# Combining Biomechanical Features and Machine Learning Approaches to Identify Fencers’ Levels for Training Support

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## Abstract

**:**

## 1. Introduction

## 2. Background and Related Works

#### 2.1. Background

#### 2.1.1. En Garde Position

#### 2.1.2. Distance Traveled

#### 2.1.3. Speed

#### 2.1.4. Lunge

#### 2.2. Related Works

- The devices used to collect data;
- The knowledge obtained from device-gathered data (3D kinematic and vertical ground reaction forces may be predicted);
- The processing of data from devices (classification methods can separate data into relevant packages that would have previously required sports scientists to spend much time on them);
- How processed data can improve our comprehension of athletic performance and injury risk prediction.

## 3. Materials and Methods

#### 3.1. Experiment Environments

#### 3.2. Data Collection

#### 3.3. Instruments

#### 3.4. Experimental Protocol

- Explosive lunge: the subject had to execute a lunge that was not demonstrative but pushed in order to hit the target as fast as possible;
- Step forward lunge: the subject was placed further away from the lunge, as the exercise consists of carrying out an offensive action in which the fencer must take a step forward to get to lunge distance in order to execute it and then stop the target;
- Step back lunge: the subject takes a step backward to get within lunge distance and then scores a hit.

#### 3.5. Data Pre-Processing

#### 3.6. Data Splitting and Dimensionality Reduction

`train_test_split`function from

`Scikit-learn`v1.0.2 library [38] with Python 3.9.0.

- $k=50$, for an overall of 650 total features;
- $k=25$, for an overall of 325 total features;
- $k=10$, for an overall of 130 total features;
- $k=5$, for an overall of 65 total features.

`Scikit-learn`v1.0.2 library, feeding in input $\mathtt{n}\_\mathtt{components}=k$. Therefore, four training and test sets have been produced.

#### 3.7. Machine Learning Algorithms

**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) $\left\{{\mathrm{T}}_{1}\left({x}_{i},{y}_{i}\right)\dots {\mathrm{T}}_{K}\left({x}_{i},{y}_{i}\right)\right\}$, 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 ${\widehat{y}}_{i}={\sum}_{k=1}^{K}{f}_{k}\left({x}_{i}\right),{f}_{k}\in F$. ${f}_{k}$ represents an independent tree structure with leaf scores, and F represents the space of all CARTs. This objective is defined as follows: $Obj\left(\mathsf{\Theta}\right)={\sum}_{i}^{n}l\left({y}_{i},{\widehat{y}}_{i}\right)+{\sum}_{k}^{K}\mathsf{\Omega}\left({f}_{k}\right)$. In the first term, we have a differentiable loss function, l, which measures the difference between $\widehat{y}$ and ${y}_{i}$ before prediction. The second regularization term, $\mathsf{\Omega}$, penalizes the complexity of the model to avoid overfitting, and it is provided by $\mathsf{\Omega}\left(f\right)=\gamma T+\frac{1}{2}\lambda {\sum}_{j-1}^{T}{w}_{j}^{2}$. 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 layer. Generally, activation functions are not linear and can take on $C\ast $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 $X=\{{x}_{1},\dots ,{x}_{n}\}$, and $Y={y}_{1},\dots ,{y}_{n}$. 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 $b=1,\dots ,B$, 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. Step (2) involves training the tree ${f}_{b}$ on $({X}_{b},{Y}_{b})$. (3) Out-of-sample prediction on unseen dataset ${x}^{*}$ is the response outcome resulting from most of the results generated from every single tree. The number of trees in the forest is the free parameter of the model, usually set to at least ${10}^{2}$.**Support Vector Machine (SVM) classifier**[43]. The SVM is a supervised learning algorithm based on the concept of optimal hyper-planes that separate observations belonging to two different classes. Assuming that n points belong to two linearly separable sets in p-dimensional space, the goal of the linear classification problem is to find a (p-1)-dimensional hyperplane that can classify two classes with the most extensive margins, e.g., the most significant distance from the nearest points in each set to the boundary. In cases where the original data cannot be linearly separable, one possibility is to map the original data onto a higher-dimensional feature space to achieve more effective separation. Hence, support vector classifiers are generalized linear classifiers based on an “augmented” feature space with significantly high dimensionality. Suppose the transformed feature vectors $h\left(x\right)$ are given by the function $h\left(x\right)$. In that case, the optimization problem can easily be transformed into a quadratic programming problem using Lagrange multipliers in which the transformed vectors are scalar products. Thanks to this trick, it is not important to know the transformation, but only the type of the kernel function $K(x,{x}^{\prime})=\langle h\left(\mathbf{x}\right),h\left({\mathbf{x}}^{\prime}\right)\rangle $. The selection of a kernel function and the regularization parameter C determine the configuration of an SVM classifier. The following functions were chosen for the hyper-parameter tuning phase: (1) $d\u2014$degree polynomials: $K(\mathbf{x},{\mathbf{x}}^{\prime})={(1+\langle \mathbf{x},{\mathbf{x}}^{\prime}\rangle )}^{d}$; (2) radial basis function (RBF): $K(\mathbf{x},{\mathbf{x}}^{\prime})=exp(-\gamma ||\mathbf{x}-{\mathbf{x}}^{\prime}{\left|\right|}^{2})$, where values of parameters d, $\gamma $, ${\kappa}_{1}$, and ${\kappa}_{2}$ span specific ranges.

`Python`, it recalled the functions of the Machine Learning contained in the

`scikit-learn`v1.0.2 library. This library was used to compare all models to identify the best suited to classify the élite and novice athletes and the model minimizing false-negative predictive values.

## 4. Results

#### 4.1. Evaluation Metrics

#### 4.2. Best Model Performance Analysis

#### 4.3. Best Model Hyperparameter Tuning

- hidden_layer_sizes’: [(sp_randint.rvs(100, 600, 1), sp_randint.rvs(100, 600, 1),),(sp_randint.rvs(100, 600, 1),)]
- activation: tanh, relu, logistic;
- solver: sgd, adam, lbfgs;
- alpha: 0.0001, 0.001, 0.01, 0.1, 0.9;
- learning_rate: "constant", "adaptive".

- hidden_layer_sizes: (586);
- activation: relu;
- solver: lbfgs;
- alpha: 0.1;
- learning_rate: constant.

#### 4.4. Experimental Setup

- Raw data acquisition of the signal;
- Creating the dataset through preprocessing;
- Applying PCA to the preprocessed data (k is determined based on the best model);
- The ML algorithm performs the prediction using the data described in the previous step.

#### 4.5. Performance Evaluation of the Absolute Best Model

## 5. Concluding Remarks and Perspectives

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Cycle of movement for lunging during the explosive lunge task (V.C.): start (

**a**), en garde (

**b**), lunge (

**c**). (

**a**) Representation of the start position during explosive lunge in the test environment. (

**b**) Representation of the en garde position during explosive lunge in the test environment. (

**c**) Representation of the final lunge position during explosive lunge in the test environment.

**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.

**Table 1.**Sociodemographic and anthropometric variables according to category (novice and élite). (All data are shown as mean ± (standard deviation) for continuous variables).

Variables | Novice | élite | Effect Size (ES) |
---|---|---|---|

Age (years) | 10.50 ± 3.14 | $16.31\pm 5.85$ | 0.72 (0.48, 0.97) |

BMI (kg/m${}^{2}$) | $18.87\pm 3.87$ | $22.29\pm 3.82$ | 0.39 (0.09, 0.73) |

W (kg) | $39.30\pm 11.87$ | $61.95\pm 11.86$ | 0.68 (0.48, 0.9) |

H (m) | $1.43\pm 0.08$ | $1.66\pm 0.12$ | 0.75 (0.63, 0.9) |

HGUARD (m) | $1.32\pm 0.08$ | $1.56\pm 0.13$ | 0.76 (0.63, 0.91) |

LLL (cm) | $73.66\pm 7.3$ | $90.00\pm 8.36$ | 0.74 (0.61, 0.9) |

CLL (cm) | $40.70\pm 6.38$ | $50.28\pm 9.58$ | 0.53 (0.26, 0.83) |

CUL (cm) | $22.70\pm 5.55$ | $27.46\pm 7.67$ | 0.44 (0.12, 0.77) |

Leq (cm) | $79.5\pm 2.67$ | $88.75\pm 2.23$ | 0.86 (0.77, 0.95) |

Model | k | Accuracy | Average | Precision | Recall | F1-Score |
---|---|---|---|---|---|---|

MLP | 5 | 0.88 | macro | 0.87 | 0.88 | 0.88 |

weighted | 0.88 | 0.88 | 0.88 | |||

SVM | 10 | 0.84 | macro | 0.83 | 0.83 | 0.83 |

weighted | 0.84 | 0.84 | 0.84 | |||

MLP | 25 | 0.84 | macro | 0.83 | 0.83 | 0.83 |

weighted | 0.84 | 0.84 | 0.84 | |||

MLP | 50 | 0.92 | macro | 0.92 | 0.92 | 0.92 |

weighted | 0.92 | 0.92 | 0.92 |

Category | Precision | Recall | F1-Score |
---|---|---|---|

Novice (0) | $90\%$ | $90\%$ | $90\%$ |

élite (1) | $93\%$ | $93\%$ | $93\%$ |

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## Share and Cite

**MDPI and ACS Style**

Aresta, S.; Bortone, I.; Bottiglione, F.; Di Noia, T.; Di Sciascio, E.; Lofù, D.; Musci, M.; Narducci, F.; Pazienza, A.; Sardone, R.; Sorino, P. Combining Biomechanical Features and Machine Learning Approaches to Identify Fencers’ Levels for Training Support. *Appl. Sci.* **2022**, *12*, 12350.
https://doi.org/10.3390/app122312350

**AMA Style**

Aresta S, Bortone I, Bottiglione F, Di Noia T, Di Sciascio E, Lofù D, Musci M, Narducci F, Pazienza A, Sardone R, Sorino P. Combining Biomechanical Features and Machine Learning Approaches to Identify Fencers’ Levels for Training Support. *Applied Sciences*. 2022; 12(23):12350.
https://doi.org/10.3390/app122312350

**Chicago/Turabian Style**

Aresta, Simona, Ilaria Bortone, Francesco Bottiglione, Tommaso Di Noia, Eugenio Di Sciascio, Domenico Lofù, Mariapia Musci, Fedelucio Narducci, Andrea Pazienza, Rodolfo Sardone, and Paolo Sorino. 2022. "Combining Biomechanical Features and Machine Learning Approaches to Identify Fencers’ Levels for Training Support" *Applied Sciences* 12, no. 23: 12350.
https://doi.org/10.3390/app122312350