Manifold Learning Research And Its Application In Face Recognition

Firstly,Let us have an examination on the PCA, LDA and ICA in Linear subspace, the fundamentals of face recognition. We have a study on their principles and algorithm and then try the methods out on the facebase. The results on the Swiss-Roll show that the Linear subspace methods have limits when treating with the nonlinear data.The past few years have seen many fruits,such as Isomap, LLE and LE.In this paper, we analyze such three manifold learning methods detailedly, learning their purpose, principles and algorithm; carrying out experiment on the Swiss-Roll and Swiss-Hole, comparing their embedding effect of knaggy data, estimating their compute complexity. Then, we apply the manifold learning methods to the embedding and rule mining, finding the low-dimensional variables which control the face image through making it visible in two dimension space. Delightingly , we find"face manifold"in the high-dimensional data.We apply the manifold learning methods to face recognition.Firstly, we recognize on"face manifold", then we use LPP to recognize the face. LPP is the linear of LE, solving the problem of Out-of-Sample for manifold learning. We also use the UDP method to face recognition.The reuslts of experiment show that the UDP method solves the classifying promblem of manifold. Based on the Laplacianfaces, we propose an improved Laplacianfaces algorithm, and reconstruct the weight matrix based on the nodes between their shortest path, which could solve the shortage of assigning weights before. Based on UDP and MFA, We propose a new method to measure nonlocal scatter,that is, LMP(Local marginal Projection),which construct the nonlocal scatter through the nearest nodes between different local, and it improves the scatter of the same locals and different local, so it solves the shortage of UDP on treating with the nonlinear data.We discuss the common framework of manifold learning based on the kernel technology, expressing the manifold learning methods by kernel matrix, and exploring the Nystr?m method to solves the kernel matrix. As an uncertain discussion, based on the two framework of ICA, We propose a project view of manifold learning,so to get the mapping relationship between the high e and low dimension space.