## 2 Materials and Methods
In our case, the following formula is used:  
\[L_{(y,\overline{y})}=-\left[y\,*\,log\left(\overline{y}\right)+(1-y)\,*\,log \left(1-\overline{y}\right)\right] \tag{3}\]  
The above formula represents the binary cross-entropy loss function; it is commonly used for binary classification problems, where the goal is to predict a binary label (0 or 1). The binary cross-entropy loss measures the dissimilarity between the true binary label y and the predicted probability \(\overline{y}\) of the positive class; it penalizes incorrect predictions more strongly and rewards accurate predictions. The objective is to minimize this cross-entropy loss, finding the optimal weights that improve the accuracy of binary classification, such is our case. Below are the steps of the model's algorithm for predicting obesity, created with the neural network:  
* Data Collection: Collect data on individuals that include features such as age, gender, height, weight, and health attributes. To import the data, pandas is used as a read_csv() function. * Data Preprocessing: Preprocess the data by normalizing the features and performing data cleaning (removing any outliers or missing values) using the following code: data = ds[-ds.isin(['/')]]. * Data Splitting and converting to categorical: Split the dataset into training and testing sets using the following code: 'from sklearn.model_selection import train_test_split', whereby'model_selection' is imported from the'sklearn' library, which providesvarious functions for dataset splitting and cross-validation. The training set is used to train the model, which is taken as a random 80% of the dataset, and the other 20% of dataset is used for testing, used to evaluate the model's performance. * Data are being converted to categorical labels using the to_categorical() function from the keras.utils.np_utils module. This is often necessary when dealing with classification problems where the output variable is a categorical variable. Model Architecture: Choose an appropriate neural network architecture. A common architecture for obesity prediction is a feedforward neural network with multiple hidden layers. Model Training: The process of training the neural network involves using the training set to update the model's weights and biases iteratively to reduce the error between the predicted outputs and the actual outputs. This paper employs modules typically used to define and train neural network models with the 'keras' library for building neural networks: Sequential--a linear stack of layers that can be defined and modified layer by layer. Dense--a fully connected layer where every input node is connected to every output node. The output of a dense layer with input x, weight matrix w, bias vector b, and activation function f is calculated as follows: output = _f_(w
* x + b) The activation function used is the ReLU (Rectified Linear Unit), which can be represented as ReLU(x) = _max_(0, x) The ReLU activation function takes an input value x and returns the maximum of 0 and x. In other words, if the input x is greater than 0, the ReLU function returns the input value x. If the input x is less than or equal to 0, the ReLU function returns 0. \[\text{ReLU(x)}=\left\{ \begin{array}{ll}x,\textit{if}&x>0\\ 0,\textit{if}&x\leq 0\end{array} \right\}\] (6) The ReLU is preferred in many cases due to its simplicity and effectiveness. It introduces non-linearity to the neural network, allowing it to model complex relationships between inputs and outputs. Additionally, ReLU has the advantage of being computationally efficient to compute and avoids the vanishing gradient problem that can occur with other activation functions such as sigmoid. \[\textit{sigmoid function}=\left\{\frac{1}{1+e^{-(wx+b)}}\right\}\] (7) The model has both ReLU and sigmoid activation functions. Overall, the model combines the power of ReLU activation functions to introduce non-linearity and capture complex patterns in the hidden layers, while utilizing the sigmoid activation function in the final layer for binary classification.