Simple principal components

We introduce an algorithm for producing simple approximate principal compon ents directly from a variance-covariance matrix. At the heart of the algori thm is a series of 'simplicity preserving' linear transformations. Each tra nsformation seeks a direction within a two-dimensional subspace that has ma ximum variance. However, the choice of directions is limited so that the di rection can be represented by a vector of integers whenever the subspace ca n also be represented by vectors of integers. The resulting approximate com ponents can therefore always be represented by integers. Furthermore the el ements of these integer vectors are often small, particularly for the first few components. We demonstrate the performance of this algorithm on two da ta sets and show that good approximations to the principal components that are also clearly simple and interpretable can result.