Statistical Signal Processing and Learning on Networks and Graphs

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Signal processing along with the resurgent AI technology have become ubiquitous to process data from all types of sources. Many data, either from networked sources such as sensor networks and social networks or from other sources such as images and videos, contain explicit or implicit structured relationships that can be best represented by a graph. These types of network data pose new challenges to signal processing research. Recent signal processing and statistical modeling technologies for data with a graph structure mainly include a) graphical modeling and learning theory, and b) graph signal processing. However, these theories and methods have not been fully investigated under various constraints posed by emerging applications to solve problems such as localization and tracking, source identification, optimal filtering over networks. In addition, in many cases, identification or learning of the unknown or implicit network/graph structures is a very challenging problem. The overall objective of the proposed research is to systematically develop new signal and data processing theories and methods for data that have explicit, such as in sensor networks, or implicit, such as in videos, underlying nonlocal graph based relationships and/or dynamic information diffusion flow, and applications in sensor/social networks, 5G Internet of things (IoT) wireless networks, multimodality multimedia content analysis, and economic big data. Specific objectives are (i) to develop general network statistical signal processing and inference models and methods over a sensor network for dynamic multiple target localization and tracking; (ii)to identify original signal sources in the presence of noise and interference for data generated by a network information diffusion process, based on the graph shift operator theory, and to develop optimal filtering and prediction methods over the network; also to develop the optimal learning algorithms to estimate the network structure if it is unknown; and (iii) to design a graph shift operator or manifold kernel that can best represent the complex nonlocal hidden correlation and statistical structures of data for better data filtering, analysis and processing. We will further apply our research to applications such as multimedia signal processing, video event detection and predictions, 5G IoT networks, social networks, finance and economic big data analysis.