Fig. 8. Detail of Cluster 3 and Cluster 4 from Figure 7 and the Numerically Generated Heterogeneous Newtonian data set.

With the EM algorithm explained in Section 4.3, the probability that each point is a member of each cluster is calculated by evaluating all Gaussian components of the Gaussian mixture model at each point, $(s_x^j({\tau }^{\mathrm{†}}),s_y^j({\tau }^{\mathrm{†}}))$.