Graph-based Virtual Sensing from Sparse and Partial Multivariate Observations

TL;DR

This paper introduces a novel graph-based methodology to exploit relationships between variables and a graph deep learning architecture, named GgNet, implementing the framework and extensively evaluated under different virtual sensing scenarios, demonstrating higher reconstruction accuracy compared to the state-of-the-art.

Abstract

Virtual sensing techniques allow for inferring signals at new unmonitored locations by exploiting spatio-temporal measurements coming from physical sensors at different locations. However, as the sensor coverage becomes sparse due to costs or other constraints, physical proximity cannot be used to support interpolation. In this paper, we overcome this challenge by leveraging dependencies between the target variable and a set of correlated variables (covariates) that can frequently be associated with each location of interest. From this viewpoint, covariates provide partial observability, and the problem consists of inferring values for unobserved channels by exploiting observations at other locations to learn how such variables can correlate. We introduce a novel graph-based methodology to exploit such relationships and design a graph deep learning architecture, named GgNet, implementing the framework. The proposed approach relies on propagating information over a nested graph structure that is used to learn dependencies between variables as well as locations. GgNet is extensively evaluated under different virtual sensing scenarios, demonstrating higher reconstruction accuracy compared to the state-of-the-art.

Figures (8)

• Figure 1: Sparse multivariate virtual sensing; available data (yellow), missing data (white), and predictions (red).
• Figure 2: Dataset as a collection of multivariate time series (left) and its nested graph representation (right). Each location is represented as a node in the inter-location graph (G), capturing generic relations between locations. Within each node in G, a smaller intra-location graph (g) models dependencies between the channels.
• Figure 3: Overview of GgNet. Temporal convolutions (blue) encode temporal patterns, $G$-convolutions (green) propagate information across the inter location graph and model dependencies between locations; $g$-convolutions (purple) propagate information across the intra-location graph and model dependencies between channels. Starred modules refer to channel-wise operations.
• Figure 4: Training and evaluation splits for MVS.
• Figure 5: (Left) Reconstruction of wind speed (poorly correlated with the other channels) in Road Town (which can exploit observations at nearby Caribbean capitals). (Right) t-SNE representation of the node embeddings learned by GgNet; colours refer to the Köppen-Geiger climate classification.