I don't think there is. The only reason Google is any good at is that they have been collecting data for well over a decade in order to do it. It's not just their web index, but they can see most peoples' email and calendar, their web searches, their location. Google also did things like "Google 411" which got them vast amounts of voice and behavioural data.

I'd be interested to see a startup go for the relevance idea, but I don't think they would have the data needed to do it.