This implies that tags are sub-resources to articles, and they aren't as per my previous post and complex resources should be composed through relationships. The better way to return the data would be include the data yourself, without requiring the use of the include parameter.
Despite this example being in the spec (I think it's a mistake for a couple of reasons), how would you expect to prove a negative from the set of items positively related to your resource?
Will return the tags associated with the articles, this isn't the entire collection of tags. The set of tags you expect to be compared to the results of this call is not returned here. I understand from your explanation what you are looking for, however this doesn't make sense.
The related link should actually be something like this:
That way, you are able to logically talk about retrieving the set of tags which are not related to the article.
Remember that filtering works on properties AND relationships. To answer the filter related popular tags, simply add that additional filter parameter.
The syntax of your filtering strategy would come into play here, but I think this demonstrates the appropriate approach.