线性支持向量机linear support vector machine

PLA?depending on randomness

VC bound? whichever you like!

Eout(w) <= Ein(w) + Omiga(h)

Gaussian-like 测试资料与训练资料有一些区别（测量误差）

同样是线性拟合，好的超平面拥有更好的对测量误差的容忍度。（costfunction会更小！）

考虑到高斯噪声，样本离超平面越远，就有更高的噪声容忍度。

<==> more robust to overfitting <==> robustness of hyperplane

定义一个线的分类效果，就是看这个线离最近的资料的距离，越远越好。

robustness === fatness distance to closes xn

找出最fat线。

max fatness(w)

subject to w classifies every(xn, yn) correctly fatness(w) = min distance(xn, w)

fatness: formally called margin

Large-Margin Separating Hyperplane

Distance to Hyperplane

max w marg(w)

subject to exery ynwT xn > 0 margin(w) = min n=1,…,N distance(xn,w)

shorten x and w distance needs w0 and w1,…,wd differently (to be derived)

w0 取名b(bias截距)

// h(x) = sign(wT * x + b

wT是平面的法向量

//

distance(x, b, w) =