Acceleration and Re-start of the Alternating Least Squares Algorithm for Non-linear Principal Components Analysis

In principal components analysis (PCA) of mixture of quantitative and qual-itative data, we require to quantify qualitative data. The alternating least squares (ALS) algorithm can be used for PCA including such quantification. However, the ALS algorithm is linear convergence and its speed is very slow in the ap-plication of PCA to very large mixed data. In order to circumvent the problem of its slow convergence, Kuroda et al. (2011) provided an acceleration of the ALS algorithm using the vector " (v") algorithm of Wynn (1962). In this paper, we try to further increase the speed of convergence of the v " acceleration of the ALS algorithm using a re-starting procedure. Numerical experiments ex-amine how the re-starting procedure works effectively to reduce the number of iterations and computation time of the v " acceleration of the ALS algorithm