11.3EM算法
文档摘要
11.3 EM 算法 $$ r{n, k} = \frac{\pi{k}\,\mathcal{N}(\boldsymbol{x}{n}|\boldsymbol{\mu}{k}, \boldsymbol{\Sigma}{k})}{\sum{j} \pi{j}\,\mathcal{N}(\boldsymbol{x}{n}|\boldsymbol{\mu}{j}, \boldsymbol{\Sigma}{j}) }. \tag{11.53} $$ $$ \begin{align} \boldsymbol{\mu}{k} &= \frac{1}{N{k}} \sum\limits{n=1}^{N} r{n, k}\boldsymbol{x}{n}, \tag{11.
11.3 EM 算法
r_{n, k} = \frac{\pi_{k}\,\mathcal{N}(\boldsymbol{x}_{n}|\boldsymbol{\mu}_{k}, \boldsymbol{\Sigma}_{k})}{\sum_{j} \pi_{j}\,\mathcal{N}(\boldsymbol{x}_{n}|\boldsymbol{\mu}_{j}, \boldsymbol{\Sigma}_{j}) }. \tag{11.53}
\begin{align} \boldsymbol{\mu}_{k} &= \frac{1}{N_{k}} \sum\limits_{n=1}^{N} r_{n, k}\boldsymbol{x}_{n}, \tag{11.54}\\ \boldsymbol{\Sigma}_{k} &= \frac{1}{N_{k}} \sum\limits_{n=1}^{N} r_{n, k} (\boldsymbol{x}_{n} - \boldsymbol{\mu}_{k})(\boldsymbol{x}_{n} - \boldsymbol{\mu}_{k})^{\top}, \tag{11.55}\\ \pi_{k} &= \frac{N_{k}}{N}. \tag{11.56} \end{align}
p(x) = {\color{blue} 0.29\mathcal{N}(x|-0.275, 0.06) } + {\color{orange} 0.28\mathcal{N}(x|-0.50, 0.25) } + {\color{green} 0.43\mathcal{N}(x|3.64, 1.63) }. \tag{11.57}
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