Statistical Signal Processing and Learning on Networks and Graphs

信号处理沿着复苏的人工智能技术已经变得无处不在，可以处理来自各种类型来源的数据。来自传感器网络和社交网络等网络源或来自图像和视频等其他源的许多数据都包含显式或隐式的结构化关系，这些关系可以通过图形来最好地表示。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，针对具有图形结构的数据的信号处理和统计建模技术主要包括a）图形建模和学习理论，以及B）图形信号处理。然而，这些理论和方法还没有得到充分的研究下所提出的新兴应用，以解决问题，如定位和跟踪，源识别，网络上的最优滤波的各种约束。此外，在许多情况下，未知或隐式网络/图结构的识别或学习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，用于具有显式（如传感器网络）或隐式（如视频）的数据，底层基于非局部图的关系和/或动态信息扩散流，以及传感器/社交网络，5G物联网（IoT）无线网络，多模态多媒体内容分析，经济大数据。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）基于图移位算子理论，在存在噪声和干扰的情况下，识别由网络信息扩散过程产生的数据的原始信号源，并开发网络上的最佳滤波和预测方法;还开发最佳的学习算法，以估计网络结构，如果它是未知的;和（iii）设计一个图形移动操作或流形内核，可以最好地表示复杂的非局部隐藏的相关性和统计结构的数据，更好的数据过滤，分析和处理。我们将进一步将我们的研究应用于多媒体信号处理，视频事件检测和预测，5G物联网网络，社交网络，金融和经济大数据分析等应用。

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.