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

SUMMARYThis work presents a new approach which derives a learned data representation method through matrix factorization on the complex domain. In particular, we introduce an encoding matrix-a new representation of data-that satisfies the simplicial constraint of the projective basis matrix on the field of complex numbers. A complex optimization framework is provided. It employs the gradient descent method and computes the derivative of the cost function based on Wirtinger's calculus.

This paper proposes an automatic singing evaluation system. The system provides the user with the score that was assessed by acoustic features and the rhythmic similarity between the original song and the user input. The assessment system is divided into two stages. In the first stage, acoustic similarities are measured by dynamic time warping (DTW). In the second stage, the rhythmic similarity is measured by analysing the optimal path of DTW by quadratic polynomial regression. Finally, the similarity of two stages is combined into one score by corresponding weights. The experimental results show the good performance for the automatic singing evaluation system. 1

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This study presents a joint dictionary learning approach for speech emotion recognition named locality preserved joint nonnegative matrix factorization (LP-JNMF). The learned representations are shared between the learned dictionaries and annotation matrix. Moreover, a locality penalty term is incorporated into the objective function. Thus, the system's discriminability is further improved.