It depends on your definition of alone. I feel alone in a positive way when I'm with my boyfriend and only him; I feel alone in a negative way in a crowd; I feel alone in a neutral way when its just me.
I think the first one confuses people. To me, he doesn't count as a person. People are scary, he's not, he's more than a person to me. The two of us being physically in the same room, him working on what he wants to, me work on what I want to do (*cough*posting-on-wrong-planet*cough*), feels like a very positive version of solitude to me.
As a whole, I get lonely. I want social contact, but I want it controlled. Contact with him doesn't need to be controlled - we live together even. There are times I want to explicitly be doing my own things, but with him I don't need to be physically alone.
I want time with only him, I want time not dealing with people, and I want time with people. The problem is that I want time where I actually feel involved, not separate and watching them, and want to actually feel like I matter to them. These make it such that I'm often lonelier in a group than I am physically alone.