### Update 2021JUL21.md

parent 7f9cb92e
 ... ... @@ -19,8 +19,8 @@ In summary, in addition to finding the the hyper-parameters $\pi, \mu, \Sigma_{ ### Pseudo code - Algorithm 1. EM for the Fusion of GMMs 1. Run K-means clustering on the high-quality data to generate the assignment of the voxels$R^{(0)}$. 2. Initialise the means$\mu_{k}$, covariances$\Sigma_{k}$, and mixing coefficients$\pi_k$using the K-means assignment$R^{(0)}$, and evaluate the initial likelihood. 3. Initialise the transformation matrix$\mathbf{U}$using Algorithm 3. 2. Initialise the means$\mu_{k}^{L}$,$\mu_{k}^{H}$, covariances$\Sigma_{k}^{L}$,$\Sigma_{k}^{H}$, and mixing coefficients$\pi_k$using the K-means assignment$R^{(0)}$, and evaluate the initial likelihood. 3. Initialise the transformation matrix$\mathbf{U} = \mathbf{MN}^{T}$, where$\mathbf{MDN}^{T}$is the SVD of$\sum_{k=1}^{K}\mu_{k}^{H}(\mu_{k}^{L})^{T}$. 4. For iteration =$1, 2, ...$, do - **E-step.** Evaluate the responsibilities using the current parameter values -$\gamma(y_{nk}) = \frac{\pi_{k}\mathcal{N}(\mathbf{x}^{L}_{n} | \mu_{k}, \Sigma_{k}^{L})\mathcal{N}(\mathbf{Ux}^{H}_{n} | \mu_{k}, \Sigma_{k}^{H})}{\sum_{j=1}^{K}\pi_{j}\mathcal{N}(\mathbf{x}^{L}_{n} | \mu_{k}, \Sigma_{k}^{L})\mathcal{N}(\mathbf{Ux}^{H}_{n} | \mu_{k}, \Sigma_{k}^{H})}$... ... @@ -31,7 +31,7 @@ In summary, in addition to finding the the hyper-parameters$\pi, \mu, \Sigma_{ - $\pi_k = \frac{N_{k}}{N}$ - $\mathbf{U}=$ - Evaluate the likelihood and check for convergence. 5. Using $\mu_{k}, \Sigma_{k}^{L}, \pi_{k}$ to assignment unseen data. 5. Using $\mu_{k}, \Sigma_{k}^{L}, \pi_{k}$ to assignment unseen data points. ### Simulation results #### We considered three scenarios ... ...
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