Interpretation of X-ray spectral data using self-organising maps and hierarchical clustering: a study of Vilhelm Hammershøi’s use of painting materials

The goal of the Vilhelm Hammershøi Digital Archive project of the National Gallery of Denmark is to understand the Danish painter Vilhelm Hammershøi's painting methods by compiling a comprehensive amount of data on his use of materials and working methods through visual and technical examination of a large number of his paintings, and to make this information available to researchers and the public in an open access digital resource. A clear understanding of the full suite of pigments across the paintings requires determination of which materials comprise the palettes of the ground and paint layers. Scanning electron microscopy/energy-dispersive x-ray spectroscopy and macro x-ray fluorescence spectroscopy were selected as the key analytical techniques due to their ability to yield chemical information at the elemental level. This article presents a method that combines unsupervised machine learning and cluster analysis techniques, to automatically reduce the large x-ray spectral data to sets of distinct clusters that share similar spectra, making it possible to identify materials more precisely. The proposed method allowed the grouping of materials by chemical composition, which enabled an optimal understanding of the pigments used in the ground layers sampled from a large number of paintings as well as in the paint layer examined at the surface of one selected painting. The method performed well when compared with other well-established data mining techniques, and it helped reduce the time necessary for the interpretation of the analytical results significantly. Through this approach, a basis for a more nuanced view of Hammershøi's artistic idea and technical development will be generated.