感知器PLA算法

　　看了台湾大学林轩田的机器学习第二章感知器算法，做一些笔记备忘。理论部分以后再补，直接上代码：

%感知器算法实例
% creat the value of w
x0 = ones(20, 1);
%creat datasets,(x_1,x_2)
x1 = rand(20, 2)*10;
x = [x0, x1];
test = rand(20, 1);
y = ones(20, 1);
for i=1:20
    if x1(i, 1)>6
        y(i) = -1;
    end
end

j=1;
for i=1:20
    if y(i)==-1
        u(j) = x1(i, 1);
        v(j) = x1(i, 2);
        j = j+1;
    end
end
scatter(u, v, 'or');
hold on;

j=1;
u=[];
v=[];
for i=1:20
    if y(i)==1
        u(j) = x1(i, 1);
        v(j) = x1(i, 2);
        j = j+1;
    end
end
scatter(u, v, 'xk');
hold on;
%Example of PLA algorithm
w = [0, 0, 0];
while true
    pd = false;
    for i=1:20
        t = x(i, :);
        if w*t'*y(i)<=0
            w = w + y(i)*t;
            pd = true;
            break;
        end

    end

    if pd == false
        break;
    end
end
w
v = linspace(0, 10, 100);
u = -w(3)/w(2)*v - w(1)/w(2);
plot(u, v, '.');
hold on 
%Next is the code of PLA algorithm by Nerual Network Toolbox  
t = 1;
y(y==-1)=0;
net = newp([0, 10; 0, 10], t);
net = train(net, x1', y');

newt = sim(net, x1');
iw = net.iw;
b = net.b;
ww = [b{1}, iw{1}];
vv = linspace(0, 10, 100);
uu = -ww(3)/ww(2)*v - ww(1)/ww(2);
plot(uu, vv, '.k');

　　得到的结果如下：

　　黄色部分是按照理论写的代码，而黑色是根据神经网络工具箱跑出来的结果。