I have a dateset of around a million observations, and each observation (300 features) belongs to one of around 300 groups. The set of observations of one group does not directly correspond to the observations of another group in some meaningful way. There is no domain knowledge to help. I wish to cluster the groups themselves, rather than the individual observations. I make use of dimensionality reduction.
To achieve this I have had two ideas. The first, clustering all observations, then deriving the clustering of the groups via this clustering, by for example taking the mean, or majority vote of the individual observations / group. The second idea is to try to create many statistics to describe a group, and then cluster based on these statistics rather than the individual observations of a group.
I am not quite convinced of either idea and have trouble finding any further information on this problem. Is there a standard method of doing this?