Steve, I have two thoughts for you (I had three, but other people already talked about that, lol).
First, and most common, someone else in the neighborhood also has a similar opener using a similar frequency to yours, so when they operate their door, yours follows in duet. They are probably wondering why *their* door is doing ghostly things when you operate yours and maybe if you drive around the neighborhood with you clicker you'll find out where/who. Changing your frequency/code/whatever is probably the easiest cure.
Second, maybe one or more of the safety devices (infrared, touch sensors etc) that are supposed to sense when the door touches a kid/car and/or there's some obstruction in the door path are misbehaving and thinking the door hit something thus retracting it to the open position. Sometimes the sensors are misaligned, sometimes there's a torque sensor that makes the door open if it thinks it's putting too much force in closing the door -- it all depends on the door and mechanism and I've never had an automatic garage door myself, but friends and family have had similar annoyances. Sometimes you do have to call a representative from the company that has the door opener under warranty.
Good luck and I hope that it's easy to make improvements and fix it!
