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srchcha

1-D minimization using Charalambous' method

Syntax

[a,gX,perf,retcode,delta,tol] = srchcha(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf)

Description

srchcha is a linear search routine. It searches in a given direction to locate the minimum of the performance function in that direction. It uses a technique based on Charalambous' method.

[a,gX,perf,retcode,delta,tol] = srchcha(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf) takes these inputs,

net

Neural network

X

Vector containing current values of weights and biases

Pd

Delayed input vectors

Tl

Layer target vectors

Ai

Initial input delay conditions

Q

Batch size

TS

Time steps

dX

Search direction vector

gX

Gradient vector

perf

Performance value at current X

dperf

Slope of performance value at current X in direction of dX

delta

Initial step size

tol

Tolerance on search

ch_perf

Change in performance on previous step

and returns

a

Step size that minimizes performance

gX

Gradient at new minimum point

perf

Performance value at new minimum point

retcode

Return code that has three elements. The first two elements correspond to the number of function evaluations in the two stages of the search. The third element is a return code. These have different meanings for different search algorithms. Some might not be used in this function.

0  Normal
1  Minimum step taken
2  Maximum step taken
 3  Beta condition not met
delta

New initial step size, based on the current step size

tol

New tolerance on search

Parameters used for the Charalambous algorithm are

alpha

Scale factor that determines sufficient reduction in perf

beta

Scale factor that determines sufficiently large step size

gama

Parameter to avoid small reductions in performance, usually set to 0.1

scale_tol

Parameter that relates the tolerance tol to the initial step size delta, usually set to 20

The defaults for these parameters are set in the training function that calls them. See traincgf, traincgb, traincgp, trainbfg, and trainoss.

Dimensions for these variables are

Pd

No-by-Ni-by-TS cell array

Each element P{i,j,ts} is a Dij-by-Q matrix.

Tl

Nl-by-TS cell array

Each element P{i,ts} is a Vi-by-Q matrix.

Ai

Nl-by-LD cell array

Each element Ai{i,k} is an Si-by-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)

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];

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 traincgf network training function and the srchcha search function are to be used.

Create and Test a Network

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

Train and Retest the Network

net.trainParam.searchFcn = 'srchcha';
net.trainParam.epochs = 50;
net.trainParam.show = 10;
net.trainParam.goal = 0.1;
net = train(net,p,t);
a = sim(net,p)

Network Use

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

To prepare a custom network to be trained with traincgf, using the line search function srchcha,

  1. Set net.trainFcn to 'traincgf'. This sets net.trainParam to traincgf's default parameters.

  2. Set net.trainParam.searchFcn to 'srchcha'.

The srchcha function can be used with any of the following training functions: traincgf, traincgb, traincgp, trainbfg, trainoss.

Definitions

The method of Charalambous, srchcha, was designed to be used in combination with a conjugate gradient algorithm for neural network training. Like srchbre and srchhyb, it is a hybrid search. It uses a cubic interpolation together with a type of sectioning.

See [Char92] for a description of Charalambous' search. This routine is used as the default search for most of the conjugate gradient algorithms because it appears to produce excellent results for many different problems. It does require the computation of the derivatives (backpropagation) in addition to the computation of performance, but it overcomes this limitation by locating the minimum with fewer steps. This is not true for all problems, and you might want to experiment with other line searches.

More About

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Algorithms

srchcha locates the minimum of the performance function in the search direction dX, using an algorithm based on the method described in Charalambous (see reference below).

References

Charalambous, C., "Conjugate gradient algorithm for efficient training of artificial neural networks," IEEE Proceedings, Vol. 139, No. 3, June, 1992, pp. 301–310.

See Also

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