[{title:"object 1",description:"description 1",members:[{profile:{id:"123",},data:{}},{profile:{id:"abc",},data:{}},{profile:{id:"def",},data:{}},]},{title:"object 2",description:"description 3",members:[{profile:{id:"aaa",},data:{}},{profile:{id:"bbb",},data:{}},{profile:{id:"ccc",},data:{}},]},]

db.collection.find({members:{"$not":{$elemMatch:{"profile.id":"aaa"}}}})