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The increasing availability of motion sensors and video cameras in living spaces has made possible the analysis of motion patterns and collective behavior in a number of situations. The visualization of this movement data, however, remains a challenge. Although maintaining the actual layout of the data space is often desirable, direct visualization of movement traces becomes cluttered and confusing as the spatial distribution of traces may be disparate and uneven. We present proximity-based visualization as a novel approach to the visualization of movement traces in an abstract space rather than the given spatial layout. This abstract space is obtained by considering proximity data, which is computed as the distance between entities and some number of important locations. These important locations can range from a single fixed point, to a moving point, several points, or even the proximities between the entities themselves. This creates a continuum of proximity spaces, ranging from the fixed absolute reference frame to completely relative reference frames. By combining these abstracted views with the concrete spatial views, we provide a way to mentally map the abstract spaces back to the real space. We demonstrate the effectiveness of this approach, and its applicability to visual analytics problems such as hazard prevention, migration patterns, and behavioral studies.