Feature Extraction Based On Manifold Learning And Its Applications To Face Recognition

Face recognition is an active research topic in real-world biometrics applications. Face recognition can be defined as the identification of individuals according to the effective features obtained from the images of their faces. In the procedure of face recognition, since there are only small numbers of high-dimensional training samples, how to extract the key features for dimensionality reduction and recognition has become one difficult issue in current research.Manifold learning is a hot research topic in the areas of pattern recognition and computer vision. The aim of manifold learning is to seek a low-dimensional smooth manifold in a high-dimensional data space and obtain the corresponding embedding maps for dimensionality reduction and data visualization. Manifold learning based feature extraction algorithms have been widely applied for face recognition and achieved promising performance; however, there are still several problems in these algorithms, such as parameter selection, sensitivity to noise and insufficient discriminative power. In this dissertation, we give an analysis of these problems in existing manifold learning based algorithms, and propose several novel feature extraction algorithms. The main works and contributions of this dissertation are summarized as follows:(1) To overcome the problems existed in several typical locality preserving strategies such as insufficient discriminative power, we propose an algorithm called local maximal margin discriminant embedding (LMMDE). LMMDE takes consideration of intra-class compactness and inter-class separability of samples lying in each manifold, which effectively reduce the between-class overlaps due to the distorted neighborhood relationship. Moreover, the feature extraction criterion of LMMDE is defined based on the maximum margin criterion (MMC), which successfully avoids the small sample size problem.(2) Based on linear discriminant analysis (LDA) and discriminant locality preserving projections (DLPP), we propose minimum-distance discriminant projection (MDA) algorithm and discriminant local median preserving projections (DLMPP) algorithm.LDA can see only the global structure of the data and fails to discover the neighborhood relationship between samples. To solve the problem, MDP incorporates the intra-class similarity weight and inter-class similarity weight into the objective function of LDA:the former one can measure the distance between each data point and the intra-class center, while the later one does not only characterize the distance between the data point and the inter-class center but also can reflect the relation between the between-class distance and the within-class distance.To solve the problems existed in discriminant locality preserving projections (DLPP) such as losing effective image information and similarity weight, we propose a novel algorithm called discriminant local median preserving projections (DLMPP). DLMPP makes use of class medians to calculate the between-class distances to preserve the useful details in the images. Besides, it designs a different similarity weighting mechanism to be apt to preserve neighborhood structure of intra-class samples with little noise such that the robustness of recognition performance is further improved.(3) To overcome the difficulty of parameter selection of most of manifold learning algorithms in the procedure of graph construction, a parameter-free graph construction strategy is designed, which can actively determine neighbors of each data point and assign corresponding edge weights by using the cosine distance. The graph construction strategy doesn’t need any parameters, which makes graph construction more efficient and concise than traditional k-nearest neighbor graph. With the proposed graph construction strategy, we propose a novel feature extraction algorithm called parameter-free locality preserving projection (PLPP) based on LPP. In addition, considering that the class information could make the algorithm more discriminative, we propose a supervised parameter-free locality preserving projection (SPLPP) algorithm by incorporating the class information into the criterion function of PLPP.(4) To overcome the difficulty of neighbor parameter selection of marginal fisher analysis (MFA) in the construction of the intrinsic graph and the penalty graph, a novel algorithm called nearest-neighbor (NN) classifier motivated marginal discriminant projection (NN-MDP) is proposed. Motivated by the NN classifier, NN-MDP defines the intrinsic graph and the penalty graph with the purpose of preventing data samples from being wrongly categorized. In contrast to MFA, NN-MDP can actively construct the intrinsic graph and penalty graph without unknown parameters, so it can lower the computational complexity. Moreover, the extracted features are more suitable for the NN classifier due to the motivation of reducing the recognition error brought by the NN classifier.