Biobjective sparse principal component analysis

Principal Components are usually hard to interpret. Sparseness is considered as one way to improve interpretability, and thus a trade-off between variance explained by the components and sparseness is frequently sought. In this note we address the problem of simultaneous maximization of variance explained and sparseness, and a heuristic method is proposed. It is shown that recent proposals in the literature may yield dominated solutions, in the sense that other components, found with our procedure, may exist which explain more variance and at the same time are sparser.