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Ying-Qiu Zheng
archive
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c61680c6
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c61680c6
authored
Jul 25, 2021
by
Ying-Qiu Zheng
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Update 2021JUL21.md
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@@ -31,7 +31,7 @@ Algorithm 1. EM for the Fusion of GMMs
```
-
**M-step.**
Re-estimate the parameters using the current responsibilities by setting the derivatives to zero
```
math
\mu_{k}^{\text{new}} = \frac{1}{N_{k}}(\Sigma^{H}_{k} + \Sigma^{L}_{k} )^{-1}\sum_{n=1}^{N}\gamma(y_{nk})(\Sigma_{k}^{H}\mathbf{Ux}^{H}_{n} + \Sigma_{k}^{L}\mathbf{x}_{n}^{L} )
\mu_{k}^{\text{new}} = \frac{1}{N_{k}}(
(
\Sigma^{H}_{k}
)^{-1}
+
(
\Sigma^{L}_{k}
)^{-1}
)^{-1}\sum_{n=1}^{N}\gamma(y_{nk})(
(
\Sigma_{k}^{H}
)^{-1}
\mathbf{Ux}^{H}_{n} +
(
\Sigma_{k}^{L}
)^{-1}
\mathbf{x}_{n}^{L} )
```
### Simulation results
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