## 2 Data Processing and Network Description
### Temporal Singular Spectrum Graph  
This paper proposes an improved transformation method for visualizing sequential data called Temporal Singular Spectrum Graph (TSSG). The specific implementation is as follows:  
* Preprocessing. For a sequence \(S=\{s_{1},s_{2},\ldots,s_{N}\}\) with length \(N\), the sequence is first standardized by the following formula:  
Figure 1: Flowchart of the algorithm. \[x_{i}=\frac{(s_{i}-\mu)}{\sigma}, \tag{4}\]  
where \(\mu\) represents the mean of the sequence, and \(\sigma\) represents the standard deviation of the sequence. In this method, for each value in the sequence data, it is subtracted by the mean of the sequence and then divided by the standard deviation of the sequence. This transformation ensures that each value in the sequence becomes a deviation from the mean, relative to the standard deviation of the sequence. It normalizes the variables to the same scale, making them comparable in numerical terms and improving the accuracy of subsequent classifiers. As a result, a new sequence \(X=(x_{1},\ x_{2},\ldots,x_{n})\) is obtained, with a mean of 0 and a standard deviation of 1. * Constructing trajectory matrix. For the given sequence, a sliding window is defined with a window length of \(L\), satisfying \(L\leq\frac{T}{2}\). Simultaneously, \(K\) is defined as \(K=N-L+1\), which is used to construct the trajectory matrix. The first column of the matrix represents \(y_{1}\) to \(y_{L}\), the second column represents \(y_{2}\) to \(y_{L+1}\), etc., until the \(L\)-th column represents \(y_{K}\) to \(y_{N}\). The resulting trajectory matrix is as follows: \[\mathbf{Y} =\left(x_{ij}\right)_{ij=1}^{L,K}\] \[=\left( \begin{array}{ccccc}y_{1}&y_{2}&y_{3}&\ldots&y_{K}\\ y_{2}&y_{3}&y_{4}&\ldots&y_{K+1}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ y_{L}&y_{L+1}&y_{L+2}&\ldots&y_{N}\end{array} \right)\,\] (5) The matrix \(\mathbf{Y}\) is a Hankel matrix, where \(y_{i,j}=y_{i-1,j+1}\). Singular Value Decomposition (SVD). The matrix \(\mathbf{Y}\) is subjected to Singular Value Decomposition, resulting in matrices \(\mathbf{U}\),\(\mathbf{V}\),\(\mathbf{\Sigma}\), where \(\mathbf{U}\) and \(\mathbf{V}\) are orthogonal matrices, and \(\mathbf{\Sigma}\) is the singular value matrix. The singular values are denoted as \(\sigma\) and are sorted in descending order: \(\sigma_{1}\geq\sigma_{2}\geq\ldots\geq\sigma_{L}\geq 0\). The contribution value \(C_{i}\) is defined as  
Visualization. The reconstructed sequence \(R\) is copied \(k\) times along the column direction, and then the transpose of \(R\) is obtained as a \(k\times 1\) column vector. This process generates two matrices: one where each row is equal to \(R\), and another where each column is equal to \(R\). By subtracting these two matrices, a \(k\times k\) matrix \(\mathbf{M}\) is obtained, representing the Euclidean distance between every pair of points. Similar to a recursive graph, each row and column of matrix \(\mathbf{M}\) contains information about the entire sequence. Finally, the matrix \(\mathbf{M}\) is transformed into a grayscale image using max-min normalization, resulting in the desired image. Figure 2 illustrates the transformed images of signal sequences from the RadioML2018.01a dataset, from which we can see that TSSG can effectively capture the information of the original signals. The figure showcases four different signals (32 PSK, QPSK, OOK, 64 QAM) represented as TSSG, generated under 30 dB SNR. Each signal is divided into the I and Q components. In the waveform plots, the I component is depicted in blue, while the Q component is shown in red. To better visualize the characteristics of these signals, each group of images consists of the TSSG of the I component on the left and the TSSG of the Q component on the right. From Figure 2, we can clearly observe the characteristics of the original signals. Rapidly changing signals in the waveform plot are represented by abrupt color transitions, while smoothly changing signals appear as regions of solid color.