By clicking on the Public Profile link on LinkedIn, you can change privacy settings that control what information is displayed on your profile to users who are not connected to you in any way on LinkedIn.  It is best to make your public profile visible to everyone but only show your name, industry, location, number of recommendations, and headline.  This will make it possible for people who are looking specifically for you to identify you and send you a connection request and will also limit the amount of information harvesting that can be done by people you do not know. 