Inference of Spatio-Temporal Functions Over Graphs via Multikernel Kriged Kalman Filtering
Inference of Spatio-Temporal Functions Over Graphs via Multikernel Kriged Kalman Filtering
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DOI：
10.1109/tsp.2018.2827328
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发表时间：
2017-11
影响因子：
5.4
通讯作者：
V. Ioannidis;Daniel Romero;G. Giannakis
中科院分区：
文献类型：
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作者：
V. Ioannidis;Daniel Romero;G. Giannakis
图上的时空变化信号的推断在大量的网络科学相关应用中自然出现。一个经常遇到的挑战涉及重建这样的动态过程，给定它们的值在一个子集的顶点和时刻。本论文开发了一个图形感知的基于核的克里格卡尔曼滤波器，占时空变化，并提供有效的在线重建，即使是动态演变的网络拓扑结构。基于内核的学习框架通过利用图形信号相对于底层图形所表现出的平滑性来绕过对统计信息的需求。为了解决选择合适的内核的挑战，建议的过滤器相结合的多内核选择模块。这种数据驱动的方法在预先选择的字典的线性跨度内选择与信号动态动态一致的内核。新的多核学习算法利用拉普拉斯核矩阵的特征结构来降低计算复杂度。使用合成和真实的数据进行的数值测试表明，相对于最先进的替代方案，该新型方法具有优越的上级重建性能。
Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To address the challenge of selecting the appropriate kernel, the proposed filter is combined with a multikernel selection module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly within the linear span of a preselected dictionary. The novel multikernel learning algorithm exploits the eigenstructure of Laplacian kernel matrices to reduce computational complexity. Numerical tests with synthetic and real data demonstrate the superior reconstruction performance of the novel approach relative to state-of-the-art alternatives.