The derivation process of BP neural network

Http://www.cnblogs.com/biaoyu/archive/2015/06/20/4591304.html

A detailed explanation of the derivation process of BP neural network

BP algorithm is one of the most effective multilayer neural network learning methods, its main characteristics is the signal forward transmission, and error transmission, through the constant adjustment of network weights, so that the final output of the network and the desired output as close as possible to achieve training purposes.

The structure and description of multilayer neural network

The following figure is a typical multilayer neural network.

Usually a multilayer neural network consists of L-layer neurons, wherein the 1th layer is called the input layer, the last layer (the L layer) is called the output layer, and the other layers are called the hidden layer (the 2nd layer ~ L-1 layer).

Make the input vector:

x⃗=[x1x2...xi...xm],i=1,2,..., m

The output vector is:

y⃗=[y1y2...yk...yn],k=1,2,..., N

The output of the neurons in the hidden layer is:

H (L) =[