Technological progress allows for an ever-faster acquisition of hyperspectral data, challenging the users to keep up with interpreting the recorded data. Matrix Factorization, the representation of data sets by bases (or loads) and coefficient (or score) images is long used to support the interpretation of complex data sets. We propose in this publication Simplex Volume Maximization (SiVM) for the analysis of XRF imaging data sets. SiVM selects archetypical data points that represents the data set and thus provides easily understandable bases, preserves the non-negative character of XRF data sets and has low demands concerning computing resources. We apply SiVM on an XRF data set of Hans Memling’s Portrait of a man from the Lespinette family from the collection of the Mauritshuis Museum and discuss capabilities and shortcomings of SiVM.