Regularized D-LDA for face recognition

Linear discriminant analysis (LDA) is derived from the optimal Bayes classifier when classes are assumed to be Gaussian with identical covariance matrices. However, it is well known that the distribution of face images under a perceivable variation in viewpoint, illumination or facial expression, is highly nonlinear and complex. Quadratic discriminant analysis (QDA), which relaxes the identical covariance assumption and allows for nonlinear discriminant boundaries to be formed, seems to be a better choice. However. the applicability of QDA to problems such as face recognition, where the number of training samples is much smaller than the dimensionality of the sample space, is problematic due to the increased number of parameters to be learned. We propose a new regularized discriminant analysis method that effectively solves the so-called "small sample size" problem in very high-dimensional face image space. Extensive experimentation performed on the FERET database indicates that the proposed methodology outperforms traditional methods such as eigenfaces, QDA and direct LDA in a number of application scenarios.