Semi-supervised Discriminant Analysis Based On Riemannian Manifolds

At present, with the rapid development of science and technology, people are facing more and more complicated complex data. How will these massive data effectively use is one of the important research subjects in modern science and technology. A large number of experiments show that most of the collected data exists of nonlinear manifold structure. Based on this, the manifold learning has been paid more and more attention. In recent years, manifold as the Euclidean space is widely applied in the fields of machine learning and pattern recognition, and has become a hot topic in the study of this theory. A lot of experiments proved the manifold structure has effect on the algorithm. This paper introduced the manifold is a Riemann manifold, and carry on discriminant analysis algorithm in it. The algorithm of the traditional discriminant analysis only considers the statistical information of labeled sample data, and ignores the unlabeled samples. A large amount of data information is lost, so that lead the classification accuracy is not accurate. In view of this, based on the idea of graph regularization, this paper puts forward a new semi supervised discriminant analysis algorithm on Riemann manifold framework, and this algorithm is applied to the visual classification tasks. Its core idea is to use nonsingular covariance matrix to express the point on the Riemann manifold, and use JBLD(Jensen-Bregman LogDet Divergence) to measure the similarity between point and point of Riemann manifolds. The specific practices are following as these: Firstly, the data points are mapped to the Riemann tangent space, and get the data to be quantitative representation. Secondly, through the sample data with the label and no label structure neighbor graph to characterize local geometric structure of the Riemann tangent space, and the objective function as a regularization term is added to Fisher discriminant analysis geodesic linear. Thirdly, minimize the objective function to gain the optimal transform matrix, and makes a classification in the transform of Riemann manifold. In this paper, set experiments in the Cambridge gesture, Brodatz and ETHZ visual classification data which show that the algorithms presented in this paper with a great improvement in classification accuracy.This thesis consists of five parts. The first chapter describes the background and significance of this issue, the main current research as well as research article. The second chapter introduces the related theory of manifold discriminant analysis algorithm of Riemann manifold. The third chapter proposes a novel SDARMF algorithm based on FGDA. The fourth chapter uses this algorithm to experiment to get a high recognition rate. The last part of this paper summarizes the whole work and prospects the future research.