Spectral energy change method
In the previous subsection, the graph structure data construction was achieved by the autocorrelation matrix method, but this method does not fully utilize the time-frequency characteristics, therefore, this paper proposes the spectral energy change method. This method constructs the graph structure data by analyzing the energy change of each frequency and the relative magnitude of energy between different frequencies. At the same time, this method can make maximum use of the original time-frequency features as the features of each node.
First, the whole time-frequency characteristics are divided into five parts: low frequency (
L), low and medium frequency (ML), medium frequency (
M), medium and high frequency (MH) and high frequency (
H), as shown in Fig.
10. The original frequency spectrum can be expressed as follows.
$$\begin{aligned} {\varvec{Dp} = [\varvec{DP}_L \varvec{DP}_\mathrm{{ML}} \varvec{DP}_M \varvec{DP}_\mathrm{{MH}} \varvec{DP}_H]^T} \end{aligned}$$
(22)
where
$$\begin{aligned} {\left\{ {\begin{array}{l} {\varvec{DP}_L = [\varvec{Dp}_1 \varvec{Dp}_2 \cdots \varvec{Dp}_{{F_0}/5}]}^T\\ {\varvec{DP}_{ML} = [\varvec{Dp}_{{F_0}/5 + 1} \varvec{Dp}_{{F_0}/5 + 2} \cdots \varvec{Dp}_{2{F_0}/5}]}^T\\ {\varvec{DP}_M = [\varvec{Dp}_{2{F_0}/5 + 1} \varvec{Dp}_{2{F_0}/5 + 2} \cdots \varvec{Dp}_{3{F_0}/5}]}^T\\ {\varvec{DP}_{MH} = [\varvec{Dp}_{3{F_0}/5 + 1} \varvec{Dp}{ _{3{F_0}/5 + 2} \cdots \varvec{Dp}_{4{F_0}/5}]}}^T\\ {\varvec{DP}_H = [\varvec{Dp}_{4{F_0}/5 + 1} \varvec{Dp}_{4{F_0}/5 + 2}\cdots \varvec{Dp}_{F_0}]}^T \end{array}} \right. } \end{aligned}$$
(23)
Different frequency bands contain the energy values of different frequency components at different time points. Depending on the moment, the average energy of different frequency bands is obtained separately. Taking the low-frequency band as an example,
$$\begin{aligned} {\varvec{DP}'_L(i) = \frac{5}{{{F_0}}}\sum \limits _{j = 1}^{{F_0}/5} {\varvec{Dp}_j}(i)} \end{aligned}$$
(24)
where
\(\varvec{DP}'_L\) denotes the average energy of low-frequency band at i moment. The average energy values of all frequency bands at different moments form the matrix
\(\varvec{\Gamma }\).
Next, construct graph structure data based on
\(\varvec{\Gamma }\). Define a mapping relation
\(\varsigma\),
$$\begin{aligned} \varsigma (\varvec{\Gamma }) \rightarrow \varvec{\Gamma }' \end{aligned}$$
(25)
where
\(\varvec{\Gamma }'\) is still a matrix and
\(\varvec{\Gamma }' \in {R^{5*{N_{SB}}}}\), has the same dimension as
\(\varvec{\Gamma }\). In
\(\varvec{\Gamma }'\), the elements of each column are rearranged according to the order of the size of elements in each column of
\(\varvec{\Gamma }\). That is, the average energy of different frequency bands at different moments with respect to the corresponding frequency bands is removed and replaced by the relationship between the magnitudes of the average energy of different frequency bands, while the relationship between the energy changes of the same frequency bands at different moments is retained. In short, constructing graph structure data with matrix
\(\varvec{\Gamma }'\) means rearranging the average energy values of different frequency bands at the same moment according to the magnitude of energy values, and defining a node of the graph with that value, and then connecting the nodes belonging to the same frequency band at different moments.
In practice, since the average energy value of the lower frequency band is always higher than the average energy of other frequency bands, this prevents the set of nodes generated by the lower frequency band from intertwining with the set of nodes generated by the other frequency bands. Therefore, a simple processing of the original data is required before constructing the graph structure data, defining
$$\begin{aligned} \varsigma (f(\varvec{\Gamma })) \rightarrow \varvec{\Gamma }' \end{aligned}$$
(26)
where
\(f( \cdot )\) is the operator, based on the matrix row vectors, subtracting the average value of each row vector, and finally interleaving the nodes constructed with different frequency bands. Figure
11 shows the schematic diagram of the graph structure data. Each circle in the figure represents a node, and the nodes with the same color indicate that they come from the same frequency band.
After the above steps, the graph structure data construction is finally achieved. In order to retain the original time-frequency features to the maximum extent, the time-frequency features are divided into features corresponding to nodes according to frequency bands and moments. Taking the moment
i of the low-frequency band as an example, the corresponding node features are
$$\begin{aligned} \varvec{x}_L(i) = [\varvec{Dp}_1(i) \varvec{Dp}_2(i) \cdots \varvec{Dp}_{{F_0}/5}(i)]^T \end{aligned}$$
(27)