ABSTRACT

In this chapter we discuss several forms of nonlinear principal components analysis (NLPCA) that have been proposed over the years. Our starting point is that ordinary or classical principal components analysis (PCA) is a well-established technique that has been used in multivariate data analysis for well over 100 years. But PCA is intended for numerical and complete data matrices, and cannot be used directly on data that contain missing, character, or logical values. At the very least, in such cases the interpretation of PCA results has to be adapted, but often we also require a modification of the loss functions or the algorithms.