First, you are correct - items can only belong to one cluster. I think the problem is that I probably wasn't clear enough on what an item is.
In our context, items are "StackOverflow users", so an individual user will belong only to one cluster of users who have a similar profile; in this case this means that a cluster groups users who tend to use the same tags a lot, and also tend to be inactive in the same set of tags.
Note that items are users, and not tags. Two very different groups of users could be sharing a high level of activity in the same tag. A tag doesn't belong to one cluster: a tag might be used unusually high for one or more clusters.
I made up a small, fictional example below, to illustrate how that could work. Suppose I just had 2 tags, SQL and mySQL. I am going to assume that the world contains 3 types of people: people who don't care about databases, and people who do - and for people who care about databases, they are split between mySQL users, vs, say, SQL Server, with no overlap. It's a bit exaggerated, but hopefully not entirely unrealistic.
In this case, this is what I would see: 3 clusters of individuals.
- on the left/middle you have people who don't care. Both SQL and mySQL is low
- on the right/top you have the mySQL DBAs: their usage of mySQL is high, but they also use the tag SQL a lot.
- on the right/bottom, you have the non-mySQL DBAs: their usage of mySQL is low, but the also use the tag SQL a lot.
In that case, both clusters on the right share a high usage of the SQL tag, but they are very different on another dimension (mySQL); an individual user will be assigned to only one cluster, but multiple clusters can have a high usage in the same tag.
I hope this helps! Thanks again for the question,