Use of convexity for finding pure variables in two-way data from mixtures

The principles for finding pure (or key) variables in two-way non-negative data from mixtures are discussed. It is shown that with a normalization to constant projection on a given vector one obtains a convex and bounded representation of the data with the pure variables as extreme points. An algorithm based upon this observation is compared with other methods for the same purpose and tested using data from the literature.