Identifying critical variables of principal components for unsupervised feature selection

Principal components analysis (PCA) is probably the best-known approach to unsupervised dimensionality reduction. However, axes of the lower-dimensional space, i.e., principal components (PCs), are a set of new variables carrying no clear physical meanings. Thus, interpretation of results obtained in the lower-dimensional PCA space and data acquisition for test samples still involve all of the original measurements. To deal with this problem, we develop two algorithms to link the physically meaningless PCs back to a subset of original measurements. The main idea of the algorithms is to evaluate and select feature subsets based on their capacities to reproduce sample projections on principal axes. The strength of the new algorithms is that the computation complexity involved is significantly reduced, compared with the data structural similarity-based feature evaluation.