Description

The plyr package is a set of clean and consistent tools that implement the split-apply-combine pattern in R. This is an extremely common pattern in data analysis: you solve a complex problem by breaking it down into small pieces, doing something to each piece and then combining the results back together again.

Details

Principal Component Analysis (PCA) is simply an eigenanalysis of a covariance matrix, G. Its eigenvalues λ_j can be interpreted as the variance of G in the direction of the eigenvector v_j, and λ_j / ∑ λ_k as the proportion of variance explained by v_j. Often, G is well-approximated using the first M eigenvectors and eigenvalues, which we call the model space.

The orthogonal complement of the model space (that is, the space spanned by the remaining eigenvectors), we call the nearly null space. The nearly null space is interesting as a space of low variability, which may be particularly important in, for instance, evolutionary biology. This package provides functions for analyzing the nearly null space and finding interesting structures of low variability, as defined by a quadratic simplicity measure. It is an expanded reimplementation in R of the method described by Gaydos et al (2013).

References

T.L. Gaydos, N.E. Heckman, M. Kirkpatrick, J.R. Stinchcombe, J. Schmitt, J. Kingsolver, J.S. Marron. (2013). Visualizing genetic constraints. Annals of Applied Statistics 7: 860-882.