CVPR 2011 (2011)
June 20, 2011 to June 25, 2011
Yadong Mu , Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore
Jian Dong , Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore
Xiaotong Yuan , Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore
Shuicheng Yan , Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore
Exact recovery from contaminated visual data plays an important role in various tasks. By assuming the observed data matrix as the addition of a low-rank matrix and a sparse matrix, theoretic guarantee exists under mild conditions for exact data recovery. Practically matrix nuclear norm is adopted as a convex surrogate of the non-convex matrix rank function to encourage low-rank property and serves as the major component of recently-proposed Robust Principal Component Analysis (R-PCA). Recent endeavors have focused on enhancing the scalability of R-PCA to large-scale datasets, especially mitigating the computational burden of frequent large-scale Singular Value Decomposition (SVD) inherent with the nuclear norm optimization. In our proposed scheme, the nuclear norm of an auxiliary matrix is minimized instead, which is related to the original low-rank matrix by random projection. By design, the modified optimization entails SVD on matrices of much smaller scale, as compared to the original optimization problem. Theoretic analysis well justifies the proposed scheme, along with greatly reduced optimization complexity. Both qualitative and quantitative studies are provided on various computer vision benchmarks to validate its effectiveness, including facial shadow removal, surveillance background modeling and large-scale image tag transduction. It is also highlighted that the proposed solution can serve as a general principal to accelerate many other nuclear norm oriented problems in numerous tasks.
large-scale image tag transduction, accelerated low-rank visual recovery, random projection, observed data matrix, low-rank matrix, sparse matrix, exact data recovery, convex surrogate, nonconvex matrix rank, robust principal component analysis, R-PCA, singular value decomposition, SVD, nuclear norm optimization, optimization complexity, computer vision benchmarks, facial shadow removal, surveillance background modeling
Shuicheng Yan, Yadong Mu, Xiaotong Yuan and Jian Dong, "Accelerated low-rank visual recovery by random projection," CVPR 2011(CVPR), Providence, RI, 2011, pp. 2609-2616.