Research On Manifold Learning Algorithms And The Applications In Image Recognition

With the development of science and technology, especially the coming of information era, the data resources which people processed become more and more larger, especially the image data. Its high dimension, large amount, nonlinear and quick growing rate make it difficult to deal with the data effectively by the traditional linear methods. Thus, a new high-dimensional data analysis called manifold learning, emerged as the information age require. manifold learning has been become a hot research spot, and gradually applied in high-dimensional data analysis, signal processing, biometrics identification, and so on.Manifold learning, mainly retrieves the low-dimensional manifold structure from high-dimensional sample data. In other words, it finds the low-dimensional manifolds in high-dimensional space, and constructs the corresponding mapping, ultimately realizes the data visualization, or dimensional reduction. As to image data, it can find the low-dimensional geometric structure embedded in high-dimensional space, which form from the original image data, and dig out the inherent laws and the intrinsic information.This thesis is based on topologic theory and Riemannian geometry, and has conducted some investigation in manifold learning algorithms, the strength of the robust of manifold learning algorithms, and its applications in image recognition. Firstly, we conduct some investigation in manifold learning theory and algorithms, analyse its advantage and disadvantage, find out the manifold learning algorithm—Locally Linear Embedding(LLE), which suits image recognition most. Secondly, in order to strengthen the robust of LLE algorithm, a new LLE algorithm based on distance measure and united optimization is proposed. This algorithm improves the Euclidean distance of LLE, and unites the solving of denotation coordinate optimizing equation with the solving of embedding coordinate optimizing equation. The new algorithm decreases the mumber of selected neighbor points and improves the noise resisting ability, while is also effective for sparse source data. Finally, in order to improve the speed of face recognition, according to the relations of image preprocessing, feature extraction and face recognition, a new face recognition method based on LLE and Least Squares Support Vector Machines(LS-SVM) is proposed. First of all, to reduce the effect of light intensity on face images, this method uses mean and variance normalization of gray scale to make the pre-processing face images have the same mean and variance. Then it uses PCA and LLE to extract the features of the face images to reduce the identificationerror, while reserves the topological structure of various face types. Afterward it uses LS-SVM to train the feature sets and recognize the faces to improve the recognition speed. The experimental results show that the proposed method improves the speed of face recognition, and has a high recognition rate.