Fig. 1

Three clustering results based on the conventional GMM method by randomly using 3 sets of initial parameters. Table 1 shows the three groups of selected initial sample points. For each set of initial parameters, the initial weight of the k-th Gaussian component is set as \(\:{\alpha\:}_{k}^{0}=1/13\), the initial covariance matrix of the k-th Gaussian component is set as \(\:{\varvec{C}}_{k}^{0}=\left[\begin{array}{cc}86.57&\:1.89\\\:1.89&\:97.09\end{array}\right]\), the initial mean of the k-th Gaussian component is listed in Table 1.