Dimension-Reducing Components for Multivariate Data

Gasser for many fruitful discussions, the referees for their constructive criticism, and the editor and an associate editor for suggestions that improved the presentation. Principal components are the benchmark for linear dimension reduction, but they are not always easy to interpret. For this reason, some alternatives have been pro-posed in recent years. These methods produce components that, unlike principal components, are correlated and/or have non-orthogonal loadings. We show in this article that the criteria commonly used to evaluate principal components are not adequate for evaluating such components, and propose two new criteria that are more suitable for this purpose