Three-view Synthetic data

10000 instances of three-view numerical data set with 4 clusters and 2 feature components are considered. The data points in each view are generated from a 2-component 2-variate Gaussian mixture model (GMM) where their mixing proportions $\alpha_1^{(1)}=\alpha_1^{(2)}=\alpha_1^{(3)}=\alpha_1^{(4)}=0.3$; $\alpha_2^{(1)}=\alpha_2^{(2)}=\alpha_2^{(3)}=\alpha_2^{(4)}=0.15$; $\alpha_3^{(1)}=\alpha_3^{(2)}=\alpha_3^{(3)}=\alpha_3^{(4)}=0.15$ and $\alpha_4^{(1)}=\alpha_4^{(2)}=\alpha_4^{(3)}=\alpha_4^{(4)}=0.4$. The means $\mu_{ik}^{(1)}$ for the first view are $[-10 ~-5)]$,$[-9 ~ 11]$, $[0~ 6]$ and $[4~0]$; The means $\mu_{ik}^{(2)}$ for the view 2 are $[-8 ~-12]$,$[-6 ~ -3]$, $[-2~ 7]$ and $[2~1]$; And the means $\mu_{ik}^{(3)}$ for the third view are $[-5 ~-10]$,$[-8 ~ -1]$, $[0~ 5]$ and $[5~-4]$. The covariance matrices for the three views are $\Sigma_1^{(1)}=\Sigma_1^{(2)}=\Sigma_1^{(3)}=\Sigma_1^{(4)}=\left[ \begin{array}{cc} 1 & 0\\0&1\end{array}\right]$; $\Sigma_2^{(1)}=\Sigma_2^{(2)}=\Sigma_2^{(3)}=\Sigma_2^{(4)}=3 \left[ \begin{array}{cc} 1 & 0\\0&1\end{array}\right]$; $\Sigma_3^{(1)}=\Sigma_3^{(2)}=\Sigma_3^{(3)}=\Sigma_3^{(4)}=2 \left[ \begin{array}{cc} 1 & 0\\0&1\end{array}\right]$; and $\Sigma_4^{(1)}=\Sigma_4^{(2)}=\Sigma_4^{(3)}=\Sigma_4^{(4)}=0.5 \left[ \begin{array}{cc} 1 & 0\\0&1\end{array}\right]$. These $x_1^{(1)}$ and $x_2^{(1)}$ are the coordinates for the view 1, $x_1^{(2)}$ and $x_2^{(2)}$ are the coordinates for the view 2, $x_1^{(3)}$ and $x_2^{(3)}$ are the coordinates for the view 3. While the original distribution of data points for cluster 1, cluster 2, cluster 3, and cluster 4 are 1514, 3046, 3903, and 1537, respectively.