## 2 Methods
### Simulation Example
#### 2.3.2 Machine Learning Algorithm for Classification
**Feature Selection:** Feature selection is an important aspect of the success of machine learning algorithms. A good choice of features helps improve classification performance, lower computational complexity, build more generalizable models and decrease the required storage [61]. The aim of feature selection is to extract features from data that represent the characteristics of each of the classes or groups. Since we are interested in tracking the stability of the human sensorimotor system and only the real part of estimated poles in the complex plane governs the stability, we only use the real part of the estimated poles for the rest of our analysis. We explore two sets of choices (C1 and C2) for feature selection. These choices of features are then used as input to the SVM to classify whether a particular individual is healthy or has PPD. **C1:** Since we are interested in the trend of the real part of the estimated poles over a period of time, the percentage changes in the real parts of poles with respect to the baseline (the estimated poles from the simulated response of the first movement control test) and the percentage change in the successive difference in the real parts of poles between simulated responses over a period of time are the features worth considering. However, in reality, it is very likely that the clinical task is not performed at fixed intervals of time for all subjects. Hence, we consider the rate of percentage change (either per month or per year) for both of the above-mentioned quantities as features. Based on preliminary simulation results, we find that only three features are sufficient for robust classification, namely, minimum percentage change rate in the real part of the poles, maximum percentage change rate in the successive difference between tests, and real part from the first clinical movement control test. The calculation of the percentage change rate in the real part of the poles and percentage change rate in the successive difference between tests are given in Table 1. Here, \(N\) is the total number of clinical movement control tests that are conducted possibly at irregular time intervals. \(T_{k}\) is the time duration between two trials, where \(k=1,2,\cdot\cdot\cdot,N-1\). \(x_{1}\) to \(x_{N}\) are the real parts of estimated poles, with subscripts indicating the test number. **C2:** For a second choice of features, since we are interested in determining whether the real part of estimated poles has an increasing trend, we use hypothesis testing as a tool to detect a statistically significant increasing trend in the presence of noisy data. With this approach, we use the statistical value of slope and the constant of the real part of estimated poles as features for the classification algorithm. Further, we also take the real part of the estimated poles of the simulation response of the first movement control test as the third feature as an indicator of the baseline for each individual. 2. Support Vector Machine for Longitudinal Analysis (LSVM) A recently developed method, called Longitudinal Support Vector Machine (LSVM) [62], is a method specifically developed for longitudinal data. Here, each data point takes the form of a single time series. LSVM is shown to have higher accuracy compared to SVM, linear discriminant analysis (LDA), and functional linear discriminant analysis (FLDA). Note that once we have real parts of estimated poles over a period of time, this method is formulated such that an additional feature selection is not required. \begin{table}
\begin{tabular}{l l} \hline \hline
**Features** & **Formula For Calculation** \\ \hline C1: & 1. Percentage change rate in real part of pole \\  & 2. Percentage change rate in successive difference \\  & of real part of poles between tests \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculation of features for C1 from the estimated poles.