Funnily enough, my Note 3 did exactly the same thing at Christmas. It was sitting on my desk next to me and I saw the screen light up. It then proceeded to call the first person in my address book. Fortunately that number was itself, so it couldn't get through. I did a factory reset and it hasn't happened since. It was the weirdest thing ever watching it do that all by itself like some invisible hand was controlling it.
I agree a factory reset is a good option.