Research On Dimension Reduction Algorithms Based On Manifold Learning

Data dimensionality reduction is the process that high dimensional data is mapped into the low-dimensional space. Dimensionality reduction based on manifold learning is an important part of dimensionality reduction research. Manifold learning can extract the potential nonlinear manifold structural information of high-dimensional samples and get their compact low-dimensional embeddings. The process of manifold learning is same as the human brain mechanisms of visual cognition. After nearly two decades of development, a number of manifold learning algorithms have been developed, which promise to be useful for analyzing the high-dimensional data that lie on or near a submanifold of the observation space. So manifold learning has been widely used in many fields of information processing, like pattern recognition, machine learning and data mining and so on. Therefore, they play an increasingly important role in face recognition, fingerprint recognition, gait recognition, document classification, image retrieval and cluster analysis, and data visualization applications. The main contents of this paper include:In this paper, we improve the graph embedding framework model, by introducing supervised lraning, tensor learning and sparse subspace learning methods into manifold learning framework. From a unified point view, the systematic framework can provide more information for understanding the common properties and intrinsic difference in different algorithms, and then guide to develop the new algorithm based on manifold learning.By analysis of the developed graph embedding framework, most of the traditional methods, like PCA and LPP, do not make good use of the sample label information. In order to solve this problem for classification, we propose discriminant orthogonal elastic preserving projections(DOEPP) which by incorporating the merits of the local geometry and the global Euclidean information, and discriminant information of the training set. DOEPP uses the training dada to rebuild the prior graph and local graph to approximate the high-dimensional manifold structure of the samples. And to preserve the discrimiative information, the orthogonality of the projection matrix and maximum margin criterion constraints are imposed into its objective function. At last, according to the basic matrix knowledge, we transform the maximization of the objective function into the generalized eigenvalues problem. The face recognition experiment results show recognition rate of our proposed method is superior to most of the existing manifold learning algorithms.The traditional manifold learning methods often adopt kNN local graph model or ? ?ball graph model to reconstruct the manifold structure. When the samples consist of the noise, like the block occlusion, pixel corruption and disguise face in face recognition, the structures of these graph models will change tremendously. Based on the studies, the sparse representation model is able to eliminate the noise impact. After analysing the coding residual’s distribution deeply and using sparse coding coefficients to measure the similarity weights of edges, based on the robust sparse representation model, we propose two new robust sparse graph models(RSG): RRL2 and RRSL2. These two graph models introduce the sparsity of the samples into the process of graph construction by solving RSG model and then greatly improve the robustness to the noise. Lastly, on the basis of RRL2 and RRSL2 graph model, we propose sparse discriminant locality preserving projections(SDLPP) and sparse DOEPP and further improve manifold learning algorithm classification performance. The experimental results of the simulated data and five face databases verify our proposed algorithms reasonable and effective.