Neural Network Toolbox™

Create feed-forward backpropagation network with feedback from output to input

Syntax

• net = newnarx(P,T,ID,OD,[S1 S2...S(N-l)],{TF1 TF2...TFNl}, 
  BTF,BLF,PF,IPF,OPF,DDF)
  

Description

newnarx(P,T,ID,OD,[S1 S2...S(N-l)],{TF1 TF2...TFNl}, BTF,BLF,PF,IPF,OPF,DDF) takes

P	R x Q1 matrix of Q1 sample R-element input vectors
T	SN x Q2 matrix of Q2 sample SN-element input vectors
ID	Input delay vector
OD	Output delay vector
Si	Size of ith layer, for N-1 layers, default = [ ]. (Output layer size SN is determined from T.)
TFi	Transfer function of ith layer. (Default = 'tansig' for hidden layers and 'purelin' for output layer.)
BTF	Backpropagation network training function (default = 'trainlm')
BLF	Backpropagation weight/bias learning function (default = 'learngdm')
PF	Performance function (default = 'mse')
IPF	Row cell array of input processing functions. (Default = {'removeconstantrows','mapminmax'})
OPF	Row cell array of output processing functions. (Default = {'removeconstantrows','mapminmax'})
DDF	Data divison function (default = 'dividerand')

and returns an N-layer feed-forward backpropagation network with external feedback.

The transfer function TFi can be any differentiable transfer function such as tansig, logsig, or purelin.

The d delays from output to input FBD must be integer values greater than zero placed in a row vector.

The training function BTF can be any of the backpropagation training functions such as trainlm, trainbfg, trainrp, traingd, etc.

Caution    trainlm is the default training function because it is very fast, but it requires a lot of memory to run. If you get an out-of-memory error when training, try one of the methods below.

• Slow trainlm training, but reduce memory requirements, by setting net.trainParam.mem_reduc to 2 or more. (See help trainlm.)
• Use trainbfg, which is slower but more memory efficient than trainlm.
• Use trainrp, which is slower but more memory efficient than trainbfg.

The learning function BLF can be either of the backpropagation learning functions learngd or learngdm.

The performance function can be any of the differentiable performance functions such as mse or msereg.

Examples

Here is a problem consisting of sequences of inputs P and targets T to be solved with a network.

• P = {[0] [1] [1] [0] [-1] [-1] [0] [1] [1] [0] [-1]};
  T = {[0] [1] [2] [2]  [1]  [0] [1] [2] [1] [0]  [1]};
  

A two-layer feed-forward network with a two-delay input and two-delay feedback is created. The network has one hidden layer of five tansig neurons.

• net = newnarx(P,T,[0 1],[1 2],5);
  

The network is simulated and its output plotted against the targets.

• Y = sim(net,P);
  plot(1:11,[T{:}],1:11,[Y{:}],'o')
  

The network is trained for 50 epochs. Again the network's output is plotted.

• net = train(net,P,T);
  Yf = sim(net,P);
  plot(1:11,[T{:}],1:11,[Y{:}],'o',1:11,[Yf{:}],'+')
  

Algorithm

Feed-forward networks consist of Nl layers using the dotprod weight function, netsum net input function, and the specified transfer functions.

The first layer has weights coming from the input. Each subsequent layer has a weight coming from the previous layer. All layers have biases. The last layer is the network output.

Each layer's weights and biases are initialized with initnw.

Adaption is done with trains, which updates weights with the specified learning function. Training is done with the specified training function. Performance is measured according to the specified performance function.

See Also

newcf, newelm, sim, init, adapt, train, trains

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