A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks

The use of graph-based models had already been a key element in applications such as route planning (e.g., Dijkstra's algorithm) [3], community detection (e.g., clique percolation or Louvain algorithms) [4] or the analysis of complex networks such as biological and social networks [5, 6]. The representation of manifolds by means of graphs in the field of semi-supervised learning is another example of graph-powered applications [7]. Overall, the GSP framework [8] has enabled the use and development of novel techniques on data residing in graphs, thus emerging as an alternative to classical machine learning techniques that do not make explicit use of data structure. In this way, the graph topology, which represents the relationships between the graph's nodes, is fed to graph-based models that explicitly model the structure of the data [9]. A wide variety of concepts have been applied to signals defined over graphs, such as signal shift, translation, convolution, or filtering [10]. An important concept of the GSP is the notion of signal smoothness, also expressed via the total variation (TV) or the Dirichlet energy, which are quadratic forms and can be used to evaluate how a signal fits a given graph structure or vice-versa [11]. This idea is linked with the Graph Discrete Fourier Transform (GDFT) that makes use of the graph topology to obtain the graph Fourier basis and allow the computation of the transform coefficients of a graph signal and also led to the development of graph filters [12]. In the field of machine learning, graphs have been used as regularizers in optimization problems, e.g., the regularization of neural networks for semi-supervised learning tasks [13].