Choropleth Mapping with Uncertainty: A Maximum Likelihood–Based Classification Scheme

Abstract

Choropleth mapping provides a powerful way to visualize geographical phenomena with colors, shadings, or patterns. In many real-world applications, geographical data often contain uncertainty. How to incorporate such uncertainty into choropleth mapping is challenging. Although a few existing methods attempt to address the uncertainty issue in choropleth mapping, there are limitations to widely applying these methods due to their strong assumption on the distribution of uncertainty and the way in which similarity or dissimilarity is assessed. This article provides a new classification scheme for choropleth maps when data contain uncertainty. Considering that in a choropleth map, units in the same class are assigned with the same color or pattern, this new approach assumes the existence of a representative value for each class. A maximum likelihood estimation–based approach is developed to determine class breaks so that the overall within-class deviation is minimized while considering uncertainty. Different methods—including linear programming, dynamic programming, and an interchange heuristic—are developed to solve the new classification problem. The proposed mapping approach has been applied to map the median household income data from the American Community Survey and simulated disease occurrence data. Test results show the effectiveness of the new approach. The linkage between the new approach and the existing methods is also discussed. Key Words: choropleth mapping, map classification, maximum likelihood estimation, uncertainty.