Subspace Approximation of Face Recognition Algorithms: An Empirical Study

We present a theory for constructing linear subspace approximations to face-recognition algorithms and empirically demonstrate that a surprisingly diverse set of face-recognition approaches can be approximated well by using a linear model. A linear model, built using a training set of face images, is specified in terms of a linear subspace spanned by, possibly nonorthogonal vectors. We divide the linear transformation used to project face images into this linear subspace into two parts: 1) a rigid transformation obtained through principal component analysis, followed by a nonrigid, affine transformation. The construction of the affine subspace involves embedding of a training set of face images constrained by the distances between them, as computed by the face-recognition algorithm being approximated. We accomplish this embedding by iterative majorization, initialized by classical MDS. Any new face image is projected into this embedded space using an affine transformation. We empirically demonstrate the adequacy of the linear model using six different face-recognition algorithms, spanning template-based and feature-based approaches, with a complete separation of the training and test sets. A subset of the face-recognition grand challenge training set is used to model the algorithms and the performance of the proposed modeling scheme is evaluated on the facial recognition technology (FERET) data set. The experimental results show that the average error in modeling for six algorithms is 6.3% at 0.001 false acceptance rate for the FERET fafb probe set which has 1195 subjects, the most among all of the FERET experiments. The built subspace approximation not only matches the recognition rate for the original approach, but the local manifold structure, as measured by the similarity of identity of nearest neighbors, is also modeled well. We found, on average, 87% similarity of the local neighborhood. We also demonstrate the usefulness of the linear model for algorithm-dependent indexing of face databases and find that it results in more than 20 times reduction in face comparisons for Bayesian, elastic bunch graph matching, and one proprietary algorithm.