Appendix for Maximum Weighted Likelihood via Rival Penalized EM for Density Mixture Clustering with Automatic Model Selection

Supposing k is equal to the true mixture number k 1⁄4 3, we randomly located three seed points m1, m2, and m3 in the input space as shown in Fig. 2a, where the data constitute three well-separated clusters. Moreover, we initialized each of the js to be an identity matrix, and all js to be zero, i.e., we initialized 1 1⁄4 2 1⁄4 3 1⁄4 13 . Also, we set the learning rates 1⁄4 0:001 and 1⁄4 0:0001. We performed the learning of RPEM and showed the Q value of (26) over the epochs in Fig. 2b. It can be seen that the Q value has converged after 40 epochs. Fig. 2a shows the positions of three converged seed points, which are all stably located at the corresponding cluster centers. A snapshot of the converged parameter values is: