I often tell my DSLR photography students to "fill the frame" when composing shots. I also recently wrote about how not including the entire motorcycle makes for an image with more impact. That said, another composition technique follows just the opposite of those and calls for using negative space in the frame to be part of the photograph.
In the above image instead of filling the frame with the palm tree, or using a rule of thirds type of composition, the palm tree is composed as to look small and isolated allowing the negative space itself to be the main subject of the photograph. Filling the frame with negative space gives the impression of great expansion, or rather, no end once the eye reaches the edge of the frame. The viewer's eye continues on past the edges filled in by their own imagination of what goes beyond.
Post a link to your example of negative space composition in the comments below.