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@@ -997,7 +997,7 @@ $$
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$$
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-再将此式代回$\boldsymbol{w}^{\mathrm{T}} \mathbf{S}_{b}^{\phi} \boldsymbol{w}$可得
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+再将此式代回$\boldsymbol{w}^{\mathrm{T}} \mathbf{S}_{w}^{\phi} \boldsymbol{w}$可得
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$$
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@@ -1038,12 +1038,12 @@ $$
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$$
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-将上述三项的化简结果代回再将此式代回$\boldsymbol{w}^{\mathrm{T}} \mathbf{S}_{b}^{\phi} \boldsymbol{w}$可得
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+将上述三项的化简结果代回再将此式代回$\boldsymbol{w}^{\mathrm{T}} \mathbf{S}_{w}^{\phi} \boldsymbol{w}$可得
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$$
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\begin{aligned}
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-\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}\\
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+\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}\\
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&=\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}\\
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&=\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}\\
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&=\boldsymbol{\alpha}^{\mathrm{T}} \mathbf{N}\boldsymbol{\alpha}\\
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