Multilayer perceptron

General

A multilayer perceptron is a feedforward artificial neural network. This means the signal inside the neural network flows from input layer passing hidden layers to output layer. While training the error correction of neural weights are done in the opposite direction. This is done by the backpropagation algorithm.

Error of network

If the neural network is initialized by random weights it has of course not the expected output. Therefore training is necessary. While supervised training known inputs and their corresponded output values are presented to the network. So it is possible to compare the real output with the desired output. The error is described as the following algorithm:

$E={1 \over 2}\sum _{i=1}^{n}(t_{i}-o_{i})^{2}$

$E$ network error

$n$ count of input patterns

$t_{i}$ desired output

$o_{i}$ calculated output

Backpropagation

The learning algorithm of a single layer perceptron is easy compared to a multilayer percetron. The reason is that just the output layer is directly connected to the output, but not the hidden layers. Therefore the calculation of the right weights of the hidden layers is mathematical difficult. To get the right delta value for changing the weights of hidden neuron is described in the following equation:

$\Delta w_{ij}=-\alpha {\partial E \over \partial w_{ij}}=\alpha \delta _{j}x_{i}$

$\Delta w_{ij}$ delta value $w_{ij}$ of neuron connection $i$ to $j$

$\alpha$ learning rate

$\delta _{j}$ the error of neuron $j$

$x_{i}$ input of neuron $i$

$t_{j}$ desired output of output neuron $j$

$o_{j}$ real output of output neuron $j$.