An optimization approach for mapping and measuring the divergence and correspondence between paths

Many domains of empirical research produce or analyze spatial paths as a measure of behavior. Previously, approaches for measuring the similarity or deviation between two paths have either required timing information or have used ad hoc or manual coding schemes. In this paper, we describe an optimization approach for robustly measuring the area-based deviation between two paths we call ALCAMP (Algorithm for finding the Least-Cost Areal Mapping between Paths). ALCAMP measures the deviation between two paths and produces a mapping between corresponding points on the two paths. The method is robust to a number of aspects in real path data, such as crossovers, self-intersections, differences in path segmentation, and partial or incomplete paths. Unlike similar algorithms that produce distance metrics between trajectories (i.e., paths that include timing information), this algorithm uses only the order of observed path segments to determine the mapping. We describe the algorithm and show its results on a number of sample problems and data sets, and demonstrate its effectiveness for assessing human memory for paths. We also describe available software code written in the R statistical computing language that implements the algorithm to enable data analysis.