It's more complicated than that, an LDA clusters documents into topics but it's non-trivial to determine what the topic is. You can use the head words of a tf.idf analysis but those still don't necessarily equate to topics. For what you're looking for I think you'd need ontology tagging so a bunch of tweets mentioning soccer players would give a topic word like 'soccer'. The problem then becomes the granularity to ascribe topic to, for example, should it be soccer or sports? Should it be more specific still. Then there's the non-obvious things like a plane goes down and the topic would likely be aviation, but that hardly gives any new information. Representing 20 topics on twitter is very difficult problem. Someone dies and the topic of "death" shows up, not very useful. I'm not disagreeing with you but rather saying that what you're suggesting is a very difficult problem to do in any useful and meaningful way.