Discriminant Manifold Learning And Face Recognition

Manifold leaning technology intuitively discovers the intrinsic geometrical structure in the high-dimensional data and has been one of the active research topics in high-dimensional data analysis, pattern recognition, machine learning and document analysis. Previous works have demonstrated that the manifold learning based discriminant approaches can effectively improve the performance of face recognition. Motivated by this, the dissertation starts with discriminant manifold learning and makes an in-depth study of the image geometry representation, including intrinsic geometrical structure, variability geometrical structure and discriminant geometrical structure, based on graph theory. The main work and contributions are as follows:First, a novel method, namely Stable Local Discriminant Embedding (SLDE) is proposed for dimensionality reduction. SLDE defines three adjacency graphs, namely geometrical adjacency graph, diversity adjacency graph and margin adjacency graph, to model the geometry of data. The geometrical adjacency graph characterizes the intrinsic geometrical structure which reflects the similarity of data, the diversity adjacency graph characterizes the most important modes of variability of data, and the margin adjacency graph characterizes the discriminant information. And then, similarity scatter, diversity scatter and margin scatter are calculated from the corresponding graphs respectively. Finally, a concise feature extraction criterion is raised by maximizing the diversity and margin scatters while minimizing the similarity scatter. Moreover, SLDE avoids solving the inverse of a matrix in obtaining the optimal projection vectors, which reduces the computational complexity. Experimental results on several standard face databases demonstrate the effectiveness of the SLDE.Second, Two-dimensional Stable Local Discriminant Embedding (2DSLDE) is presented for face recognition, which directly calculates the similarity scatter, diversity scatter and margin scatter from the image matrices rather than image vectors. In this way,2DSLDE effectively reduces the impact of the small sample size problems and the computational complexity. Experiments on several standard face databases demonstrate the effectiveness of2DSLDE.