Algorithm 1 Training steps for the MLP model

Input: Training set $D={\{(x^{(n)},y^{(n)})\}}_{n=1}^N$, validation set $\mathcal{V}$, learning rate ${\alpha }_{\varphi }$, number of network layers L, number of neurons $M_l$, activation function for each layer $f_l$, where $1\le l\le L$.

1. Randomly initialize the weight matrix $W$ and bias matrix $b$ for each layer;

2. Randomly disrupt the samples in the training dataset $D$;

3. For n = 1…N do;

4. Samples $(x^{(n)},y^{(n)})$ are selected from the training set $D$ as inputs to the MLP network;

5. Calculate the input and activation values for each layer;

6. Calculate the error for each layer according to the backpropagation algorithm;

7. Calculate the gradient for each layer of this sample;

8. Update the weight matrix $W$ and bias matrix $b$ for each layer;

9. End.

10. Until a pre-determined number of iterations is reached, or the model has the required accuracy on the validation set, the model training is completed and the results are output.