Orthogonal Simple Component Analysis

A new methodology to aid interpretation of a principal component analysis is presented. While preserving orthogonality, each eigenvector is replaced by a vector, close to it in angle terms, whose entries are small integers. We call such vectors simple. The approach is exploratory, a range of sets of pairwise orthogonal simple components being systematically obtained, from which the user may choose. Examples and simulations show that this approach effectively combines simplicity, retention of optimality and computational efficiency. Further, when the population eigenvectors have simple structure, this can be recovered using only the information from the sample. The methodology can also be used to simplify a given subset of components. An efficient algorithm for the computationally challenging problem of producing orthogonal components is provided.