Multifactor Analysis for Face Recognition Based on Factor-Dependent Geometry

The success of multifactor analysis, such as Multilinear Principal Component Analysis (MPCA), results from its ability to decompose the characteristics of each sample vector into multiple parameters associated with multiple factors. MPCA parameterizes each factor based on the average structure of the submanifolds that are created by varying only this factor. This averaging process is based on the assumption that the influences of multiple factors are independent, and thus each submanifold is influenced only by one factor. Only if this assumption is true can the average shape sufficiently represent individual submanifolds. In this paper, we show that if the original shapes of such submanifolds vary greatly, their average shape merely illustrates the general tendencies influenced by each factor. In a real data set, such significant variance is not rare; when this occurs, MPCA's parameters cannot sufficiently cover individual submanifolds. To break these limitations of MPCA, we propose semi-decomposable parameters that still decompose the influences of multiple factors while also representing the interdependence of the factors. The factor-dependent parameters obtained by our method preserve individual submanifolds without averaging. Thus, we do not lose the shape of each submanifold, which makes these novel parameters appropriate for accurate classification of each sample as a result of sufficient coverage. The accuracy of experiments on face recognition demonstrates the advantages of our method over leading methods for multifactor analysis.