网络参数的近似熵
Approximate entropy of network parameters
摘要：
我们在网络理论的框架内研究近似熵的概念。近似熵是最初在动力系统和时间序列的背景下提出的不确定性度量。我们首先定义了一个纯粹的结构熵，通过计算所谓的幻灯片序列的近似熵获得。这是度序列的替代，它是由图的频率划分建议的。我们研究了标准无标度网络和Erdens-Rényi网络的这个量。利用Pincus的经典结果，我们证明了我们的熵测度随网络规模收敛到一定的二进制香农熵。第二步，特别注意由动态过程产生的网络，我们研究水平可见性图的近似熵。可见性图允许自然地将时间相关性的概念与网络相关联，因此提供了动态服装的测量。我们表明，近似熵区分不同复杂性的过程所产生的可见性图。结果在更大程度上探讨了这些网络的动力系统的研究。最后考虑在这两种方法的光在癌症基因组学中产生的某些生物数据的应用。
英文摘要：
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural entropy obtained by computing the approximate entropy of the so called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdős-Rényi networks. By using classical results of Pincus, we show that our entropy measure converges with network size to a certain binary Shannon entropy. On a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs permit to naturally associate to a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.
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