Explain the Perceptron model with Bias

The perceptron model with bias is a fundamental building block of artificial neural networks, particularly in the realm of supervised learning for binary classification tasks.
1. Components of Perceptron with Bias:

• Input Features (𝑥1,𝑥2,…,𝑥𝑛): These are the features of the input data, which could represent anything from pixel values in an image to numerical attributes in a dataset.
• Weights (𝑤1,𝑤2,…,𝑤𝑛): Each input feature is associated with a weight that determines its importance in the classification process. These weights are adjusted during training to minimize errors.
• Bias (𝑏b): The bias term is an additional parameter in the perceptron model that allows the decision boundary to be shifted. It can be thought of as the threshold that the weighted sum of inputs must surpass for the perceptron to output a certain class.
• Activation Function: In the basic perceptron model, the activation function is a step function that outputs 1 if the weighted sum of inputs plus bias is greater than zero, and 0 otherwise. Mathematically, the output 𝑦y of the perceptron is:
  

2. Operation of Perceptron with Bias:

1. Initialization: Initialize the weights (𝑤1,𝑤2,…,𝑤𝑛​) and the bias (𝑏) with random or predefined values.
2. Forward Propagation:
   • Multiply each input feature (𝑥i​) by its corresponding weight (𝑤i​).
   • Sum up the weighted inputs (∑𝑖=1𝑛𝑤𝑖𝑥𝑖​).
   • Add the bias (b) to the sum.
   • Apply the activation function to the result to obtain the output (y).
3. Error Calculation: Compare the predicted output (y) to the actual output (𝑦true) and calculate the error.
4. Backpropagation:
   • Adjust the weights and bias based on the error using gradient descent or another optimization algorithm.
   • Update the weights (wi​) and the bias (b) to reduce the error and improve the accuracy of the model.
5. Repeat:
   • Repeat steps 2-4 for each training example in the dataset.
   • Iterate through the entire dataset multiple times (epochs) until the model converges or until a stopping criterion is met.