## 2 Methods
### Simulation Example
#### 2.3.2 Machine Learning Algorithm for Classification  
Once we estimate poles from the measured data, the next step is to apply a classification algorithm for classifying whether a particular data (for example, one of the traces in Figure 3) is from the data set representing a healthy individual or the data set representing an individual with PPD. In the healthy individual data set, despite variabilities due to numerous factors, we do not expect the estimates of poles to have a significant trend of moving towards the right half of the complex plane. On the other hand, for the data set representing individuals with PPD, we expect at least one of the estimates of poles to have a significant trend of moving towards the right half of the complex plane. Now, one way to identify this significant trend compared to healthy individuals is to use simple statistical tests or a classifier based on simple thresholds. Exploring this approach with the synthetic data, we find that a reliable classification using a threshold alone is not a robust approach. This is partly due to the significant overlap between poles of the human sensorimotor system for healthy and PPD groups in simulated data (representing inter-subject variability), and perhaps partly due to the stochastic variability as apparent in Figure 3. Therefore, we explore machine learning algorithms for a more robust classification. Typically, the input  
Figure 2: Output of the simulation example representing data from a single clinical movement control test with different variances of noise. Here, the sensorimotor delay value is 0.105 s with the addition of system and measurement noise of variance 0, 0.01, and 0.1, respectively. to the machine learning algorithm is a set of features derived from the data. For instance, to classify whether a particular individual has a benign or malignant tumor, the tumor size and age at diagnosis are possible features to consider [59]. Using these features, a machine learning algorithm trains a model that best describes the relationship between input (features) and output (class) for those data and uses this model to classify the new data. In the following subsections, we briefly describe two machine learning algorithms. 1. Support Vector Machine: Support Vector Machine (SVM) [60] is a supervised machine learning algorithm, that given the training data with their features and class labels identified a priori, determines the maximum margin hyperplane in feature space. Maximum margin hyperplane is a plane in feature space from which the distance to the nearest data points of both classes is maximized. Once the maximum margin hyperplane is determined, depending on the position of the new data set in the feature space, that is, whether new data are lying below the hyperplane or above the hyperplane, each new data set is classified as either Class 1 or Class 2. In the case of outliers in data or data that are not linearly separable, a variant of SVM is used that  
Figure 3: The real part of estimated poles from the synthetic data set representing the sensorimotor loop system for ten individuals over nine time units (each unit may represent several months) for (**a**) a gradual increment in delay, and (**b**) a gradual increment in gain. Out of 10 individual data, 5 represent simulated healthy individuals (solid blue), and 5 represent simulated PPD (dashed red). These data also show the regular or irregular nature of clinical movement control tests over time units. Simulations with gradual increments in gain are at regular intervals, and simulations with gradual increments in delay are with regular and irregular intervals of clinical movement control tests. It is clear that due to the stochasticity, the trends are not clearly distinguishable (especially if there are only a few data points), and hence, a robust classification algorithm is needed. finds a non-linear boundary to separate both classes of data. For further details, refer to [60].