Matrix factorization (MF) and its extensions have been intensively studied in computer vision and machine learning. In this paper, unsupervised and supervised learning methods based on MF technique on complex domain are introduced. Projective complex matrix factorization (PCMF) and discriminant projective complex matrix factorization (DPCMF) present two frameworks of projecting complex data to a lower dimension space. The optimization problems are formulated as the minimization of the real-valued functions of complex variables. Motivated by independence among extracted features, Fisher linear discriminant is used as hard constraint on supervised model. Experimental results on facial expression recognition (FER) show improved classification performance in comparison to real-valued features of both unsupervised and supervised NMFs.