Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Geometry, topology > Differential geometry,integral geometry > Differential Geometry > Riemannian geometry

The Research of Feature Extraction Based on Lorentzian Manifold

Author TangKeWei
Tutor SuZhiXun
School Dalian University of Technology
Course Computational Mathematics
Keywords Feature Extraction Supervised dimensional reduction Semi-supervised dimensional reduction Lorentzian geometry Face Recognition
CLC O186.12
Type Master's thesis
Year 2010
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The essence of feature extraction is to project a high dimensional sample into a low dimensional feature subspace which is benefit to classification. Many correlated algorithms have been proposed in the past few decades. Lorentzian Discriminant Projection (LDP) is a recently proposed algorithm, which has the higher recognition ratio than some classical algorithms such as PCA, LDA, MFA and so on. However, LDP is a supervised linear algorithm based vector. The linear algorithm can’t extract the sample’s nonlinear structure and the algorithm based vector will lose the local spatial information. Moreover, in some practical applications, labeled data are often, however, hard to obtain. This makes it necessary to utilize semi-supervised dimensional reduction algorithms while most of the classical dimensional reduction algorithms are supervised. There has been significant recent interest in extending supervised algorithms to semi-supervised form which preserve local structures of the unlabeled samples. But how to choose the homogeneous points is still an open problem.After the deep analysis and research of the classical approach, I firstly propose the Kernel LDP and Laplace LDP. Then, I propose a framework which can extend supervised dimensional algorithm to semi-supervised case. The kernel LDP using’kernel trick’can extract the nonlinear structure of the data well. The Laplace LDP can keep the local spatial information well. The proposed framework using sparse Lorentzian can not only find the homogeneous points of the unlabeled samples in a more natural way,but also can keep both the local structure of the unlabeled samples and their global geometrical structure. The experimental results on face recognition show that my proposed algorithms can achieve better recognition accuracy.

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