PM10, show that the signal smoothness-based technique behaves better than the other two, and used together with the Laplacian interpolation is near-optimal with respect to the linear regression method. Moreover, in the case of heterogeneous networks, the results show a reconstruction accuracy similar to the in-situ calibrated sensors. Thus, the use of the network data increases the robustness of the network against possible sensor failures.

Some results on the Gaussian Markov Random Field construction problem based on the use of invariant subgraphs

“…This result is relevant to applications such as those in Furtlehner et al (2021), Ferrer-Cid et al (2021 and Loftus et al (2021). If the assumption of the data being sampled from a GMRF is reasonable, then the MLE is similar to the sample covariance matrix while also having a sparse inverse matrix.…”

“…If the GMRF model is reasonable, then this MLE will be similar to the sample covariance matrix but will also benefit from the computational advantages of having a sparse inverse. In this direction, several methods that allow to learn the underlying graph structure have been developed (see Furtlehner et al 2021;Ferrer-Cid et al 2021;Loftus et al 2021 for some recent examples). Here, we solve this GMRF construction problem restricted to a certain type of subgraphs (which we will call invariant subgraphs) and then solve the whole GMRF construction problem by considering MGMRFs over forests.…”

Volterra Graph-Based Outlier Detection for Air Pollution Sensor Networks

“…Spectral decomposition of data using principal component analysis (PCA) is widely used [21]- [23], as well as residual-based techniques, where a spatial model is fitted and large sample residuals indicate the existence of outlierness [15]. However, in this specific paradigm of air pollution, different techniques have been used for modeling these networks, from spatial models [24] to graphs [25]. Indeed, the growing field of graph signal processing (GSP) has shown its flexibility in describing this type of network as well as providing classical signal processing techniques for their analysis [26], [27].…”

“…Most studies build graphs based on the geographical distance between nodes, although this approach performs well for some phenomena, networks that measure air pollution and other phenomena can be very complex. Therefore, as shown in [25], [31], the use of graphs learned from the data, resulting in a smooth structure with respect to the measured data, is a good candidate for these air pollution sensor networks, and the one we explore in this work. This approach is based on the fact of having a network of sensors where there are implicit relationships between the sensors that compose it so that the different sensors can benefit from the information of other sensors.…”

GraphHD: Efficient graph classification using hyperdimensional computing

“…The demand for alternatives is clear given the growing number of graph learning applications in resource-constrained scenarios. Examples range from IoT malware detection [11] to air pollution monitoring sensor networks [12].…”