Weighted least squares for archetypal analysis with missing data

Archetypal analysis expresses observations in terms of a limited number of archetypes, defined as convex combinations of observed units. Such archetypes are found by minimizing a suitable loss function according to the ordinary least squares approach. The technique usually requires a data matrix without missing values. Obviously, this limits its applicability whenever at least one data entry is not available. For this purpose, extensions of archetypal analysis with missing data are developed. In line with recent advances in this domain, this is done by introducing a weighting system giving null weights to the missing entries that are imputed in order to determine the archetypes. This can be done by approaching the problem by means of weighted least squares. The effectiveness of the proposals, also in comparison with existing techniques, is explored by applications to simulated and real data sets.