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1-D minimization using Charalambous' method
[a,gX,perf,retcode,delta,tol] = srchcha(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf)
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) |
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.
net = newff([0 5],[2 1],{'tansig','logsig'},'traincgf'); a = sim(net,p)
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)
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,
The srchcha function can be used with any of the following training functions: traincgf, traincgb, traincgp, trainbfg, trainoss.
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.