Neural Network Toolbox™

Scaled conjugate gradient backpropagation

Syntax

• [net,TR,Ac,El] = trainscg(net,TR,trainV,valV,testV)
  info = trainscg('info')
  

Description

trainscg is a network training function that updates weight and bias values according to the scaled conjugate gradient method.

trainscg(net,TR,trainV,valV,testV) takes these inputs,

net	Neural network
TR	Initial training record created by train
trainV	Training data created by train
valV	Validation data created by train
testV	Test data created by train

and returns

net	Trained network
TR	Training record of various values over each epoch

Each argument trainV, valV, and testV is a structure of these fields:

X	N x TS cell array of inputs for N inputs and TS time steps. X{i,ts} is an Ri x Q matrix for the ith input and TS time step.
Xi	N x Nid cell array of input delay states for N inputs and Nid delays. Xi{i,j} is an Ri x Q matrix for the ith input and jth state.
Pd	N x S x Nid cell array of delayed input states.
T	NoxTS cell array of targets for No outputs and TS time steps. T{i,ts} is an Si x Q matrix for the ith output and TS time step.
Tl	Nl x TS cell array of targets for Nl layers and TS time steps. Tl{i,ts} is an Si x Q matrix for the ith layer and TS time step.
Ai	Nl x TS cell array of layer delays states for Nl layers, TS time steps. Ai{i,j} is an Si x Q matrix of delayed outputs for layer i, delay j.

Training occurs according to trainscg's training parameters, shown here with their default values:

net.trainParam.epochs	100		Maximum number of epochs to train
net.trainParam.show	25		Epochs between displays (NaN for no displays)
net.trainParam.showCommandLine	0		Generate command-line output
net.trainParam.showWindow	1		Show training GUI
net.trainParam.goal	0		Performance goal
net.trainParam.time	inf		Maximum time to train in seconds
net.trainParam.min_grad	1e-6		Minimum performance gradient
net.trainParam.max_fail	5		Maximum validation failures
net.trainParam.sigma	5.0e-5		Determine change in weight for second derivative approximation
net.trainParam.lambda	5.0e-7		Parameter for regulating the indefiniteness of the Hessian

trainscg('info') returns useful information about this function.

Network Use

You can create a standard network that uses trainscg with newff, newcf, or newelm. To prepare a custom network to be trained with trainscg,

1. Set net.trainFcn to 'trainscg'. This sets net.trainParam to trainscg's default parameters.
2. Set net.trainParam properties to desired values.

In either case, calling train with the resulting network trains the network with trainscg.

Examples

Here is a problem consisting of inputs p and targets t to be solved with a network.

• p = [0 1 2 3 4 5];
  t = [0 0 0 1 1 1];
  

Here a two-layer feed-forward network is created. The network's input ranges from [0 to 10]. The first layer has two tansig neurons, and the second layer has one logsig neuron. The trainscg network training function is to be used.

• net = newff([0 5],[2 1],{'tansig','logsig'},'trainscg');
  a = sim(net,p)
  

Here the network is trained and retested.

• net = train(net,p,t);
  a = sim(net,p)
  

See newff, newcf, and newelm for other examples.

Algorithm

trainscg can train any network as long as its weight, net input, and transfer functions have derivative functions. Backpropagation is used to calculate derivatives of performance perf with respect to the weight and bias variables X.

The scaled conjugate gradient algorithm is based on conjugate directions, as in traincgp, traincgf, and traincgb, but this algorithm does not perform a line search at each iteration. See Moller (Neural Networks, Vol. 6, 1993, pp. 525 to 533) for a more detailed discussion of the scaled conjugate gradient algorithm.

Training stops when any of these conditions occurs:

• The maximum number of epochs (repetitions) is reached.
• The maximum amount of time is exceeded.
• Performance is minimized to the goal.
• The performance gradient falls below min_grad.
• Validation performance has increased more than max_fail times since the last time it decreased (when using validation).

Reference

Moller, Neural Networks, Vol. 6, 1993, pp. 525-533

See Also

newff, newcf, traingdm, traingda, traingdx, trainlm, trainrp, traincgf, traincgb, trainbfg, traincgp, trainoss

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