## 3 Results  
### Consideration of Feature Extraction Required for Machine Learning Applications  
This section considers the feature extraction required for machine learning (ML) applications based on the frequency symbolic method. The subsequent sections detail the specific use cases, including the inputs, outputs, and ML approaches to be employed for each case. The basic steps in any artificial intelligence (AI) system development are as follows:  
1. Data Collection. 2. Feature Extraction (Data Conversion for applicable inputs of the ML system). 3. Target Definition (what is the target of the ML system?). 4. Model Selection. 5. Model Training. 6. Model Evaluation. 7. Parameter Tuning. Figure 1: Typical FSM steps and extracted feature sets. The key purpose of this work is to estimate the feature extraction and target definition steps from the list above. The data collection step could be accomplished by analyzing a set of parametric circuits with different parameters and configurations or by collecting statistics on configurations applied during FSM usage by researchers. The next steps, such as selection, training, and evaluation of the model are out of scope of this work and will be considered in further phases of the research. The feature extraction step in ML system development is devoted to converting input data into a vector of features, which later become the direct inputs to the ML model. The feature data type should typically be one of two types: numerical or categorical. Numerical values can take any continuous or discrete value within a given range. Categorical values can take one of the predefined values, such as [\"Yes\", \"No\"] or [\"Low\", \"Medium\", \"High\"]. Figure 1 shows the feature sets that can be extracted at different steps of FSM usage. The aforementioned feature sets are delineated and designated with unique identifiers:  
* I1 (Input type 1)--features extracted from the system of differential equations. * I2 (Input type 2)--features extracted from the transfer equation. * M1 (Method features 1)--features extracted from the System of Linear Algebraic Equations (SLAE) obtained using FSM. * O1 (Output features 1)--features extracted from the symbolic transfer function obtained using FSM. In consideration of the FSM steps illustrated in Figure 1, we present the selected list of features in Tables 1-4. As the ML application to the FSM progresses, we will provide more precise details regarding these features. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature ID and Short Name** & **Description** & **Data Type** & **Valid Range** \\ \hline I2.1 & & Order of the left part of the transfer equation. & Numerical & Positive integer number \\ \hline I2.2 & & Order of the right part of the transfer equation. & Numerical & Positive integer number \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proposed list of feature set I2 extracted in machine learning application to FSM. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature ID and Short Name** & **Description** & **Data Type** & **Valid Range** \\ \hline I1.1 & & Order of the left part & \\ Number of LC components & & & \\ \hline I1.2 & & Order of the right part of the transfer equation. & Numerical & Positive integer number \\ \hline I1.2 & & Order of the right part of the transfer equation. & Numerical & Positive integer number \\ \hline I1.3 & & Order of the right part of the transfer equation. & Numerical & Positive integer number \\ \hline I1.4 & & Order of the right part of the transfer equation. & Numerical & Positive integer number  
An example of the calculation of the complexity of a symbolic expression is shown in a separate chapter at the end of this article. Target Definition. This step is appointed to determine data and its type that is desired as output of the ML system. The output data can also be of numerical or categorical type. An example of target values is shown in Table 5.