How to make a connection with academics on Linkedin that they would accept?
I consider LinkedIn to be pretty low-stakes interaction, so I merely want to avoid being linked to spammers and frauds.  My own policy, then, is that I will accept LinkedIn invitations from anybody who I actually know who they are, either by a) having had a non-trivial interaction with them (including by phone or electronically) or b) indirect interactions such as reading their papers.

Other people may have more stringent policies, but in my opinion, it's reasonable to request a connection with anybody you have a relationship with: the worst that will happen is that they will ignore it.