Discriminant Analysis Methods Based On Image Sets Representation

Currently, the data dimensionality reduction techniques are widely used in patternrecognition and related fields. In the process of solving practical problems, the data collectedare often cumbersome and complex. Numerous studies show that: most of the datas havenonlinear structure of manifolds, manifold learning algorithm is more concerned by majorityof scholars. A new algorithm based on images sets is presented in this paper, and it achievesgood results in the experiments.The first chapter states manifold learning algorithm summarization. This paper showssome mathematics concepts about manifold learning. It discusses from the bud, produce,developed to a mature of manifold. Lists several typical manifold learning algorithms fromnon-linear, linear, based on the matrix representation, respectively.The second chapter gives the Grassmannian manifold theory. Firstly, it elaborates patternrecognition based on image sets methods and describes the generation and prospects of basedon image sets methods. Secondly, gives the specific derivation process of the algorithms. Infact, this paper presents a algorithm based Grassmannian manifold is a new algorithm basedon image sets.Finally,it elaborates Grassmannian manifold theory, and gives mathematicaldefinition as well theorem proving about Grassmann manifold.The third chapter presents a new Grassmannian manifold learning algorithm. Recentresearch has shown that better recognition performance can be attained through representingimage sets as points on Grassmannian manifolds. However, the conventional discriminantanalysis methods based on such manifolds take into account only the statistical information oflabeled samples and suffer from ignoring unlabeled samples. To address this issue，based onmanifold regularization, a novel method, called Semi-supervised Discriminant Analysis onGrassmannian Manifold(SDAGM), is presented and applied to image sets recognitionproblem. In SDAGM, a nearest neighbor graph is constructed to capture the local geometricalstructure of all samples on Grassmannian manifold and incorporated into the objectivefunction of Discriminant Analysis on Grassmannian manifold as a regularization term. Notonly does the proposed algorithm consider the label information, but also utilize a consistencyassumption. The feasibility and effectiveness of SDAGM are verified on several standard datasets with promising results...