论文标题
时间顶点和边缘信号的自适应关节估计
Adaptive Joint Estimation of Temporal Vertex and Edge Signals
论文作者
论文摘要
当边缘信号的更改影响顶点信号的时间动力学时，图形上共存的时间顶点（节点）和边缘信号的自适应估计是关键任务。但是，当前的图形信号处理算法主要仅考虑图形顶点上存在的信号，并忽略了信号可以驻留在边缘上的事实。我们提出了一种自适应关节顶点边缘估计（AJVEE）算法，用于通过随时间变化的回归来共同估计随时间变化的顶点和边缘信号，并结合了顶点信号滤波和边缘信号滤波。伴随AJVEE是一种基于Hodge Laplacian（Alms-Hodge）的新提出的自适应最不均方形程序，该程序的灵感来自经典的自适应过滤器，结合了简单的过滤和简单的回归。 AJVEE能够通过将两个在顶点和边缘上指定的施舍霍奇合并为统一配方，可以在顶点和边缘共同操作。正在讨论一个更普遍的案例将AJVEE扩展到顶点和边缘之外。在实验现实世界的交通网络和人口迁移率网络上，我们已经确认我们提出的AJVEE算法可以准确，共同跟踪图表上时变的顶点和边缘信号。
The adaptive estimation of coexisting temporal vertex (node) and edge signals on graphs is a critical task when a change in edge signals influences the temporal dynamics of the vertex signals. However, the current Graph Signal Processing algorithms mostly consider only the signals existing on the graph vertices and have neglected the fact that signals can reside on the edges. We propose an Adaptive Joint Vertex-Edge Estimation (AJVEE) algorithm for jointly estimating time-varying vertex and edge signals through a time-varying regression, incorporating both vertex signal filtering and edge signal filtering. Accompanying AJVEE is a newly proposed Adaptive Least Mean Square procedure based on the Hodge Laplacian (ALMS-Hodge), which is inspired by classical adaptive filters combining simplicial filtering and simplicial regression. AJVEE is able to operate jointly on the vertices and edges by merging two ALMS-Hodge specified on the vertices and edges into a unified formulation. A more generalized case extending AJVEE beyond the vertices and edges is being discussed. Experimenting on real-world traffic networks and population mobility networks, we have confirmed that our proposed AJVEE algorithm could accurately and jointly track time-varying vertex and edge signals on graphs.
