Advancing Precision, Recall, F-score, and Jaccard Index: An Approach for Continuous, Ratio-scale Measurements

Abstract

Gridded data representing attribute estimates at the ratio scale are increasingly common for modelling spatial-environmental variables, including class area estimates (e.g. built-up surface area), population abundance, or vegetation-related measurements such as canopy height. The accuracy of gridded data, including classifications of remotely-sensed data, is usually assessed with measures based on confusion matrices with site-specific class allocations. Yet, these measures cannot be applied to attribute estimates at the ratio-scale. Here, we introduce an approach to extend commonly used agreement measures derived from a confusion matrix (i.e. Jaccard index, Precision, Recall and F-score) to non-negative, continuous ratio-scale attributes. The proposed measures, cJaccard, cPrecision, cRecall and cF-score, have been tested on synthetic datasets, and in a realistic scenario using gridded data measuring built-up surface area. They are viable equivalents to their binary counterparts, invariant to imbalanced data, and suitable for evaluating the agreement of various types of data representing ratio-scale attribute estimates.