The Study Of Transformation From Time Series To Complex Networks

In everyday life, we always encounter a variety of very complex network, such as:Internet network, interpersonal networks, communication networks and aviation network and so on. Although the networks become even more complex, but people always feel the world is getting smaller and life get efficient. Complex networks is belong to traditional graph theory, it can be seen as a collection of individuals with characteristics and mutually connected nodes, each individual as one of the nodes, the individual as a direct link edges in the graph. However, complex network is generally relatively large size of the network and generally formed by a complex evolution, the characteristics of the node itself is complex and connecting structure is very sparse and complex, which makes it different from traditional graph(e.g. lattice graph and random graph). Complex networks always hold the following feature:distribution with heavy tails, high clustering coefficient, community structure and hierarchy, and so on. Hsue-shen Tsicn had given the complexity of the network provides a more rigorous definition: A graph can be called as complex networks if it hold several or all of these features:self-organizing, self-similar, attractor, small-world, scale-free. There are two very classic network: small-world networks and scale-free networks. Small-world networks is always very large in node but very small in diameter, that is, any node is very easy to get to another node with only a handful of edges. That is, we often say six degrees of separation, people will feel more and more small planet into a global village. Scale-free networks are characterized by the degree distribution following power law distribution. A small number of nodes connect to the majority node which become the center of the network, while the majority of the nodes has only a few connections. Such as weibo-following-networks, some celebrities have high degree of concerning. In principle, for a system, if one exists, and interaction with a large number of structural units, can be abstracted as a complex network. This makes complex networks has become a powerful tool for the study of complex systems in biology, physics, chemistry, sociology, and so has a very wide range of applications.So, can the complex network be a tool to study the time series? The most prominent problem is how to convert the time series to complex networks. There are already many researchers proposing a number of very effective conversion strategies. Among them, Lucas Lacasa proposed the so-called Visibility Graph and has got very outstanding results. Here we think the time series as bar chart in a two-dimensional plane. All the data is treated as a "bar", we can "see" the other pillars on these bars. A bar can see another bar if and only if there is no obstacle between them. In this way, we treat each "bar" as a node, if the two "bars" can see each other, then they can be connected in the associated graph. Based on this strategy, the time series can be converted to a complex network very easily. In this way, networks always hold: full connectivity, each node can "see" its neighbours, it is all connected graphs; isotropic, which is determined by the reversibility of light; uniqueness, the visibility criterion is invariant under rescaling of both horizontal and vertical axes, and under horizontal and vertical translations. Lucas Lacasa also noted that by this strategy, the periodic series is transformed into regular graph, random series into a random graph, fractal series into scale-free networks.Although there are many outstanding works based on visibility graph., the basic strategy is still time-consuming. As we all know, the number of nodes in complex network is even larger. If the strategy is not very effective, it is surely an obstacle to future studies. This article is focused on geometric characteristics of visibility graph to find a even more optimized transformation. Confirmation and experiments are given to demonstrate the effectiveness of the proposed strategy. By studying the relationship between Hurst exponent of time series and its transformed networks, a new way to estimate Hurst exponent is given.