But I think what you are asking is how such a method would come up with its own trends, given just a stream of tweets. This is a supervised approach (http://en.wikipedia.org/wiki/Supervised_learning), so for now, you would need to train it (possibly online) by giving it examples of what should be a trend and what shouldn't. It would be interesting to make it semi-supervised (http://en.wikipedia.org/wiki/Semi-supervised_learning) so that you would only need to provide a small number of labels.
But I think what you are asking is how such a method would come up with its own trends, given just a stream of tweets. This is a supervised approach (http://en.wikipedia.org/wiki/Supervised_learning), so for now, you would need to train it (possibly online) by giving it examples of what should be a trend and what shouldn't. It would be interesting to make it semi-supervised (http://en.wikipedia.org/wiki/Semi-supervised_learning) so that you would only need to provide a small number of labels.