Just a few possibilities:
- background (education, experience)
- specific industry experience
- technical skill set
- nontechnical skill set
- space (iphone, web app, desktop, social media, business, gaming)
- end user (consumer, SMB, enterprise)
- model (freemium, advertising, subscription, licenses)
- geography
- source of capital (bootstrap, incubator, angels, VC)
- goal (lifestyle business, exit in x years)
- special domain expertise
- pet peeves
- favorite things already done
- philosophical beliefs of how things should be done
I could go on and on, but you kinda get the idea. If enough of these meaningful "dimensions" could be identified and codified, you could probably narrow down a search to a few very good possibilities fairly quickly. Business idea, anyone?