## 3 Materials and Methods
### Machine Learning Algorithms  
In order to determine the best classifier to predict the athlete class (novice or elite), we analyzed the following models:  
* **eXtreme Gradient Boosting (XGBoost) classifier**[40]. The most crucial factor behind the success of XGBoost is its scalability in all scenarios due to several essential systems and algorithmic optimizations. It is an ensemble of \(K\) classification and regression trees (CART) \(\{\mathrm{T}_{1}(x_{i},y_{i})\dots\mathrm{T}_{K}(x_{i},y_{i})\}\), where \(x_{i}\) is the given training set of descriptors associated with a prediction of the class label, \(y_{i}\). A CART assigns a real score to every leaf (outcome or target), so a combination of all prediction scores is used to get the final score, as indicated in \(\hat{y_{i}}=\sum_{k=1}^{K}f_{k}(x_{i}),f_{k}\in F\). \(f_{k}\) represents an independent tree structure with leaf scores, and \(F\) represents the space of all CARTs. This objective is defined as follows: \(\mathrm{Obj}(\Theta)=\sum_{i}^{l}l(y_{i},\hat{y_{i}})+\sum_{k}^{K}\Omega(f_{k})\). In the first term, we have a differentiable loss function, \(l\), which measures the difference between \(\hat{y}\) and \(y_{i}\) before prediction. The second regularization term, \(\Omega\), penalizes the complexity of the model to avoid overfitting, and it is provided by \(\Omega(f)=\gamma T+\frac{1}{2}\lambda\sum_{j=1}^{T}w_{j}^{2}\). A leaf score is determined by the number of leafs \(T\) and the number of leafs \(w\). The constants \(\gamma\) and \(\lambda\) control how much regularization occurs. Using regularization, shrinkage, and descriptor subsampling are additional methods of preventing overfitting. * **Multilayer Perceptron (MLP)**[41]. It is a supervised learning algorithm that uses a feed-forward neural network technique. It consists of a layer of input, a hidden layer of threshold logic units (TLUs), and a layer of output. The hidden layers are all connected, and each TLU computes a weighted sum of its inputs before applying an activation function to provide a result that will be used as input for the next  
Figure 3: Feature dataset signals during explosive lunge cycle: accelerations (**a**), angular velocities (**b**), pelvis angles (**c**), muscle envelopes (**d**). (**a**) Acceleration signals along IMU reference system axes. (**b**) Angular velocity signals along IMU reference system axes. (**c**) Pelvis angle signals along pelvis reference system axes. (**d**) Muscles envelope signals of the four target muscles. layer. Generally, activation functions are not linear and can take on C*1-differential forms. Back-propagation algorithms are based on making predictions and measuring performance (error) for every training instance. Thus, each layer is reversed to assess the contribution of each connection to the error; then, edge weights are modified to improve performance. * **Random forest (RF) classifier**[42]. It is one of the best classifiers in terms of predictability and efficiency for high-dimensional datasets. It is a supervised learning algorithm based on constructing a collection of decision trees. For prediction, the RF model produces a variety of decision trees in the training phase, intending to reduce the variance of the final result by determining the class predicted most commonly by each tree within the forest. RF training algorithm consists of incorporating bootstrap aggregation to trees under training. \((X,Y)\) denotes the pair of training set \(X\) and target vector \(Y\), where \(X=\{x_{1},\ldots,x_{n}\}\), and \(Y=y_{1},\ldots,y_{n}\). By replacing a random sample from \(X\) with a repeated (\(B\) times) extraction, the trees are fitted to this sample and repeated. In particular, for \(b=1,\ldots,B\), the procedure is as follows: (1) Random sampling with replacement of \(n\) observations from the training set \(X\) to obtain \((X_{b},Y_{b})\) subsets. To reduce the correlation between trees originating from bagging, the cardinality of the subset is usually of order \(\sqrt{p}\) for a classification problem with \(p\) features.