Discarding variables in a principal component analysis: algorithms for all-subsets comparisons
In multivariate data analysis, when the number of original variables is large, the principal components themselves may be difficult to interpret and, in order to surpass this problem, the variables that have low correlations with those principal components are usually ignored. But this practice is potentially misleading and it may be preferable to search for small subsets of the original variables that approximate the relevant principal components in some optimal way. The author proposes algorithms for the comparison of all possible subsets according to some most important comparison criteria proposed by McCabe; Robert and Escoufier; Cadima and Jolliffe. The branch and bound algorithms based on adaptations of Furnival and Wilson's implicit enumeration algorithm for regression analysis are presented. The computational effort of the proposed algorithms is studied.
scientific article; zbMATH DE number 1865451