Scaling additional contributions to principal components analysis

Principal components analysis (PCA) is of great use in representation of multi-dimensional data sets, often providing a useful compression mechanism. Sometimes, input data sets are drawn from disparate domains, such that components of the input are heterogeneous, making them difficult to compare in scale. When this occurs, it is possible for one component to dominate another in the PCA at the expense of the information content of the original data. We present an approach to balancing the contributions of different components that is constructive; it generalises to the case of the addition of several variables. Conjectures about improved approaches and more complex data sets are presented. The approach is demonstrated on two current research applications.