Commit 30f7fa14 authored by Ying-Qiu Zheng's avatar Ying-Qiu Zheng
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Update 2021JUL21.md

parent 04d75700
......@@ -29,7 +29,7 @@ In summary, in addition to finding the the hyper-parameters $`\pi, \mu, \Sigma_{
- $`\Sigma_{k}^{L} = \frac{1}{N_{k}}\sum_{n=1}^{N}\gamma(y_{nk})(\mathbf{x}^{L}_{n} - \mathbf{\mu}_{k}^{L})(\mathbf{x}^{L}_{n} - \mathbf{\mu}_{k}^{L})^{T}`$
- $`\Sigma_{k}^{H} = \frac{1}{N_{k}}\sum_{n=1}^{N}\gamma(y_{nk})(\mathbf{Ux}^{H}_{n} - \mathbf{\mu}_{k}^{L})(\mathbf{Ux}^{H}_{n} - \mathbf{\mu}_{k}^{L})^{T}`$
- $`\pi_k = \frac{N_{k}}{N}`$
- $`\mathbf{U}=\mathbf{MN}^{T}`$ where $`\mathbf{MDN}^{T}`$ is the svd of $`\sum_{k=1}^{K}\gamma(y_nk)\mu_{k}^{L}(\mathbf{x}_{n}^{H})^{T}(\sum_{n=1}^{N}\mathbf{x}_{n}^{H}(\mathbf{x}_{n}^{H})^{T})`$
- $`\mathbf{U}=\mathbf{MN}^{T}`$ where $`\mathbf{MDN}^{T}`$ is the svd of $`\sum_{k=1}^{K}\gamma(y_nk)\mu_{k}^{L}(\mathbf{x}_{n}^{H})^{T}(\sum_{n=1}^{N}\gamma(y_{nk})\mathbf{x}_{n}^{H}(\mathbf{x}_{n}^{H})^{T})`$
- Evaluate the likelihood and check for convergence.
5. Using $`\mu_{k}^{L}, \Sigma_{k}^{L}, \pi_{k}`$ to assignment unseen low-quality data points.
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