Additive clustering and qualitative factor analysis methods for similarity matrices

We review methods of qualitative factor analysis (QFA) developed by the author and his collaborators over the last decade and discuss the use of QFA methods for the additive clustering problem. The QFA method includes, first, finding a square Boolean matrix in a fixed set of Boolean matrices with simple structures to approximate a given similarity matrix, and, second, repeating this process again and again using residual similarity matrices. We present convergence properties for three versions of the method, provide cluster interpretations for results obtained from the algorithms, and give formulas for the evaluation of factor shares of the initial similarities variance.I am indebted to Professor P. Arabie and the referees for valuable comments and editing of the text.