RBF神经网络

1 注意：若矩阵不为方阵，则采用伪逆！

2.简单神经网络，用于线性可分。

3.依然仅一个神经元，但做了空间转换，解决非线性分类问题

4.简单小例子

5.RBF定义

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6.小例子

7.代码

=====rbf_approx======

 clc;
 clear;
 close all;


 ld=400; %generate the 400 learing data

 x=rand(2,ld); %0-1, two dimention vector
 x=(x-0.5)*1.5*2; %-1.5, 1.5
 x1=x(1,:);
 x2=x(2,:);
 F=20+x1.^2-10*cos(2*pi*x1)+x2.^2-10*cos(2*pi*x2);


 % x is input,F is ouput.F is indeed not known by the learner. Now ,the
 %RBF network is trained.
 net=newrb(x,F);

 %generate the testing data
 interval=0.1;
 [i, j]=meshgrid(-1.5:interval:1.5);
 row=size(i);
 tx1=i(:);
 tx1=tx1';
 tx2=j(:);
 tx2=tx2';
 tx=[tx1;tx2];

 %testing,tx is testing data,ty is sim output,using our RBF.
 ty=sim(net,tx);

 v=reshape(ty,row);
 figure
 subplot(1,3,2)
 mesh(i,j,v);% v is testing output data.

 zlim([0,60])%plot the original functioninterval=0.1;[x1, x2]=meshgrid(-1.5:interval:1.5);F = 20+x1.^2-10*cos(2*pi*x1)+x2.^2-10*cos(2*pi*x2);subplot(1,3,1)mesh(x1,x2,F);% F is real function output data.
 zlim([0,60])%plot the errorsubplot(1,3,3)mesh(x1,x2,F-v);zlim([0,60])

====rbf_exact====

 %Generate some training data
 clc;
 clear;
 interval=0.01;
 x1=-1.5:interval:1.5;
 x2=-1.5:interval:1.5;
 F = 20+x1.^2-10*cos(2*pi*x1)+x2.^2-10*cos(2*pi*x2);
 net=newrbe([x1;x2],F)

 ty=sim(net,[x1;x2]);
 figure
 plot3(x1,x2,F,'g');
 figure
 plot3(x1,x2,ty,'b');

8.运行结果

9.小总结