Face recognition is a widely adopted technology with numerous applications, such as mobile phone unlock, mobile payment, surveillance, social media and law enforcement. There has been tremendous progress in enhancing the accuracy of face recognition systems over the past few decades, much of which can be attributed to deep learning. Despite this progress, several fundamental problems in face recognition still remain unsolved. These problems include finding a salient representation, estimating intrinsic dimensionality, representation capacity, and demographic bias. With growing applications of face recognition, the need for an accurate, robust, compact and fair representation is evident.In this thesis, we first develop algorithms to obtain practical estimates of intrinsic dimensionality of face representations, and propose a new dimensionality reduction method to project feature vectors from ambient space to intrinsic space. Based on the study in intrinsic dimensionality, we then estimate capacity of face representation, casting the face capacity estimation problem under the information theoretic framework of capacity of a Gaussian noise channel. Numerical experiments on unconstrained faces (IJB-C) provide a capacity upper bound of 27,000 for FaceNet and 84,000 for SphereFace representation at 1% FAR. In the second part of the thesis, we address the demographic bias problem in face recognition systems where errors are lower on certain cohorts belonging to specific demographic groups. We propose two de-biasing frameworks that extract feature representations to improve fairness in face recognition. Experiments on benchmark face datasets (RFW, LFW, IJB-A, and IJB-C) show that our approaches are able to mitigate face recognition bias on various demographic groups (biasness drops from 6.83 to 5.07) as well as maintain the competitive performance (i.e., 99.75% on LFW, and 93.70% TAR @ 0.1% FAR on IJB-C). Lastly, we explore the global distribution of deep face representations derived from correlations between image samples of within-class and cross-class to enhance the discriminativeness of face representation of each identity in the embedding space. Our new approach to face representation achieves state-of-the-art performance for both verification and identification tasks on benchmark datasets (99.78% on LFW, 93.40% on CPLFW, 98.41% on CFP-FP, 96.2% TAR @ 0.01% FAR and 95.3% Rank-1 accuracy on IJB-C). Since, the primary techniques we employ in this dissertation are not specific to faces only, we believe our research can be extended to other problems in computer vision, for example, general image classification and representation learning.
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