Colour names and psychophysical colour categories play an important role on human communication. For several application areas from computer vision to Internet shopping, it would be useful to manage colour information using methods of computational colour naming in a similar manner as people do in their everyday life. In this study, we applied two computational methods, the nonnegative matrix factorization and self-organizing maps, to derive basic colours from a spectral database of Munsell colours, and a subset of it. The subset was generated to include only the most saturated samples of each Munsell Hue and Munsell Value pair of the original database. Using both the methods and both the databases, we calculated the sets of 3, 4, 6, and 8 basis vectors to represent the focal colours of colour categories. Colour names of the calculated focal colours were investigated using the results by Sturges and Whitfield as a reference. Nonnegative matrix factorization yields calculated colours more compatible with human basic colours, but the spectra generated by self-organizing maps are more similar to natural spectra as their shape is smoother. (C) 2010 Wiley Periodicals, Inc. Col Res Appl, 35, 294-303, 2010; Published online 14 January 2010 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20569