linear304.m

非线性问题的线性拟合问题的源程序 非线性问题的线性拟合问题的源程序用MATLAB实现

%% Linear Fit of Nonlinear Problem
% A linear neuron is trained to find the minimum sum-squared error linear fit to
% a nonlinear input/output problem.
%
% Copyright 1992-2002 The MathWorks, Inc.
% $Revision: 1.16 $  $Date: 2002/03/29 19:36:17 $

%%
% P defines four 1-element input patterns (column vectors).  T defines
% associated 1-element targets (column vectors).  Note that the relationship
% between values in P and in T is nonlinear.   I.e. No W and B exist such that
% P*W+B = T for all of four sets of P and T values above.

P = [+1.0 +1.5 +3.0 -1.2];
T = [+0.5 +1.1 +3.0 -1.0];

%%
% ERRSURF calculates errors for a neuron with a range of possible weight and
% bias values.  PLOTES plots this error surface with a contour plot underneath.
% 
% The best weight and bias values are those that result in the lowest point on
% the error surface.  Note that because a perfect linear fit is not possible,
% the minimum has an error greater than 0.

w_range =-2:0.4:2;  b_range = -2:0.4:2;
ES = errsurf(P,T,w_range,b_range,'purelin');
plotes(w_range,b_range,ES);

%%
% MAXLINLR finds the fastest stable learning rate for training a linear network.
% NEWLIN creates a linear neuron.  NEWLIN takes these arguments: 1) Rx2 matrix
% of min and max values for R input elements, 2) Number of elements in the
% output vector, 3) Input delay vector, and 4) Learning rate.

maxlr = maxlinlr(P,'bias');
net = newlin([-2 2],1,[0],maxlr);


%%
% Override the default training parameters by setting the maximum number of
% epochs.  This ensures that training will stop.

net.trainParam.epochs = 15;

%%
% To show the path of the training we will train only one epoch at a time and
% call PLOTEP every epoch (code not shown here).  The plot shows a history of
% the training.  Each dot represents an epoch and the blue lines show each
% change made by the learning rule (Widrow-Hoff by default).

% [net,tr] = train(net,P,T);
net.trainParam.epochs = 1;
net.trainParam.show = NaN;
h=plotep(net.IW{1},net.b{1},mse(T-sim(net,P)));     
[net,tr] = train(net,P,T);                                                    
r = tr;
epoch = 1;
while epoch < 15
   epoch = epoch+1;
   [net,tr] = train(net,P,T);
   if length(tr.epoch) > 1
      h = plotep(net.IW{1,1},net.b{1},tr.perf(2),h);
      r.epoch=[r.epoch epoch]; 
      r.perf=[r.perf tr.perf(2)];
      r.vperf=[r.vperf NaN];
      r.tperf=[r.tperf NaN];
   else
      break
   end
end
tr=r;

%%
% The train function outputs the trained network and a history of the training
% performance (tr).  Here the errors are plotted with respect to training
% epochs.
%
% Note that the error never reaches 0.  This problem is nonlinear and therefore
% a zero error linear solution is not possible.

plotperf(tr,net.trainParam.goal);

%%
% Now use SIM to test the associator with one of the original inputs, -1.2, and
% see if it returns the target, 1.0.
%
% The result is not very close to 0.5!  This is because the network is the best
% linear fit to a nonlinear problem.

p = -1.2;
a = sim(net, p)