A methodology for translating positional error into measures of attribute error, and combining the two error sources

This paper summarizes our efforts to investigate the nature, behavior, and implications of positional error and attribute error in spatiotemporal datasets. Estimating the combined influence of these errors on map analysis has been hindered by the fact that these two error types are traditionally expressed in different units (distance units, and categorical units, respectively. We devised a conceptual model that enables the translation of positional error into terms of thematic error, allowing a simultaneous assessment of the impact of positional error on thematic error – a property that is particularly useful in the case of change detection. Linear algebra-based error model combines these two error types into a single measure of overall thematic accuracy. This model was tested in a series of simulations using artificial maps, in which complex error patterns and interactions between the two error types, were introduced. The model accommodated most of these complexities, but interaction between the two error types was found to violate model assumptions, and reduced its performance. A systematic study of the spatiotemporal structure of error in actual datasets was thus conducted. Only weak and insignificant interactions were found between the two error types. Application of this error model to real-world time series data indicated that such data are much less accurate than is typically thought. These results highlight the importance of reducing positional error. The second part of our paper presents an analysis of how to reduce the impacts of positional error through aggregation (i.e., increasing the observation grain). Aggregation involves information loss, and thus, the choice of a proper cell size for aggregation is important. A model was developed to quantify the decay in impact of positional error, with increasing cell size. Applying the model to actual data sets, a major reduction in effective positional error was found for cell sizes ranging between 3-10 times the average positional error (RMSE). The model may help users in deciding on an optimal aggregation level given the tradeoff between information loss and accuracy gains.