Semi-supervised learning in Spectral Dimensionality Reduction

Biometric face data are essentially high dimensional data and as such are susceptible to the well-known problem of the curse of dimensionality when analyzed using machine learning techniques. Various dimensionality reduction methods have been proposed in the literature to represent high dimensional data in a lower dimensional space. Research has shown that biometric face data are non-linear in structure, and when subject to analysis using linear dimensionality reduction methods, such as PCA and LDA, important information is lost. However, manifold learning methods (LLE, Laplacian Eigenmaps, Isomap) are able to preserve the original non-linear structure of high dimensional data in lower dimensional space, resulting in much less information loss. Despite the success in preserving the non-linear structure of data, manifold learning methods suffer from two problems. First the generalization problem, that is, the proposed methods operate in batch mode and are not extendable to new unseen test data. Second, the classification problem, that is, the inability of the manifold learning methods to incorporate labeled information into their learning algorithms. The aim of this dissertation, is to provide a comprehensive survey of the existing methods in the literature that contribute to the problems of manifold learning where generalization and classification are necessary. In this dissertation, we will present Graph Embedding and Semi-supervised Graph Embedding as the approved approaches to advance the applicability of manifold learning methods in the application of biometric face recognition. This dissertation will provide a comprehensive presentation of the existing literature, and provide a framework under which new Semi-Supervised Manifold Learning methods could be proposed and studied. In addition, this thesis, presents a new semi-supervised manifold learning method, which has superior performance in face recognition, against the similar approaches of semi-supervised learning.