臉部表情辨識場景的實驗包含整個臉部和遮蔽臉部的識別，本研究提出的方法比較普遍大家使用的 NMF和 CMF方法提升了更好的識別結果。此方法也達到停止條件，並且比 NMF和 CMF方法的擴張快得許多。;This work proposes novel methods of matrix factorization on the complex domain to obtain both extracted features and coefficient matrix with high recognition results in a face recognition and facial expression recognition problems. The real data matrix is transformed into a complex number based on the Euler representation of complex numbers. The basic complex matrix factorization (CMF) is modified using several constraints and is investigated in this study. The basic CMF is modified into Sparse Complex Matrix Factorization using Ridge Term (SCMF-L2) which adds sparse L2-norm constraint in the coefficient. This study also develops novel constraint which enforces pixel dispersion penalty on the basis matrix called Spatial Constrained Complex Matrix Factorization (SpatialCMF). This study also builds novel constraint which uses the combination of pixel images representation and class annotation constraints for training data named as Coupled Complex Matrix Factorization (CoupledCMF). The proposed methods compare with prevalent NMF methods and extensions of CMF methods, including sparse complex matrix factorization (SCMF) and graph complex matrix factorization (GCMF) which adds sparse L1-norm and graph constraints, respectively. The gradient descent method is used to solve optimization problems. Experiments on face recognition and facial expression recognition scenarios that involve a whole face and an occluded face reveal that the proposed methods provide better recognition results that common NMF and CMF methods. The proposed methods also reach the stopping condition and converge much faster than the extensions of NMF and CMF methods.
