随机图信号的一类双随机移位算子及其有界性
A Class of Doubly Stochastic Shift Operators for Random Graph Signals and their Boundedness
摘要：
提出了一类双随机图移位算子（GSO），证明了它具有：（i）局部平稳随机图信号的$L_{2}$ -上有界性;（ii）\textit{i.i.d.}随机图信号的$L_{2}$ -等距性，其中顶点的邻域大小渐近增加;（iii）保持任何图信号的均值.这些属性是通过统计一致性分析的图形移位，并通过利用双随机GSO作为马尔可夫（扩散）矩阵和作为一个无偏期望算子的双重作用。在现实世界中的多传感器信号滤波设置的双随机GSO类的实际效用。
英文摘要：
A class of doubly stochastic graph shift operators (GSO) is proposed, which is shown to exhibit: (i) lower and upper $L_{2}$-boundedness for locally stationary random graph signals; (ii) $L_{2}$-isometry for \textit{i.i.d.} random graph signals with the asymptotic increase in the incoming neighbourhood size of vertices; and (iii) preservation of the mean of any graph signal. These properties are obtained through a statistical consistency analysis of the graph shift, and by exploiting the dual role of the doubly stochastic GSO as a Markov (diffusion) matrix and as an unbiased expectation operator. Practical utility of the class of doubly stochastic GSOs is demonstrated in a real-world multi-sensor signal filtering setting.
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