Forráskód Böngészése

修复【6.6.4 式(6.70)的推导】中的错误

)s 1 éve
szülő
commit
a5666092a9
1 módosított fájl, 3 hozzáadás és 3 törlés
  1. 3 3
      docs/chapter6/chapter6.md

+ 3 - 3
docs/chapter6/chapter6.md

@@ -997,7 +997,7 @@ $$
 $$
 
 
-再将此式代回$\boldsymbol{w}^{\mathrm{T}} \mathbf{S}_{b}^{\phi} \boldsymbol{w}$可得
+再将此式代回$\boldsymbol{w}^{\mathrm{T}} \mathbf{S}_{w}^{\phi} \boldsymbol{w}$可得
 
 
 $$
@@ -1038,12 +1038,12 @@ $$
 $$
 
 
-将上述三项的化简结果代回再将此式代回$\boldsymbol{w}^{\mathrm{T}} \mathbf{S}_{b}^{\phi} \boldsymbol{w}$可得
+将上述三项的化简结果代回再将此式代回$\boldsymbol{w}^{\mathrm{T}} \mathbf{S}_{w}^{\phi} \boldsymbol{w}$可得
 
 
 $$
 \begin{aligned}
-\boldsymbol{w}^{\mathrm{T}} \mathbf{S}_{b}^{\phi} \boldsymbol{w}&=\boldsymbol{\alpha}^{\mathrm{T}} \mathbf{K} \mathbf{K}^{\mathrm{T}} \boldsymbol{\alpha}-m_0\boldsymbol{\alpha}^{\mathrm{T}} \hat{\boldsymbol{\mu}}_{0} \hat{\boldsymbol{\mu}}_{0}^{\mathrm{T}} \boldsymbol{\alpha}-m_1\boldsymbol{\alpha}^{\mathrm{T}} \hat{\boldsymbol{\mu}}_{1} \hat{\boldsymbol{\mu}}_{1}^{\mathrm{T}} \boldsymbol{\alpha}\\
+\boldsymbol{w}^{\mathrm{T}} \mathbf{S}_{w}^{\phi} \boldsymbol{w}&=\boldsymbol{\alpha}^{\mathrm{T}} \mathbf{K} \mathbf{K}^{\mathrm{T}} \boldsymbol{\alpha}-m_0\boldsymbol{\alpha}^{\mathrm{T}} \hat{\boldsymbol{\mu}}_{0} \hat{\boldsymbol{\mu}}_{0}^{\mathrm{T}} \boldsymbol{\alpha}-m_1\boldsymbol{\alpha}^{\mathrm{T}} \hat{\boldsymbol{\mu}}_{1} \hat{\boldsymbol{\mu}}_{1}^{\mathrm{T}} \boldsymbol{\alpha}\\
 &=\boldsymbol{\alpha}^{\mathrm{T}} \cdot\left(\mathbf{K} \mathbf{K}^{\mathrm{T}} -m_0\hat{\boldsymbol{\mu}}_{0} \hat{\boldsymbol{\mu}}_{0}^{\mathrm{T}} -m_1\hat{\boldsymbol{\mu}}_{1} \hat{\boldsymbol{\mu}}_{1}^{\mathrm{T}} \right)\cdot\boldsymbol{\alpha}\\
 &=\boldsymbol{\alpha}^{\mathrm{T}} \cdot\left(\mathbf{K} \mathbf{K}^{\mathrm{T}}-\sum_{i=0}^{1} m_{i} \hat{\boldsymbol{\mu}}_{i} \hat{\boldsymbol{\mu}}_{i}^{\mathrm{T}} \right)\cdot\boldsymbol{\alpha}\\
 &=\boldsymbol{\alpha}^{\mathrm{T}} \mathbf{N}\boldsymbol{\alpha}\\