If you haven't seen it, Dirk made a good suggestion here: Active community members
While it doesn't help if you don't have a reference set of data to compare activations against, I posted another possible method here: Is there any way to pull a report on user account reactivations within the last 7 days?
We had to tackle this in the early days of our community and set up a scheduled task to pull a list of active users with the REST API, then compared an identical pull the following day, then removing duplicates. Not the most elegant (or scalable depending on the size of your community), but it did work.
Hope that helps,