Journal of Classification 4:7-31 (1987) Journal of Classification ©1987Springer-Verlag New YorkInc. Additive Clustering and Qualitative Factor Analysis Methods for Similarity Matrices B. G. Mirkin Central Economics-Mathematics Institute of USSR's Academy Abstract: 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 algo- rithms, and give formulas for the evaluation of "factor shares" of the initial similarities variance. Keywords: Additive Clustering; Qualitative factor analysis; Macrostructures; Average compactness. Introduction A model and corresponding algorithms for the additive clustering of similarity matrices (ADCLUS) have been described by Shepard and Arabie (1979), Arabie and Carroll (1980), and Arabie, Carroll, DeSarbo, and Wind (1981). A three way generalization of this model (INDCLUS) and a corresponding method have also been described by Carroll and Arabic (1983). The additive clustering model assumes an approximate representa- tion of the initial similarity matrix in the form of a weighted sum of Boolean (0, 1) matrices with simple structures that correspond to dusters. A similar idea motivates the methods of qualitative factor analysis elaborated by the I am indebted to Professor P. Arabie and the referees for valuable comments and editing of the text. Author's Address: Boris G. Mirkin, Central Economics-Mathematics Institute, Krasikova str. 32, Moscow 117418, U.S.S.R.