We evaluated the performance of nine machine learning regression algorithms and their ensembles for sub-pixel estimation of impervious areas coverages from Landsat imagery. The accuracy of imperviousness mapping in individual time points was assessed based on RMSE, MAE and R 2 . These measures were also used for the assessment of imperviousness change intensity estimations. The applicability for detection of relevant changes in impervious areas coverages at sub-pixel level was evaluated using overall accuracy, F-measure and ROC Area Under Curve. The results proved that Cubist algorithm may be advised for Landsat-based mapping of imperviousness for single dates. Stochastic gradient boosting of regression trees (GBM) may be also considered for this purpose. However, Random Forest algorithm is endorsed for both imperviousness change detection and mapping of its intensity. In all applications the heterogeneous model ensembles performed at least as well as the best individual models or better. They may be recommended for improving the quality of sub-pixel imperviousness and imperviousness change mapping. The study revealed also limitations of the investigated methodology for detection of subtle changes of imperviousness inside the pixel. None of the tested approaches was able to reliably classify changed and non-changed pixels if the relevant change threshold was set as one or three percent. Also for five percent change threshold most of algorithms did not ensure that the accuracy of change map is higher than the accuracy of random classifier. For the threshold of relevant change set as ten percent all approaches performed satisfactory.
In this work nine non-linear regression models were compared for sub-pixel impervious surface area mapping from Landsat images. The comparison was done in three study areas both for accuracy of imperviousness coverage evaluation in individual points in time and accuracy of imperviousness change assessment. The performance of individual machine learning algorithms (Cubist, Random Forest, stochastic gradient boosting of regression trees, k-nearest neighbors regression, random k-nearest neighbors regression, Multivariate Adaptive Regression Splines, averaged neural networks, and support vector machines with polynomial and radial kernels) was also compared with the performance of heterogeneous model ensembles constructed from the best models trained using particular techniques. The results proved that in case of sub-pixel evaluation the most accurate prediction of change may not necessarily be based on the most accurate individual assessments. When single methods are considered, based on obtained results Cubist algorithm may be advised for Landsat based mapping of imperviousness for single dates. However, Random Forest may be endorsed when the most reliable evaluation of imperviousness change is the primary goal. It gave lower accuracies for individual assessments, but better prediction of change due to more correlated errors of individual predictions. Heterogeneous model ensembles performed for individual time points assessments at least as well as the best individual models. In case of imperviousness change assessment the ensembles always outperformed single model approaches. It means that it is possible to improve the accuracy of sub-pixel imperviousness change assessment using ensembles of heterogeneous non-linear regression models.