Do you basically accept any connection invite, regardless if you know them?
I more or less work in Sales - thus, connecting with people is what I do for a living, and the strength of my network is the strength of my business and the bushiness I generate for my clients.
I send out a good number of requests to connect myself with others - but I always make it clear WHY I am connecting in the brief comment box. I in turn get a decent amount of offers to connect because I am reasonably active on LinkedIn. I typically give the persons profile a quick going over - if it's some distant contact, just looking to build up their contact list, and they have not included a personal note and reason for the reach-out, I'll typically just pass on it.
But if it's a 2nd connection, and they have sent along a personal note, I'll always say "yes" - reach back out with an eMail. Thank them for connecting and if there is any over-lap in what each of us do, see if there are mutual ways that we can help one another. That often leads to a phone call.
In the old days stuff like this was done via a "Cold Call" - and while Cold Calls still happen (I still do them - probably 5 -10/day), a reach out and connection on LinkedIn tends to be a bit to a lot warmer, and more reliable.
If anyone here would like to connect via LinkedIn I'm at https://www.linkedin.com/in/flecksteve/
Steve Fleck @stevefleck | Blog