Visibility Graph Analysis of Geophysical Time Series: Potentials and Possible Pitfalls

Posted 2020-11-23 dulun

Tasks: invest papers  3 篇. 研究主动权在我手里.  I have to. 

1. the benefit of complex network: 

complex network theory has been particularly successful in providing unifying统一的 concepts and methods for understanding the structure and dynamics of complex systems in many areas of science, ranging from power grids over social networks to neuronal networks.

2. the network is recurrence;  

3. VGs obtained from periodic signals appear as a concatenation of a finite number of network motifs. ?really?

4. 如何衡量一个高的节点, 根据节点的度/roles of graphs. 

the degree of a vertex in the VG characterizes the maximality property. however, this finding is not completely general. since there can be specific conditions (e.g., a concave behavior over a certain period of time) which can lead to highly connected vertices that do not coincide with local maxima, for example, in case of a Conway series.

并不是只有高的节点degree会高, 这结论不具有一般性, for example, in conway series, 最低的凹点会有更多的边. 

5. 邻边链接的重要性: the trivial connection of neighboring points in time in the VG enhances the signature of structures due to autocorrelations in the record under study.    

邻边 VS 子相关. 

Although this might be desirable for VGs and HVGs since some of their respective network properties are explicitly related with the presence of serial dependences (e.g., the typical scale of the degree distribution of HVGs, cf. Luque et al. 2009), there could be situations in which one is interested in removing the corresponding effects. In such cases, it is possible to introduce a minimum time difference for two observations to be connected in the network for removing the effect of slowly decaying autodependences, which would correspond to the Theiler window in other concepts of nonlinear time series analysis (Theiler 1990, Donner et al. 2010). 思考: 我需不需要include它们之间的自相关性.

6. 引入时间差来限制连接的两个观测值.  

7. You need to consider possible origins of pitfalls of VG analysis applied to Energy consumption. 

what‘s the pitfalls of VG analysis of your research right now. 

8. what kind of information can be obtained from VG analysis. 

i. four distributions of vertex properties: distributions of degree; local clustering coefficient; closeness centrality; and betweenness centrality.  

ii. the temporal changes in the VG properties: network transitivity T and average path length L. running windows 36o and a mutual offset of 30 days. 

9. Summary: 

由图分析TS 的两大分支, recurrence networks (Donner) and visibility graphs (Lacasa).  

However, the explicit interpretation of more complex local and global network characteristics in a visibility graph is less obvious than for recurrence networks and needs to be fully explored in future work prior to their wide potential application to real-world problems. 

VG 存在的问题: 网络特征的可解释性. 

the emergence of different topological features in VG reflects the time evolution of the network‘s architecture. 

 

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基础概念: 

1. 中心性（Centrality）是社交网络分析（Social network analysis, SNA）中常用的一个概念，用以表达社交网络中一个点或者一个人在整个网络中所在中心的程度，这个程度用数字来表示就被称作为中心度（也就是通过知道一个节点的中心性来了解判断这个节点在这个网络中所占据的重要性的概念）.

测定中心度方法的不同，可以分为度中心度（Degree centrality），接近中心度（或紧密中心度，Closeness centrality），中介中心度（或间距中心度，Betweenness centrality）等。more.

2. local clustering coefficent. more

几个用于描述网络节点距离的参数

• Average distance： 这个很好理解，就是所有两两节点之间的最短距离的平均值，最直接的描述了图的紧密程度。
• Eccentricity：这个参数描述的是从任意一个节点，到达其他节点的最大距离
• Diameter：图中的最大两个节点间的距离
• Radius：图中的最小两个节点间的距离
• Periphery： 和 Diameter 对应，那些最大节点距离等于 diameter 的节点
• Center： 和 Radius 对应，那些最大节点距离等于 radius 的节点

3. 自相关性:

金融时间序列一般由固定趋势、季节性变动和随机因素组成。如果时间序列的随机因素在各时间点上完全独立没有任何联系，那么我们很难对这一部分进行建模。幸运的是，对于一般的金融时间序列，在剔除固定趋势和季节效应后，时间序列在不同时点上是存在相关性的，这种自相关特征是我们对时间序列建模的基础。

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