Acceleration of Convergence of the Alternating Least Squares Algorithm for Nonlinear Principal Components Analysis

Principal components analysis (PCA) is a popular descriptive multivariate method for handling quantitative data. In PCA of a mixture of quantitative and qualitative data, it requires quantification of qualitative data to obtain optimal scaling data and use ordinary PCA. The extended PCA including such quantification is called nonlinear PCA, see Gifi [Gifi, 1990]. The existing algorithms for nonlinear PCA are PRINCIPALS of Young et al. [Young et al., 1978] and PRINCALS of Gifi [Gifi, 1990] in which the alternating least squares (ALS) algorithm is utilized. The algorithm alternates between quantification of qualitative data and computation of ordinary PCA of optimal scaling data.