The face recognition is a fairly controversial subject right now. A system such as this can recognize and track dangerous criminals and terrorists in a crowd, but some contend that it is an extreme invasion of privacy. The proponents of large-scale face recognition feel that it is a necessary evil to make our country safer. It could benefit the visually impaired and allow them to interact more easily with the environment. Also, a computer vision-based authentication system could be put in place to allow computer access or access to a specific room using face recognition. Another possible application would be to integrate this technology into an artificial intelligence system for more realistic interaction with humans. We propose an appearance-based face recognition method called the Laplacianface approach. By using Locality Preserving Projections (LPP), the face images are mapped into a face subspace for analysis. Different from Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) which effectively see only the Euclidean structure of face space, LPP finds an embedding that preserves local information, and obtains a face subspace that best detects the essential face manifold structure. The Laplacian faces are the optimal linear approximations to the eigen functions of the Laplace Beltrami operator on the face manifold. In this way, the unwanted variations resulting from changes in lighting, facial expression, and pose may be eliminated or reduced. Theoretical analysis shows that PCA, LDA, and LPP can be obtained from different graph models. We compare the proposed Laplacianface approach with Eigenface and Fisherface methods on three different face data sets. Experimental results suggest that the proposed Laplacianface approach provides a better representation and achieves lower error rates in face recognition. Principal Component Analysis (PCA) is a statistical method under the broad title of factor analysis. The purpose of PCA is to reduce the large dimensionality of the data space (observed variables) to the smaller intrinsic dimensionality of feature space (independent variables), which are needed to describe the data economically. This is the case when there is a strong correlation between observed variables. The jobs which PCA can do are prediction, redundancy removal, feature extraction, data compression, etc. Because PCA is a known powerful technique which can do something in the linear domain, applications having linear models are suitable, such as signal processing, image processing, system and control theory, communications, etc. The main idea of using PCA for face recognition is to express the large 1-D vector of pixels constructed from 2-D face image into the compact principal components of the feature space. This is called eigenspace projection. Eigenspace is calculated by identifying the eigenvectors of the covariance matrix derived from a set of fingerprint images (vectors).

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