title: The COMSTAT algorithm for multimodal factor analysis: an improvement of Tucker's three-mode factor analysis method.
abstract: 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.
mesh_terms: D000513:Alpha Rhythm; D003700:Delta Rhythm; D004569:Electroencephalography / Q000379:methods*; D005163:Factor Analysis, Statistical; D006801:Humans; D013826:Theta Rhythm