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PRML式(6.35)

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フィッシャーカーネルと白色化

式(6.35)に関して、"フィッシャースコアの共分散行列であり、フィッシャーカーネルは、スコアの白色化に対応している"とある。どういう意味か考える。

式(6.32)のスコア$\boldsymbol{g}$の共分散行列の逆行列を$G^T G$の形で表現できるとすると、白色化されたスコアは$G\boldsymbol{g}$と表現できる。(https://wonderfuru.com/%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AE%E7%99%BD%E8%89%B2%E5%8C%96-2-2/)

(6.33)の$(G\boldsymbol{g}_{x})^T G\boldsymbol{g}_x'$と変形できる。$G\boldsymbol{g}$は白色化されている。

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