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Manifold learning has been demonstrated as an effective way to represent intrinsic geometrical structure of samples. In this paper, a new manifold learning approach, named Local Coordinates Alignment (LCA), is developed based on the alignment technique. LCA first obtains local coordinates as representations of local neighborhood by preserving proximity relations on a patch, which is Euclidean. Then, these extracted local coordinates are aligned to yield the global embeddings. To solve the out of sample problem, linearization of LCA (LLCA) is proposed. In addition, in order to solve the non-Euclidean problem in real world data when building the locality, kernel techniques are utilized to represent similarity of the pairwise points on a local patch. Empirical studies on both synthetic data and face image sets show effectiveness of the developed approaches. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new supervised learning algorithm, which is named the Generalized Marginal Fisher Analysis (GMFA), to utilize the advantages of the Marginal Fisher Analysis (MFA) and the Generalized Singular Value Decomposition (GSVD) techniques for face recognition. The experimental results on several standard face databases demonstrate that GMFA outperforms LDA/Fisherface, LDA/GSVD and MFA. [ABSTRACT FROM AUTHOR]