Premium
Simple principal components
Author(s) -
Vines S. K.
Publication year - 2000
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/1467-9876.00204
Subject(s) - simple (philosophy) , subspace topology , integer (computer science) , principal component analysis , mathematics , transformation (genetics) , simplicity , series (stratigraphy) , algorithm , covariance matrix , matrix (chemical analysis) , variance (accounting) , simple algorithm , principal (computer security) , covariance , computer science , statistics , mathematical analysis , philosophy , materials science , business , chemistry , composite material , biology , operating system , paleontology , biochemistry , accounting , epistemology , thermodynamics , programming language , physics , gene
We introduce an algorithm for producing simple approximate principal components directly from a variance–covariance matrix. At the heart of the algorithm is a series of ‘simplicity preserving’ linear transformations. Each transformation seeks a direction within a two‐dimensional subspace that has maximum variance. However, the choice of directions is limited so that the direction can be represented by a vector of integers whenever the subspace can also be represented by vector if integers. The resulting approximate components can therefore always be represented by integers. Furthermore the elements of these integer vectors are often small, particularly for the first few components. We demonstrate the performance of this algorithm on two data sets and show that good approximations to the principal components that are also clearly simple and interpretable can result.