Clustering with additional constraints

Dear all,

suppose we have N examples (trials) of a multivariate time series. Is there a way to impose a constraint on clustering algorithms in order for each cluster to contain samples from as many trials as possible?

To the best of my knowledge, the common approach to clustering would be to simply concatenate the N trials and perform clustering on the resulting data. More often than not however, there won't be any cluster with sufficiently many assigned samples from each trial. So is there any way of forcing the clustering method to select samples from as many specific subsets as possible?

Thanks in advance for your help.

[Mircea Stoica]

Really, nobody has any idea?