perfect solution, while in [$k$-means]{}many clusters get merged incorrectly or die off. Dead clusters are those which do not get any points assigned to them. The update rule of Equation  collapses the dead clusters on to the origin.

Figure \[fig:different\_progress\_coeffs\] shows the effect of the progress coefficient on the quality of the solution found by [G-MM]{}. Different colors correspond to different initialization schemes. The solid line indicates the average objective over 50 iterations, the shaded area covers one standard deviation from the average, and the dashed line indicates the best solution over the 50 trials. Smaller progress coefficients allow for more extensive exploration, and hence, smaller variance in the quality of the solutions. On the other hand, when the progress coefficient is large [G-MM]{}is more sensitive to initialization (is more sticky) and, thus, the quality of the solutions over multiple runs is more diverse. However, despite the greater diversity, the best solution is worse when the progress coefficient is large. [G-MM]{}reduces to [$k$-means]{}if we set the progress coefficient to 1 (the largest possible value).

[0.32]{} ![Visualization of clustering solutions on the D31 dataset [@kmeans:D31] from identical initializations. Random partition initialization scheme is used. (a) color-coded ground-truth clusters. (b) solution of 