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Spectral Dimensionality Reduction
Biometric face data are essentially data of high dimensions and when subject to analysis using machine learning techniques, they are susceptible to the well-known problem of the curse of dimensionality. As a result various dimensionality reduction methods have been proposed in the literature to present 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 like PCA and LDA, much of information is lost. However, manifold learning methods (LLE, Laplacian Eigenmaps, Isomap) are able to preserve the original structure of high dimensional data in the lower dimensional space, resulting in minimum information loss. Despite the success of the manifold learning methods in discovering the non-linear structure of data, there are two main problems associated to them; First, the generalization problem which indicates that the proposed methods operate in batch mode and are not extendable to the new unseen test data, Second, the classification problem which indicates the inability of the manifold learning methods to incorporate labeled information into their learning algorithms.
With the advancements in semi-supervised learning theory and its relation with graph based methods, new frameworks have been proposed in the literature for the task of dimensionality reduction which can address the limitations of manifold learning methods.
In this research our aim is to study the manifold learning techniques under the graph-based semi-supervised learning theory.
Several applications need to verify their users to render services to only legitimate enrolled ones. Traditional identification methods such as ID-cared and passwords address the problem of verification based on “what a person possess” (ID-card) or “what a person remembers” (passwords), which can be easily breached (lost ID-cards, relieved passwords). Biometrics use a variety of physical or behavioral characteristics (example: finger print, face, gait, signature, etc) that cannot be easily stolen or shared. Biometrics aim is to provide a safer mean of identification to prevent imposters to access protected resources.
In the past decade, the pace of development of biometric applications accelerated considerably; commercial applications (employee recognition, network log in, mobile phone security, etc), government applications (defense, airport security, etc), and forensic applications (criminal investigation, corps identification, etc) are the three major customers of biometrics.