Acceleration of the alternating least squares algorithm for principal components analysis

Kuroda, M., Mori, Y., Izuka, M. and Sakakihara, M.

Alternating least squares algorithm, ε algorithm, acceleration of convergence, PRINCIPALS
Principal components analysis (PCA) is a popular descriptive multivariate methodfor quantitative data and extended to deal with qualitative data and mixed measurementlevels data. One of extended PCAs is PRINCIPALS (Principal componentsanalysis by alternating least squares) of Young et al. (1978) in whichthe alternating least squares (ALS) algorithm is utilized. This type of algorithmgenerally involves iteration steps. For the case of the enormous amount of computationsdue to analysis of very large data sets and variable selection problems,the ALS algorithm takes a long time until its convergence. For such situations,it requires to accelerate the convergence of the ALS algorithm. In this paper,we derive a new iterative algorithm for accelerating the convergence of the ALSalgorithm by using the \varepsilon algorithm of Wynn (1962). In the proposed accelerationalgorithm, the varepsilon algorithm speeds up the convergence of the sequence of theparameter estimates from ALS iterations. Numerical experiments demonstratethat the proposed acceleration algorithm improves the speed of convergence ofthe ALS algorithm and works well to reduce the computational time.

Computational Statistics and Data Analysis

Elsevier Science

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