Improving sub-pixel imperviousness change prediction by ensembling heterogeneous non-linear regression models

GEODESY AND CARTOGRAPHY Vol. 65, No 2, 2016, pp. 193-218 © Polish Academy of Sciences DOI: 10.1515/geocart-2016-0016 Improving sub-pixel imperviousness change prediction by ensembling heterogeneous non-linear regression models Wojciech Drzewiecki AGH University Faculty of Mining Surveying and Environmental Engineering Department of Geoinformation, Photogrammetry and Remote Sensing of Environment al. Mickiewicza 30, 30-059 Kraków, Poland e-mail: Received: 2 July 2016 / Accepted: 12 September 2016 Abstract: 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. Keywords: machine learning, model ensembles, sub-pixel classification, impervious areas, Landsat Unauthenticated Download Date | 1/23/17 8:20 PM 194 Wojciech Drzewiecki 1. Introduction The coverage of impervious surface areas (ISA), defined as areas preventing the infiltration of rainwater into the ground, is considered as very important environmental indicator (Arnold and Gibbons, 1996). Growing ISA percentage indicates an increase of anthropogenic impacts on the environment, what is reflected in changes of many environmental functions and processes (e.g. rainfall-runoff transformation, ground water recharge, environmental or even population health) (Arnold and Gibbons, 1996; Shahtahmassebi et al., 2014). For this reason the accurate information about ISA coverage and monitoring of its change plays an important role in many environmental studies, especially urban and hydrological ones (Caldwell et al., 2012; Dams et al., 2013; Shahtahmassebi et al., 2014; Li et al., 2016). Remote sensing is nowadays commonly used for monitoring changes in land use and land cover (LULC), including changes of imperviousness. Applications of remotely sensed data for mapping ISA have been reviewed by Weng (2012) and Lu et al. (2014a). Recently, very high spatial resolution satellite images, aerial (Nielsen et al., 2011) and even UAV photographs (Tokarczyk et al., 2015) are used for imperviousness mapping. Despite that fact, in regional scale and/or ISA change assessment applications Landsat imagery is the most frequently used (Lu et al., 2014b; Tokarczyk et al., 2015; Li et al., 2016). LULC changes may take different forms (Turner and Meyer, 1994). In case of conversion one land cover type changes completely into another. However, very often the changes are much more subtle and have a form of modification. What changes is not the LULC category, but the proportions of land cover fractions inside the considered area (pixel, object, mapping unit) still classified to the same class. For example, due to urbanization processes the housing density (and in turn the imperviousness) may increase substantially, nevertheless the area is classified as “discontinuous built-up” or “10-30% impervious” as it was before. The ISA changes usually takes a form of modifications. Their detection and assessment from high, medium and low-resolution remotely sensed images requires the use of sub-pixel analysis approaches. In case of ISA mapping done for individual cities, the spectral mixture analysis-based methods are preferred (Ridd, 1995; Lu et al., 2014a). However, when the study area is dominated by other than urban types of land cover, mixture analysis may not give the expected accuracy and the regression-based approaches provide an alternative (Lu et al., 2014b; Heremans and Van Orshoven, 2015). These methods range from building regression models with vegetation indices (Bauer et al., 2004), through regression trees applications (Yang et al., 2003) to implementation of other machine learning algorithms, like artificial neural networks (Mohapatra and Wu, 2007; Chormanski et al., 2008) or support vector machines (Walton, 2008; Esch et al., 2008). Applicability of machine learning algorithms for sub-pixel imperviousness mapping was compared in several studies (Liu and Wu, 2005; Walton, 2008; Mohapatra and Wu, 2010; Bernat and Drzewiecki, 2014; Heremans and. Van Orshoven, 2015). Each Unauthenticated Download Date | 1/23/17 8:20 PM Improving imperviousness change prediction with model ensembles 195 of these studies was focused on evaluating the ISA prediction accuracy achieved for individual point in time. But, imperviousness estimates generated for particular dates are very often subtracted from each other and used for change assessment. The methodology of change detection through sub-pixel percent imperviousness mapping was proposed by Yang et al. (2003). This approach is classified to layer arithmetic change detection techniques (Tewkesbury, 2015). It should be noted however, that the input layers and their difference have semantic meaning. Moreover, the subtracted layers may be created through sophisticated non-linear regression models or even through hybrid approach when classification and regression models are combined (Mountrakis et al., 2009; Bernat and Drzewiecki, 2014). In case of sub-pixel imperviousness change detection it is commonly assumed that to assure the highest accuracy of change map the accuracies of individual imperviousness maps should be as high as possible. Such assumption is true for post-classification change detection techniques (Hussain, 2013). However, in case of sub-pixel assessment of fractional coverages (eg. imperviousness), although (...truncated)