Understanding MultiLayer Perceptron (MLP) Models

This article explains the MultiLayer Perceptron (MLP) model, breaking down its structure, function, and application.

What is a MultiLayer Perceptron?

A MultiLayer Perceptron (MLP) is an artificial neural network consisting of multiple layers. It improves upon the singlelayer perceptron by introducing one or more hidden layers between the input and output layers.

Key Components of an MLP:

• Input Layer: Receives the initial data or features.
• Hidden Layer(s): One or more layers that perform computations on the input data.
• Output Layer: Produces the final prediction or classification.

Why Use a MultiLayer Perceptron?

Singlelayer perceptrons are suitable for linearly separable data. However, when dealing with nonlinear data, MLPs provide a more complex and accurate model. They can learn and classify data that a singlelayer perceptron cannot.

How Does an MLP Work?

The MLP operates through a process of weighted sums and activation functions:

1. Input Layer:

Receives input features. Each input corresponds to a feature of the data, such as the size of a house or the number of rooms.

2. Hidden Layer(s):

Perform computations. This involves calculating the weighted sum of the inputs, where each input is multiplied by its corresponding weight. These weights determine the importance of each input feature.

3. Output Layer:

Generates the final prediction. The weighted sum is passed through an activation function. This function determines whether a neuron should be activated or not, based on a threshold value. Common activation functions include Sigmoid, ReLU, and TanH. These functions also help normalize the output values, often to a range between 0 and 1.

MLP Structure: Feedforward and Fully Connected

The data flow in an MLP is feedforward, meaning it moves in one direction from the input layer, through the hidden layers, to the output layer. There are no cycles or loops in this process.

MLPs are also fully connected. Every neuron in one layer is connected to every neuron in the next layer. For example, each input feature (x1, x2, etc.) is connected to every neuron in the first hidden layer (H3, H4, etc.). Similarly, the output of each neuron in the hidden layer is connected to the neuron(s) in the output layer.

Numerical Example: Calculation Walkthrough

To understand how an MLP works, let's look at a simplified numerical example of the calculations involved.

Calculating H3 Input:

The input to neuron H3 in the hidden layer (h3 in) is calculated as follows:

h3_in = (x1 * w13) + (x2 * w23) + B1

Where:

• x1 and x2 are the input features.
• w13 and w23 are the weights connecting x1 and x2 to H3.
• B1 is the bias value.

Example: If x1 = 0.02, w13 = 0.15, x2 = 0.55, w23 = 0.4, and B1 = 0.3, then:

h3_in = (0.02 * 0.15) + (0.55 * 0.4) + 0.3 = 0.523

Calculating H4 Input:

Similarly, the input to neuron H4 (h4 in) is calculated as:

h4_in = (x1 * w14) + (x2 * w24) + B1

Applying the Activation Function:

The input values (h3_in, h4_in) are then passed through an activation function, such as the Sigmoid function:

Sigmoid(x) = 1 / (1 + e^(x))

For example, the output of H3 (H3_out) is calculated as:

H3_out = 1 / (1 + e^(0.523)) = 0.627

Similarly, the output of H4 (H4_out) can be calculated.

Calculating the Output Layer Input:

The input to the output neuron (O5_in) is calculated using the outputs from the hidden layer:

O5_in = (H3_out * w35) + (H4_out * w45) + B2

Final Output:

Finally, the output layer input is passed through the activation function to generate the final prediction. This prediction represents the model's estimate based on the input features.

Error and Backpropagation

The MLP's prediction is compared to the actual (labeled) output. The difference between the two is the error. The goal is to minimize this error.

Backpropagation is the process of adjusting the weights in the network to reduce the error. This involves propagating the error backward through the network and updating the weights using optimization algorithms.

Conclusion

MultiLayer Perceptrons are powerful tools for modeling complex, nonlinear relationships in data. By understanding their structure, function, and training process, you can leverage MLPs for a wide range of machinelearning tasks.