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Hyperspectral reflectance imaging in the short-wave infrared range (SWIR, “extended NIR”, ca. 1000 to 2500 nm) has proven to provide enhanced characterization of paint materials. However, the interpretation of the results remains challenging due to the intrinsic complexity of the SWIR spectra, presenting both broad and narrow absorption features with possible overlaps. To cope with the high dimensionality and spectral complexity of such datasets acquired in the SWIR domain, one data treatment approach is tested, inspired by innovative development in the cultural heritage field: the use of a pigment spectral database (extracted from model and historical samples) combined with a deep neural network (DNN). This approach allows for multi-label pigment classification within each pixel of the data cube. Conventional Spectral Angle Mapping and DNN results obtained on both pigment reference samples and a Buddhist painting (thangka) are discussed.