Graph Signal Processing in Applications to Sensor Networks, Smart Grids, and Smart Cities

This paper initiates a discussion on the application of the graph signal processing to exploration of complex and heterogeneous data and systems, and especially for the case of environmental monitoring in smart habitat of city, country, and continent. This emerging approach relates to the objects, which can be represented by a networked structure, but enables also the reconstruction of network-like associations from data when this kind of structured organization is not apparent. In this paper, the sensor network is perceived as the fundamental layer of the smart habitat, and inference is provided not only by direct operation on acquired signals, but also network model is identified for recorded ozone (O-3) data in 100 measurement points deployed in Poland. It means that a graph as a mathematical representation of the complex network is generated, which links system features and behaviors coded in measured data sets. Results of multiscale projections are commented for ozone data sets. Furthermore, in opposite to the classical signal processing, the spectral analysis for graph signals is demonstrated, including reconstruction of graph Laplacian and Fourier transform calculation for signals spanned on graph vertices. Finally, local (related to the location of sensor in network) properties and behaviors are clustered based on spectral maps generated for graph signals.