The paper presents matrix factorization frameworks on the complex domain to get both intuitive features and high performance in image representation tasks. The real data matrix is transformed to a complex number first which allows exploiting a robust dissimilarity measure based on the Euler representation of complex numbers. Wirtinger's calculus is used to compute the derivative of the cost function. The gradient descent method is utilized to solve complex optimization problems. We show that these frameworks provide feature extraction ability to face recognition models for enhanced performance. Experiments on two scenarios for face recognition including holistic face, and key points occluded face demonstrate that the proposed method of complex matrix factorization provides more faithful basis factors and consistently better recognition results as compared to standard real matrix factorization models.