# best statistical approach to study the time evolution of clustering in a data set

I am using a stochastic method for the clustering of a data set. The number of clusters that this approach returns, can differ in each iteration. On the other hand, I would like to study the evolution of clustering at different snapshot of the data. In the following plot, I ran this clustering method for $N$ times in one snap shot and then I plotted the probability of two data points being clustered in the same group in a given time.

My question:

What is the best statistical approach to compare the evolution of this two-dimensional matrix in terms of, for instance, the size of blocks which are appeared in this matrix or the shape of the whole matrix in general?