[{"_id":154,"title":"title1","authors":[{"name":"John Smith","registered":true},{"name":"Jane Doe","registered":true},],"tags":["tag1","tag2","tag3"]},{"_id":153,"title":"title2","authors":[{"name":"John Smith","registered":true},{"name":"Jane Doe","registered":true},],"tags":["tag1","tag3","tag4"]}]

db.collection.aggregate([{$match:{"authors":{$all:[{$elemMatch:{registered:true}}]}}},{$unwind:"$tags"},{$group:{_id:"$tags",titles:{"$addToSet":"$title"}}},{$project:{_id:0,tag:"$_id",titles:1,size:{$size:"$titles"}}}])