Statistical Signal Processing and Learning on Networks and Graphs

随着人工智能技术的复兴，信号处理已经无处不在，可以处理来自各种来源的数据。许多数据，无论是来自传感器网络和社交网络等网络来源，还是来自图像和视频等其他来源，都包含明确或隐含的结构化关系，这些关系可以用图表来最好地表示。这些类型的网络数据对信号处理研究提出了新的挑战。近年来针对图结构数据的信号处理和统计建模技术主要包括：a)图建模和学习理论；b)图信号处理。然而，这些理论和方法并没有在新兴应用所带来的各种限制下得到充分的研究，以解决诸如定位和跟踪，源识别，网络上的最佳过滤等问题。此外，在许多情况下，识别或学习未知或隐含的网络/图结构是一个非常具有挑战性的问题。拟议研究的总体目标是系统地开发新的信号和数据处理理论和方法，用于显式（如传感器网络）或隐式（如视频）数据、基于非局部图的底层关系和/或动态信息扩散流，以及在传感器/社交网络、5G物联网（IoT）无线网络、多模态多媒体内容分析和经济大数据中的应用。具体目标是(i)在传感器网络上开发用于动态多目标定位和跟踪的通用网络统计信号处理和推理模型和方法；（ii）根据图移算子理论，在网络信息扩散过程中产生的数据存在噪声和干扰的情况下，识别原始信号源，并在网络上开发最佳过滤和预测方法；在网络结构未知的情况下，开发最优学习算法来估计网络结构；（iii）设计最能代表数据复杂的非局部隐相关和统计结构的图移算子或流形核，以便更好地对数据进行过滤、分析和处理。我们将进一步将研究成果应用于多媒体信号处理、视频事件检测与预测、5G物联网、社交网络、财经大数据分析等领域。

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.