Nuclear Norm Based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 39; no. 1; pp. 156 - 171
• Main Authors: Yang, Jian, Luo, Lei, Qian, Jianjun, Tai, Ying, Zhang, Fanlong, Xu, Yong
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; alternating direction method of multipliers (ADMM); Convex functions; Encoding; Errors; Face recognition; Facial recognition technology; Illumination; Image classification; Lighting; Matrix converters; NMR; Nuclear magnetic resonance; Nuclear norm; Occlusion; Pixels; Regression analysis; Regression coefficients; Representations; robust regression; Robustness; sparse representation; Two dimensional models
• ISSN: 0162-8828; 1939-3539; 2160-9292
• DOI: 10.1109/TPAMI.2016.2535218

Recently, regression analysis has become a popular tool for face recognition. Most existing regression methods use the one-dimensional, pixel-based error model, which characterizes the representation error individually, pixel by pixel, and thus neglects the two-dimensional structure of the error image. We observe that occlusion and illumination changes generally lead, approximately, to a low-rank error image. In order to make use of this low-rank structural information, this paper presents a two-dimensional image-matrix-based error model, namely, nuclear norm based matrix regression (NMR), for face representation and classification. NMR uses the minimal nuclear norm of representation error image as a criterion, and the alternating direction method of multipliers (ADMM) to calculate the regression coefficients. We further develop a fast ADMM algorithm to solve the approximate NMR model and show it has a quadratic rate of convergence. We experiment using five popular face image databases: the Extended Yale B, AR, EURECOM, Multi-PIE and FRGC. Experimental results demonstrate the performance advantage of NMR over the state-of-the-art regression-based methods for face recognition in the presence of occlusion and illumination variations.