## 2 Materials and Methods
### Machine Learning
#### 2.6.2 Classification Methods  
We treated the A-scans as time series with up to 2048 elements and thus faced a non-trivial time series classification (TSC) task. We embedded all methods in a general data processing pipeline (see Figure 8) and deployed a strict leave-one-out cross-validation (LOOCV) regime for all ML-based classifications. Thus, to evaluate the performance of a model, all 25 A-scans of a given subject were used as input data for a model that has been trained on all A-scans of all other subjects. Those A-scans were either raw unprocessed or preprocessed 1D ultrasound radio frequency signals.  
We obtained a binary prediction for each A-scan of each participant (i.e., 25 predictions for each of the 120 eligible participants). Those predictions were then compared to the ground truth to obtain the F\({}_{1}\) score for each participant. These F\({}_{1}\) scores of each participant were then averaged to obtain the final F\({}_{1}\) score for the whole model.  
The ML methods used for TSC were 1-NN DTW, SVM, logistic regression, MLP, FCN, ResNet, RBF neural networks, XGBoost, LightGBM, and CatBoost.  
We include deep learning algorithms based on 1D US RF signals as those have recently been shown to be accurate in similar classification scenarios, such as the \"diagnosis of nonalcoholic fatty liver disease and hepatic fat fraction quantification when other causes of steatosis are excluded\" [41]. Other methods have been included due to their general TSC performance.  
MLPs work well as TSC baseline but do not exhibit any spatial invariance, as each time stamp has its own weight and the temporal information is lost [32]. It has been shown that FCNs can work well in TSC settings [31; 32] if convolutions are applied as sliding windows on the input signal. By applying several convolutions, it becomes possible for FCNs to learn multiple discriminative features. If the same convolutions are used for all time series, an FCN learns filters that are invariant across the time dimension [32]. ResNet was first adapted for TSC in 2017 [31] and has been refined in later work [32], in which it performed comparatively well. We included this refined architecture in our evaluation as  
Figure 8: General workflow of the complete data processing pipeline.  
we expected it to be superior to other relatively shallow architectures. RBF neural networks use radial basis functions as activation functions and typically only consist of an input layer, a hidden layer with a nonlinear RBF activation function, and a linear output layer [33]. We included this approach in our evaluation as it historically performed well on 1D US RF signals [42]. k-NN DTW algorithms classify signals based on their respective DTW distance to each other. The DTW metric is able to match patterns of different signals, regardless of their positions. Even though this algorithm has been known for decades, a comprehensive evaluation of different TSC algorithms concluded that many of the tested algorithms were no better than 1-NN DTW in a 2016 publication [24]. GBM models, consisting of ensembles of weak prediction models to achieve superior accuracies, are usually based on decision trees and have shown promising results in the past. We have already observed suitable results with GBMs in other work classifying similar 1D US RF signals to identify advanced hepatic steatosis and fibrosis using ML algorithms in patients with non-alcoholic fatty liver disease [43].  
Our aim was to obtain binary predictions to distinguish between ongoing or finished bone growth in the epiphyseal plate of the radius bone. To this end, we categorized all subjects with bone ages < 18 years and bones ages \(\geq\) 18 years into different groups. For DSP and 1-NN DTW, the pipeline processes each A-scan separately. For the ML methods, iterations over each subject create a model trained on data from all other subjects of the database. We evaluated each model by presenting it with the data from the test subject, performing a leave-one-out cross-validation.