The geographic object-based image analysis (GEOBIA) framework has gained increasing interest for the last decade. One of its key advantages is the hierarchical representation of an image, where object topological features can be extracted and modeled in the form of structured data. We thus propose to use a structured kernel relying on the concept of bag of subpaths to directly cope with such features. The kernel can be approximated using random Fourier features, allowing it to be applied on a large structure size (the number of objects in the structured data) and large volumes of data (the number of pixels or regions for training). With the so-called scalable bag of subpaths kernel (SBoSK), we also introduce a novel multi-source classification approach performing machine learning directly on a hierarchical image representation built from two images at different resolutions under the GEOBIA framework. Experiments run on an urban classification task show that the proposed approach run on a single image improves the classification overall accuracy in comparison with conventional approaches from 2% to 5% depending on the training set size and that fusing two images allows a supplementary 4% accuracy gain. Additional evaluations on public available large-scale datasets illustrate further the potential of SBoSK, with overall accuracy rates improvement ranging from 1% to 11% depending on the considered setup.