The COMSTAT algorithm for multimodal factor analysis: an improvement of Tucker's three-mode factor analysis method

Three-mode factor analysis, as developed by Tucker in 1966, is a method for nonredundant representation of data arrays with three subscripts (e.g. observations classified according to persons by variables by conditions). Tucker , however, did not succeed in obtaining a least-squares solution for his model. We derive in this paper a necessary condition for a least-squares solution and construct an algorithm which improves any given initial solution in the least-squares sense. We show that this algorithm converges to a representation satisfying the necessary conditions for a least-squares solution. The method is in no way restricted to three dimensions, but can be applied to any multimodal data array.