Research On Facial Expression Recognition Algorithms Based On Spectral Graph Theory

Facial expression recognition technique becomes more and more important under the rapid technology improvement of information and computer. Facial expression recognition is one of the most important bases of intelligent human-computer interaction, and the subject involves many research fields, including image processing, motion tracking, pattern recognition, physiology, psychology, etc. It is research hotspot of pattern recognition and artificial intelligence. In this paper, we focus on some issues on facial expression feature extraction. Based on spectral graph theory, analyze the intrinsic characters of the facial expression images, so that to extract efficient facial expression representation for classification. The main contributions are listed as follows:First, in order to discover the intrinsic structure of facial expression images, we utilize supervised spectral analysis algorithm to extract facial expression features. Compared to traditional spectral clustering algorithms and dimensional reduction algorithms, supervised spectral analysis algorithm (SSA) benefits from the following three aspects:(1) SSA does not suffer from the small-sample-size problem. It can make matrix transformation directly on data matrix and do not need any other dimensional reduction methods for preprocessing. (2) SSA utilizes the class label information of samples, construct graph according to the data points and their relationship, and the data points after projection can preserve the graph structure. (3) SSA can effectively discover the nonlinear structure hidden in the data. Experimental results show that SSA can extract facial expression features efficiently, and enhance facial expression recognition accuracy.Second, in order to enhance the discriminant power of spectral analysis algorithm, discriminant spectral analysis algorithm (DSA) is proposed. Spectral analysis algorithm mainly preserves the nonlinear intra-locality structure, that is, the local neighborhood relationship between the data points. However, it ignores the relationship between facial expression classes. To enhance the discriminant power, we introduce discriminant information to supervised spectral analysis algorithm. By taking consideration of both nonlinear intra-locality and nonlinear inter-locality structure of the original data points, we obtain discriminant subspace which can preserve both neighborhood relationship of data points and neighborhood relationship of facial expression classes. Third, vector-based dimensionality reduction methods face the shortcomings of high dimension of data matrix and high computation complexity. To overcome these problems, Two-dimensional Fuzzy Discriminant Locality Preserving Projections (2D-FDLPP) is proposed. Fuzzy assignment and discriminant information are introduced to supervised locality preserving projections, and it bases on two-dimensional iamge matrix. Matrix-based dimensionality reduction method extracts the facial expression features directly from image matrices, and does not need to convert two-dimensional image to vector. Moreover, it does not suffer from matrix singular problem, and the features contain more image information. Based on two-dimensional locality preserving projections, we utilize fuzzy k-nearest neighbor classifier to calculate the membership degree, and construct fuzzy weight matrix. Furthermore, the weighted between-class scatter, which denotes the local neighborhood structure of facial expression classes, is introduced to the object function. By preserving both local neighborhood of data points and facial expressions, we obtain more discriminant facial expression features.Fourth, the graph-preserving sparse non-negative matrix factorization algorithm is proposed. The decomposition matrices obtained from common used matrix factorization-based methods always contain negative values, which are physically meaningless in facial expression recognition. Therefore, according to non-negative matrix factorization algorithm, we add non-negative constraint to matrix factorization. Also, both graph-preserving constraint and sparseness constraint are introduced to non-negative matrix factorization. Then parts-based basis images are obtained from the constrained matrix factorization, and facial expression images are represented by combining the basis images linearly. Furthermore, the framework for constrained non-negative matrix factorization is proposed. To guarantee the stationarity of the minimal solution, the projected gradient method is used to ensure the stationarity of limit points. Experimental results show that graph-preserving sparse non-negative matrix factorization is efficient for facial expression and robust to partial occluded facial expression images.