SOS, lost in a high dimensional space

The trend in facial biometrics has been to use ever increasing image resolution, with the purpose of increasing the recognition performance by exploiting the added information. One category of biometric systems expected to benefit from the increased image resolution consists of systems based on second-order statistics (SOS) estimates, such as those based on principle component analysis (PCA). Increasing the image resolution without sufficiently increasing the number of training samples has several effects on the SOS estimates, such as a bias in the eigenvalue estimates and errors in the eigenvector estimates. We analyze how the increasing ratio of the dimensionality over the number of samples affects biometric systems, in particular those based on second-order statistics in combination with a – theoretically optimal – log-likelihood ratio classifier. We show that the classical solution to the singularity problem, PCA dimensionality reduction, is far from optimal and fails completely for very high dimensionalities and we present several solutions to adjust the SOS estimates in order to achieve close to optimal performance, such as the eigenwise correction using fixed-point eigenvalue correction, and the variance correction. Although the presented solutions are clearly superior if synthetic data is used, for real facial data they turned out to be outperformed by PCA dimensionality reduction. We found that this can be explained by the assumed underlying model of fixed position intensity sources, which cannot efficiently describe variations occurring in faces caused by moving features. We show that if facial data contains such moving features, then traditional solution to the singularity problem by dimensionality reduction based on PCA reduces the disruptive effect of these moving features on verification rates while our proposed bias correction methods actually increase this effect. This provides an explanation why PCA dimensionality outperforms the correction methods if real facial data is used.