Kernel-Based Reconstruction of Space-Time Functions on Dynamic Graphs
Kernel-Based Reconstruction of Space-Time Functions on Dynamic Graphs
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DOI：
10.1109/jstsp.2017.2726976
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发表时间：
2017-09-01
影响因子：
7.5
通讯作者：
Giannakis, Georgios B.
中科院分区：
文献类型：
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作者：
Romero, Daniel;Ioannidis, Vassilis N.;Giannakis, Georgios B.
基于图的方法遍及许多学科的推理工具包，包括社会学、生物学、神经科学、物理学、化学和工程学。在此上下文中遇到的一个具有挑战性的问题涉及确定一组顶点的属性，给定另一个子集在可能不同的时间点的属性。利用时空动态可以大大减少观察到的顶点数量，从而减少采样成本。为了缓解现有方法的局限性，本文拓宽了基于核的图函数估计框架，在可能的时间演化拓扑上重构时间演化函数。这种方法继承了基于内核的方法的通用性和通用性，不需要关于分布或二阶统计的知识。提供了系统的指导方针来构建两类具有互补优势的时空核：第一类有助于在时空频率平面上对正则化进行明智的控制，而第二类则适应时变拓扑。同时提出了批估计器和在线估计器。后者包括一种新的核卡尔曼滤波器，用于以可承受的计算成本重建时空函数。实际数据集的数值测试证实了所提出方法相对于竞争方案的优点。
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly different time instants. Leveraging spatiotemporal dynamics can drastically reduce the number of observed vertices, and hence the sampling cost. Alleviating the limited flexibility of the existing approaches, the present paper broadens the kernel-based graph function estimation framework to reconstruct time-evolving functions over possibly time-evolving topologies. This approach inherits the versatility and generality of kernel-based methods, for which no knowledge on distributions or second-order statistics is required. Systematic guidelines are provided to construct two families of space-time kernels with complementary strengths: the first facilitates judicious control of regularization on a space-time frequency plane, whereas the second accommodates time-varying topologies. Batch and online estimators are also put forth. The latter comprise a novel kernel Kalman filter, developed to reconstruct space-time functions at affordable computational cost. Numerical tests with real datasets corroborate the merits of the proposed methods relative to competing alternatives.