Abstract
In this paper, we compare two methods of mapping time series data to complex networks based on correlation coefficient and distance, respectively. These methods make use of two different physical aspects of large-scale data. We find that the method based on correlation coefficient cannot distinguish the randomness of a chaotic series from a purely random series, and it cannot express the certainty of chaos. The method based on distance can express the certainty of a chaotic series and can distinguish a chaotic series from a random series easily. Therefore, the distance method can be helpful in analyzing chaotic systems and random systems. We have also discussed the effectiveness of the distance method with noisy data.
Highlights
A complex system can be analyzed by its outputs which are typically in a form of largescale time series
This paper investigates novel methods to analyze the properties of a time series based on complex networks.[1,2,3]
We contrast the differences between the methods based on distance and linear correlation. We find that these two connection methods transform the same time series into different network graphs
Summary
A complex system can be analyzed by its outputs which are typically in a form of largescale time series. We define a node as a point in the reconstructed phase space of different dimension, i.e., a series segment of different length. The definition of connection is more important and represents the key difference among different methods to transform time series into network graphs. We contrast the differences between the methods based on distance and linear correlation We find that these two connection methods transform the same time series into different network graphs. The method based on distance can differentiate constant series, periodic series, linear series, chaotic series, and random series. It can express the certainty of chaos, but the method based on correlation coefficient cannot. The total number of nodes is n − m + 1
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