Some properties of the normed alternating least squares (ALS) algorithm

In most applications of data analysis quantitative variables are used together with qualitative variables (nominal, ordinal or even of a more complex type). One main task in data analysis is therefore to find an adequate method to analyze a variable set of such different information levels. A well-known approach for this task is the optimal scaling method, which will be illustrated shortly by the linear regression model. The optimal scaling method leads to a constrained nonlinear optimization problem in the <∼ⁿ, which cannot be solved efficiently by standard methods because of the amount of variables and restrictions. Therefore, a so-called normed alternating least squares (ALS) algorithm is proposed in the literature to solve these optimization problems. Because problems of convergence are only tangent by the literature, in this paper some convergence properties of the normed ALS algorithm are given.