## 3 Results
### Performance Evaluation of the Proposed Complex Network Method Using the Simulated Signals  
The purpose of the experiment is to use Lorenz signals and random signals as examples to verify the ability of our method to convert time series into network representations. Random time series are comprised of sequences of sequentially uncorrelated random variables. In our study, the random signals utilized consist of uniformly distributed pseudo-random numbers within the interval (0, 1). Figure 4a illustrates an example of the random time series used in our study, comprising 2000 samples (data points). To further underscore the robust applicability of the proposed method, which constructs a complex network for time series analysis, we extend our investigation to constructing networks for chaotic signals. In our experimentation, simulated chaotic signals are generated using a Lorenz system with the system function defined by Equation (10). This equation yields components \(x\), \(y\), and \(z\), corresponding to the convection velocity, temperature difference, and temperature gradient components, respectively. Figure 4b portrays an example of the \(x\) component of the Lorenz system employed in our experiment, comprising 2000 samples. \[\left\{ \begin{array}{l}\frac{dx}{dt}=-10\times(x-y)\\ \frac{dy}{dt}=30\times x-y-x\times z\\ \frac{dx}{dt}=x\times y-\frac{y}{3}\times z\end{array} \right. \tag{10}\]  
In the context of our proposed complex network methodology for constructing networks from random signals, the scalar time series undergo an initial reconstruction process into a sequence of ordinal partitions. This reconstruction is based on the phase space reconstruction method, utilizing different embedded dimensions (d = 6) with a fixed time lag (\(\tau\) = 2). In accordance with the definition of the proposed method, which constructs a complex network, each ordinal partition is considered a network node, characterized by a specific set of ordinal patterns. As shown in Figure 5a,b, the experimental results of the adjacency matrix of the unweighted network structure for the random signal and Lorenz signal x components of two thousand samples are presented, based on the proposed new method with embedded dimension d = 6 with time lag \(\tau\) = 2. Figure 4: Experimental results from random signals and Lorenz signals by the proposed network construction method. (**a**) An example of random time series; (**b**) An example of x component of Lorenz system by the proposed network construction method. We established 10 sets of Lorenz signals and 10 sets of random signals, employing the proposed method to extract the NDE and AND network features from these respective signal sets. A comparative analysis of the feature results was conducted. Figure 6a shows the AND results for the 10 sets of Lorenz signals; the range of the AND values is from 330 to 390. Figure 6b shows the AND results for the 10 sets of random signals; the range of the AND values is from 5.35 to 5.55. From Figure 6a,b, it can be concluded that the AND value of the Lorenz signal is significantly higher than that of the random signal. In Figure 6c, a box plot is presented for the NDE results, illustrating a comparison between the Lorenz signals and random signals. The median NDE value of the Lorenz signal is 4.34, while the median NDE value of the random signal is 3.42. The NDE value of the Lorenz signal is larger than that of the random signal. The time series with different characteristics exhibit significant differences in their network parameters, which is the significance demonstrated by Figure 6.  
Figure 5: Experimental results for the adjacency matrix of the network construction from random signals and Lorenz signals by the proposed network construction method using embedded dimension \(\mathrm{d}=6\) with time lag \(\tau=2\). (**a**) The result of the adjacency matrix for the random signal; (**b**) The result of the adjacency matrix for the Lorenz signal x components.