traincgb (Neural Network Toolbox)

Neural Network Toolbox

traincgb

Conjugate gradient backpropagation with Powell-Beale restarts

Syntax

[net,TR,Ac,El] = traincgb(net,Pd,Tl,Ai,Q,TS,VV,TV)

info = traincgb(code)

Description

traincgb is a network training function that updates weight and bias values according to the conjugate gradient backpropagation with Powell-Beale restarts.

traincgb(net,Pd,Tl,Ai,Q,TS,VV,TV) takes these inputs,

net -- Neural network

Pd -- Delayed input vectors

Tl -- Layer target vectors

Ai -- Initial input delay conditions

Q -- Batch size

TS -- Time steps

VV -- Either empty matrix [] or structure of validation vectors

TV -- Either empty matrix [] or structure of test vectors

and returns,

net -- Trained network

TR -- Training record of various values over each epoch:
- TR.epoch -- Epoch number
  TR.perf -- Training performance
  TR.vperf -- Validation performance
  TR.tperf -- Test performance
Ac -- Collective layer outputs for last epoch

El -- Layer errors for last epoch

Training occurs according to the traincgb'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 showing progress

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.searchFcn       Name of line search routine to use.
'srchcha'

Parameters related to line search methods (not all used for all methods):

net.trainParam.scal_tol 20
- Divide into delta to determine tolerance for linear search.
net.trainParam.alpha 0.001
- Scale factor, which determines sufficient reduction in perf.
net.trainParam.beta 0.1
- Scale factor, which determines sufficiently large step size.
net.trainParam.delta 0.01
- Initial step size in interval location step.
net.trainParam.gama 0.1
- Parameter to avoid small reductions in performance. Usually set to 0.1. (See use in srch_cha.)
net.trainParam.low_lim 0.1 Lower limit on change in step size.

net.trainParam.up_lim 0.5 Upper limit on change in step size.

net.trainParam.maxstep 100 Maximum step length.

net.trainParam.minstep 1.0e-6 Minimum step length.

net.trainParam.bmax 26 Maximum step size.

Dimensions for these variables are

Pd -- No x Ni x TS cell array, each element P{i,j,ts} is a Dij x Q matrix.

Tl -- Nl x TS cell array, each element P{i,ts} is a Vi x Q matrix.

Ai -- Nl x LD cell array, each element Ai{i,k} is an Si x Q matrix.

where

Ni = net.numInputs

Nl = net.numLayers

LD = net.numLayerDelays

Ri = net.inputs{i}.size

Si = net.layers{i}.size

Vi = net.targets{i}.size

Dij = Ri * length(net.inputWeights{i,j}.delays)

If VV is not [], it must be a structure of validation vectors,

VV.PD -- Validation delayed inputs.

VV.Tl -- Validation layer targets.

VV.Ai -- Validation initial input conditions.

VV.Q -- Validation batch size.

VV.TS -- Validation time steps.

which is used to stop training early if the network performance on the validation vectors fails to improve or remains the same for max_fail epochs in a row.

If TV is not [], it must be a structure of validation vectors,

TV.PD -- Validation delayed inputs.

TV.Tl -- Validation layer targets.

TV.Ai -- Validation initial input conditions.

TV.Q -- Validation batch size.

TV.TS -- Validation time steps.

which is used to test the generalization capability of the trained network.

traincgb(code) returns useful information for each code string:

'pnames' -- Names of training parameters.

'pdefaults' -- Default training parameters.

Examples

Here is a problem consisting of inputs p and targets t that we would like to solve 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 traincgb network training function is to be used.

Create and Test a Network

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

Train and Retest the Network
net.trainParam.epochs = 50;
net.trainParam.show = 10;
net.trainParam.goal = 0.1;
net = train(net,p,t);
a = sim(net,p)

See newff, newcf, and newelm for other examples.

Network Use

You can create a standard network that uses traincgb with newff, newcf, or newelm.

To prepare a custom network to be trained with traincgb

Set net.trainFcn to 'traincgb'. This will set net.trainParam to traincgb's default parameters.
Set net.trainParam properties to desired values.

In either case, calling train with the resulting network will train the network with traincgb.

Algorithm

traincgb 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. Each variable is adjusted according to the following:

```
X = X + a*dX;
```

where dX is the search direction. The parameter a is selected to minimize the performance along the search direction. The line search function searchFcn is used to locate the minimum point. The first search direction is the negative of the gradient of performance. In succeeding iterations the search direction is computed from the new gradient and the previous search direction according to the formula:

```
dX = -gX + dX_old*Z;
```

where gX is the gradient. The parameter Z can be computed in several different ways. The Powell-Beale variation of conjugate gradient is distinguished by two features. First, the algorithm uses a test to determine when to reset the search direction to the negative of the gradient. Second, the search direction is computed from the negative gradient, the previous search direction, and the last search direction before the previous reset. See Powell, Mathematical Programming, for a more detailed discussion of the algorithm.

Training stops when any of these conditions occur:

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

See Also

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

References

Powell, M. J. D.,"Restart procedures for the conjugate gradient method," Mathematical Programming, vol. 12, pp. 241-254, 1977.

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