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======

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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====

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%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