This paper presents an advanced method for complex matrix factorization, termed exemplar-embed complex matrix factorization with elastic net penalty (ENEE-CMF). The proposed ENEE-CMF integrates both L1 and L2 regularizations on the encoding matrix to enhance the sparsity and effectiveness of the projection matrix. Utilizing Wirtinger’s calculus for differentiating real-valued complex functions, ENEE-CMF efficiently addresses complex optimization challenges through gradient descent, enabling more precise adjustments during factorization. Experimental evaluations on facial expression recognition task demonstrate that ENEE-CMF significantly outperforms traditional non-negative matrix factorization (NMF) and similar complex matrix factorization (CMF) models, achieving superior recognition accuracy. These findings highlight the benefits of incorporating elastic net regularization into complex matrix factorization for handling challenging recognition tasks.