Mapping Heavy Metal Content in Soils with Multi-Kernel SVR and LiDAR Derived Data

Support vector regression (SVR) is a powerful machine learning technique in the framework of the statistical learning theory; while Kriging is a well-established prediction method traditionally used in the spatial statistics field. However, the two techniques share the same background of reproducing kernel Hilbert space (RKHS). SVR has recently shown promising performance in different spatial mapping tasks. In the present work, the problem of spatial data mapping is addressed using a multi-scale SVR (MS-SVR) approach. This can be considered as a multi-resolution analysis of the observed process. The multi-scale SVR approach is particularly attractive for its capability to deal, at the same time, with the nonlinear regression of the dependent variable on auxiliary variables and with the spatial interpolation. This capability makes the MS-SVR an optimal choice for automatic mapping system. In the present work MS-SVR was applied to soil heavy metal content mapping, in a study area site in the Italian Alps. The area complex landscape, modelled by both glacial and karsts phenomena, along with an heterogeneous nature of the parent material, makes the mapping of heavy metal content a difficult task to approach with linear regression or mixed geostatistical techniques. The result obtained outlines the Multi-scale SVR as a powerful technique for general inference and automatic mapping, with the only constraint of the requirement of a multi-parameter optimization