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

Area of Science:

• Behavioral science
• Computational geometry
• Data analysis

Background:

• Empirical research often analyzes spatial paths to understand behavior.
• Existing methods for path comparison often require timing data or manual coding.
• There is a need for robust, automated methods to compare spatial paths.

Purpose of the Study:

• To introduce a new optimization approach, ALCAMP (Algorithm for finding the Least-Cost Areal Mapping between Paths), for measuring area-based deviation between spatial paths.
• To develop a method that is robust to common issues in real-world path data.
• To provide a tool for analyzing human memory for paths.

Main Methods:

• Developed ALCAMP, an algorithm using an optimization approach for area-based path deviation measurement.
• ALCAMP determines path mapping based solely on the order of observed path segments, not timing information.
• The algorithm is designed to handle path crossovers, self-intersections, segmentation differences, and incomplete paths.

Main Results:

• ALCAMP successfully measures area-based deviation between spatial paths.
• The algorithm produces a mapping between corresponding points on two paths.
• Demonstrated effectiveness on sample problems, datasets, and in assessing human spatial memory.

Conclusions:

• ALCAMP offers a robust and timing-independent method for comparing spatial paths.
• The algorithm addresses limitations of previous path analysis techniques.
• Available R software facilitates the application of ALCAMP in empirical research.