Robust image hashing has been actively researched over the last decade with varied applications in image content authentication and identification under distortions. In the existing literature on robust image hashing, hash algorithms are ignorant of the class of images being hashed. There are however significant application domains such as that of face image hashing where apriori knowledge of the image class as well as permissible distortions can benefit hash algorithm design. In this paper, we present a two stage cascade of dimensionality reduction constructs for face image hashing. The first stage aims to project the face image to a space where geometric distortions manifest approximately as additive noise. For this purpose, we use the non-negative matrix approximations based hash vector developed by Monga et al. which is known to possess excellent geometric attack robustness. In the second stage, we employ oriented principal component analysis (OPCA) based on estimating signal as well as noise statistics in a learning phase and deriving a projection that mitigates the effect of noise. We obtain both experimentally based ROC curves as well as analytical ones via a detection theoretic analysis of the proposed framework. The ROC curves reveal clearly that incorporating such a learning phase greatly reduces error probabilities.