1.比较感知机的对偶形式和线性可分支持向量机的对偶性形式。
感知机原始形式： min w , b L ( w , b ) = − ∑ x i ϵ M ( y i ( w ⋅ x i + b ) ) \min_{w,b} L(w,b) = - \sum_{x_i\epsilon M}(y_i(w\cdot x_i+b)) w,bminL(w,b)=−xiϵM∑(yi(w⋅xi+b)) M M M为误分点的集合。等价于 min w , b L ( w , b ) = ∑ i = 1 N ( − y i ( w ⋅ x i + b ) ) + \min_{w,b} L(w,b) = \sum_{i=1}^N(-y_i(w\cdot x_i+b))_+ w,bminL(w,b)=i=1∑N(−yi(w⋅xi+b))+
对偶形式： w w w, b b b表示为 x i x_i xi, y i y_i yi的线性组合的形式，求其系数（线性组合的系数） w = ∑ i = 1 N α i y i x i w = \sum_{i=1}^{N}\alpha_iy_ix_i w=∑i=1Nαiyixi, b = ∑ i = 1 N α i y i b = \sum_{i=1}^{N}\alpha_iy_i b=∑i=1Nαiyi min w , b L ( w , b ) = min α i L ( α i ) = ∑ i = 1 N ( − y i ( ∑ j = 1 N α j y j x j ⋅ x i + ∑ j = 1 N α j y j ) ) + \min_{w,b} L(w,b) = \min_{\alpha_i}L(\alpha_i) = \sum_{i=1}^N(-y_i(\sum_{j=1}^{N}\alpha_jy_jx_j\cdot x_i+ \sum_{j=1}^{N}\alpha_jy_j))_+ w,bminL(w,b)=αiminL(αi)=i=1∑N(−yi(j=1∑Nαjyjxj⋅xi+
