In this paper, a dimensionality reduction method applied on facial expression recognition is investigated. An\nunsupervised learning framework, projective complex matrix factorization (proCMF), is introduced to project\nhigh-dimensional input facial images into a lower dimension subspace. The proCMF model is related to both the\nconventional projective nonnegative matrix factorization (proNMF) and the cosine dissimilarity metric in the simple\nmanner by transforming real data into the complex domain. A projective matrix is then found through solving an\nunconstraint complex optimization problem. The gradient descent method was utilized to optimize a complex cost\nfunction. Extensive experiments carried on the extended Cohn-Kanade and the JAFFE databases show that the proposed\nproCMF model provides even better performance than state-of-the-art methods for facial expression recognition
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