In most existing multi-manifold face recognition algorithms, the original data with noise are directly processed, but the noisy data often have a negative impact on the accuracy of the algorithm. In order to solve the problem, a Robust Multi-Manifold Discriminant Local Graph Embedding algorithm based on the Maximum Margin Criterion (RMMDLGE/MMC) was proposed. Firstly, a denoising projection was introduced to process the original data for iterative noise reduction, and the purer data were extracted. Secondly, the data image was divided into blocks and a multi-manifold model was established. Thirdly, combined with the idea of maximum margin criterion, an optimal projection matrix was sought to maximize the sample distances on different manifolds while to minimize the sample distances on the same manifold. Finally, the distance from the test sample manifold to the training sample manifold was calculated for classification and identification. The experimental results show that, compared with Multi-Manifold Local Graph Embedding algorithm based on the Maximum Margin Criterion (MLGE/MMC) which performs well, the classification recognition rate of the proposed algorithm is improved by 1.04, 1.28 and 2.13 percentage points respectively on ORL, Yale and FERET database with noise and the classification effect is obviously improved.

The estimation of the low-dimensional subspace data may have serious deviation under lacking of the training samples. In order to solve the problem, a novel regularized neighborhood preserving embedding algorithm based on QR decomposition was proposed. Firstly, a local Laplace matrix was defined to preserve local structure of the original data. Secondly, the eigen spectrum space of within-class scatter matrix was divided into three subspaces, the new eigenvector space was obtained by inverse spectrum model defined weight function and then the preprocess of the high-dimensional data was achieved. Finally, a neighborhood preserving adjacency matrix was defined, the projection matrix obtained by QR decomposition and the nearest neighbor classifier were selected for face recognition. Compared with the Regularized Generalized Discriminant Locality Preserving Projection (RGDLPP) algorithm, the recognition accuracy rate of the proposed method was respectively increased by 2 percentage points, 1.5 percentage points, 1.5 percentage points and 2 percentage points on ORL, Yale, FERET and PIE database. The experimental results show that the proposed algorithm is easy to implement and has high recognition rate relatively under Small Sample Size (SSS).

Considering high dimensional data image in face recognition application and Euclidean distance cannot accurately reflect the similarity between samples, a Mahalanobis distance based Local Marginal Fisher Analysis (MLMFA) dimensionality reduction algorithm was proposed. A Mahalanobis distance could be ascertained from the existing samples. Then, the Mahalanobis distance was used to choose neighbors and to reduce the dimensionality of new samples. Meanwhile, to describe the intra-class compactness and the inter-class separability, intra-class “similarity” graph and inter-class “penalty” graph were constructed by using Mahalanobis distance, and local structure of data set was preserved well. With the proposed algorithm being conducted on YALE and FERET, MLMFA outperforms the algorithms based on traditional Euclidean distance with maximum average recognition rate by 1.03% and 6% respectively. The results demonstrate that the proposed algorithm has very good classification and recognition performance.