Comparing Clustering Over Time
There are many options. One option could be to find clusters at the first time point and define a change &quot;metric&quot; at the second time point. A possible change metric is if the data points belong to the same cluster at the second time point.
You mention a variation of k-means. Since k-means is an iterative algorithm, this cluster re-assignment is what happens between each training step. The difference with this method is you are allowing the data points to move between training steps and measuring how many cluster assignments change.