Complex Matrix Factorization for Face Recognition

— This work proposes a novel method of matrix factorization on the complex domain to obtain both intuitive features and high recognition results in a face recognition system. The real data matrix is transformed into a complex number based on the Euler representation of complex numbers. Base complex matrix factorization (CMF) is developed and two extensions including sparse complex matrix factorization (SpaCMF) and graph complex matrix factorization (GraCMF) are developed by adding sparse and graph constraints. Wirtinger's calculus is used to compute the derivative of the cost function. The gradient descent method is used to solve complex optimization problems. The proposed algorithms are proved to provide effective features for a face recognition model. Experiments on two face recognition scenarios that involve a whole face and an occluded face reveal that the proposed methods of complex matrix factorization provide consistently better recognition results than standard NMFs.