Extensions of principal component analysis for nonlinear feature extraction

One of the challenges of feature extraction is the ability to deal with complexities intrinsic to vast data sets in high-dimensional spaces. Multivariate methods are generally used to identify and eliminate unnecessary dimensions so as to encourage a more parsimonious representation of the data set while retaining the maximum information content possible. In this paper, we survey multivariate statistical approaches and introduce their neural network counterparts to perform linear and nonlinear dimensionality reduction. The usefulness of the various techniques is demonstrated using real-life data