Is there any clustering methods that allows to take the time information (i.e. data order) into account ? That is, in addition to maximising intra-cluster similarity and minimising inter-cluster similarity, one could also maximise the "average time spent within a cluster" (or minimise "frequency of cluster changes"). I don't know how to do that since time (or data order) is not a spacial dimension.
As an a simple illustrative example, if we consider two clusters and we have three equally distant data points, then the two clusters may look differently depending on the order:
AAAAAABCBACBCCBBCB ===> We might want to group points A in the same cluster and points B,C in the other cluster
ABABABABAABCCCACCCCC ==> We might want to group points A,B in the same cluster and points C in the other cluster