Commit 8ca43c8a authored by Ying-Qiu Zheng's avatar Ying-Qiu Zheng
Browse files

Update 2021JUL21.md

parent bd5f874d
......@@ -29,6 +29,10 @@ Algorithm 1. EM for the Fusion of GMMs
```math
\gamma(y_{nk}) = \frac{\pi_{k}\mathcal{N}(\mathbf{x}^{L}_{n} | \mu_{k}, \Sigma_{k}^{L})\mathcal{N}(\mathbf{Ux}^{H}_{n} | \mu_{k}, \Sigma_{k}^{H})}{\sum_{j=1}^{K}\pi_{j}\mathcal{N}(\mathbf{x}^{L}_{n} | \mu_{k}, \Sigma_{k}^{L})\mathcal{N}(\mathbf{Ux}^{H}_{n} | \mu_{k}, \Sigma_{k}^{H})}
```
- **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} )
```
### Simulation results
#### We considered three scenarios
......
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