This work proposes a novel method of matrix factorization on the complex domain to obtain both extracted features and coefficient matrix with high recognition results in facial expression recognition. The real data matrix is transformed into a complex number based on the Euler representation of complex numbers. Sparse regularization in dimensionality reduction using ridge term (L2-norm) is applied into this study. Basic complex matrix factorization (CMF) is modified into sparse complex matrix factorization using ridge term (SCMF-L2) which adding sparse L2-norm constraint in the coefficient. The gradient descent method is used to solve optimization problems. Experiments on facial expression recognition scenario reveal that the proposed methods provide better recognition results that prevalent NMF and CMF methods.