从贝叶斯决策到最小距离判别法再到Fisher判别分析

Bayes准则（最小期望风险）→\rightarrow→Bayes假设检验→\rightarrow→判别分析法→\rightarrow→最小距离判别法→\rightarrow→Fisher判别分析法Bayes准则（最小期望风险）判别函数:R(Dj∣x)=∑i=1KLijP(Ci∣x),j=1,2,⋯ ,KR\left(D_j\mid \boldsymbol{x}\right)=\sum\limits_{i = 1}^{K}L_{ij}P\left(C_i\mid \boldsymbol{x}\right),\quad j = 1,2,\cdots,KR(Dj​∣x)=i=1∑K​Lij​P(Ci​∣x),j=1,2,⋯,K判别法则: 若R(Dj∣x)=min⁡1⩽i⩽KR(Di∣x)R\left(D_j\mid \boldsymbol{x}\right)= \min\limits_{1 \leqslant i \leqslant K} R\left(D_i\mid \boldsymbol{x}\right)R(Dj​∣x)=1⩽i⩽Kmin​R(Di​∣x)，则判定x\boldsymbol{x}x为CjC_jCj​↓Lij={ 1,i≠j0,i=j\downarrow L_{ij}=\begin{cases}1, i\neq j\\0, i = j\end{cases}↓Lij​={1,0,​i=ji=j​Bayes假设检验判别函数:P(Ci∣x)=p(x∣Ci)P(Ci)∑j=1Kp(x∣Cj)P(Cj),i=1,2,⋯ ,KP \left( C_i \mid {\boldsymbol x} \right) = \dfrac{ p \left( {\boldsymbol x} \mid C_i \right) P \left( C_i \right) } { \sum\limits_{j=1}^{K} p \left( {\boldsymbol x} \mid C_j \right) P \left( C_j \right)}, \quad i = 1,2,\cdots,KP(Ci​∣x)=j=1∑/