Machine learning approaches are valuable methods in hyperspectral remote sensing, especially for the classification of land cover or for the regression of physical parameters. While the recording of hyperspectral data has become affordable with innovative technologies, the acquisition of reference data (ground truth) has remained expensive and time-consuming. There is a need for methodological approaches that can handle datasets with significantly more hyperspectral input data than reference data. We introduce the Supervised Self-organizing Maps (SuSi) framework, which can perform unsupervised, supervised and semi-supervised classification as well as regression on high-dimensional data. The methodology of the SuSi framework is presented and compared to other frameworks. Its different parts are evaluated on two hyperspectral datasets. The results of the evaluations can be summarized in four major findings: (1) The supervised and semi-Supervised Self-organizing Maps (SOM) outperform random forest in the regression of soil moisture. (2) In the classification of land cover, the supervised and semi-supervised SOM reveal great potential. (3) The unsupervised SOM is a valuable tool to understand the data. (4) The SuSi framework is versatile, flexible, and easy to use. The SuSi framework is provided as an open-source Python package on GitHub.