I sometimes feel like this. I think it's because of the very fact that you're surrounded by people you're not interacting with, and/or who aren't interacting with you, it just drives the point home how isolated we really are, to feel isolated even when surrounded by people. The isolation becomes more than a physical state of not being near people; it's a mental state of not being near people, as well. In many ways, that can be even more difficult to overcome than physical isolation. (Though I know from experience that physical isolation just makes it worse.)
One time in elementary school I was with a group of friends and we went with the principal to do something in the gym. These were nice people, the principal too, but somehow they just forgot I was there with them, and completely ignored me. I sadly wandered off and nobody ever even noticed that I'd gone.
Ditto with some forums I really tried to fit into, where I posted hundreds of helpful posts, nobody noticed when I left.
I once dreamed I was at a gathering and no matter what I tried, nobody noticed me. I finally in anger and frustration said, "I wish I were invisible, that would teach them!" I noticed eventually that a few people seemed to wonder where I was, and they couldn't see me. I found a mirror and looked in it and...you guessed it. I'd turned invisible, literally.
I started crying and then I woke up. One of the worst feelings in the world.