Open AccessProceedings Article
Large-Scale Matrix Factorization with Missing Data under Additional Constraints
Kaushik Mitra,Sameer Sheorey,Rama Chellappa +2 more
- 06 Dec 2010
- Vol. 23, pp 1651-1659
TL;DR: The empirical evaluations suggest that, under the conditions of matrix completion theory, the proposed algorithm finds the optimal solution, and also requires fewer observations compared to the current state-of-the-art algorithms.
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Abstract: Matrix factorization in the presence of missing data is at the core of many computer vision problems such as structure from motion (SfM), non-rigid SfM and photometric stereo. We formulate the problem of matrix factorization with missing data as a low-rank semidefinite program (LRSDP) with the advantage that: 1) an efficient quasi-Newton implementation of the LRSDP enables us to solve large-scale factorization problems, and 2) additional constraints such as ortho-normality, required in orthographic SfM, can be directly incorporated in the new formulation. Our empirical evaluations suggest that, under the conditions of matrix completion theory, the proposed algorithm finds the optimal solution, and also requires fewer observations compared to the current state-of-the-art algorithms. We further demonstrate the effectiveness of the proposed algorithm in solving the affine SfM problem, non-rigid SfM and photometric stereo problems.
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Citations
Robust Matrix Factorization with Unknown Noise
Deyu Meng,Fernando De la Torre +1 more
- 01 Dec 2013
TL;DR: A low-rank matrix factorization problem with a Mixture of Gaussians (MoG) noise, which is a universal approximator for any continuous distribution, and hence is able to model a wider range of real noise distributions.
Denoising Hyperspectral Image With Non-i.i.d. Noise Structure
TL;DR: This paper attempts the first effort to model the HSI noise using a non-i.i.d. mixture of Gaussians (NMoGs) noise assumption, which finely accords with the noise characteristics possessed by a natural HSI and thus is capable of adapting various practical noise shapes.
•Proceedings Article
Self-paced learning for matrix factorization
Qian Zhao,Deyu Meng,Lu Jiang,Qi Xie,Zongben Xu,Alexander G. Hauptmann +5 more
- 25 Jan 2015
TL;DR: This study presents a new MF learning methodology by gradually including matrix elements into MF training from easy to complex by following a recently proposed learning fashion called self-paced learning (SPL), which has been demonstrated to be beneficial in avoiding bad local minima.
$L_{1}$ -Norm Low-Rank Matrix Factorization by Variational Bayesian Method
TL;DR: A new hierarchical Bayesian generative model is constructed for the L1-norm low-rank matrix factorization problem and a mean-field variational method to automatically infer all the parameters involved in the model by closed-form equations is designed.
119
Low-Rank Matrix Factorization under General Mixture Noise Distributions
Xiangyong Cao,Yang Chen,Qian Zhao,Deyu Meng,Yao Wang,Dong Wang,Zongben Xu +6 more
- 07 Dec 2015
TL;DR: This paper proposes a new LRMF model by assuming noise as Mixture of Exponential Power (MoEP) distributions and proposes a penalized MoEP model by combining the penalized likelihood method with MoEP distributions.
References
Exact Matrix Completion via Convex Optimization
TL;DR: It is proved that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries, and that objects other than signals and images can be perfectly reconstructed from very limited information.
A Singular Value Thresholding Algorithm for Matrix Completion
TL;DR: This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank, and develops a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms.
Semidefinite programming
Lieven Vandenberghe,Stephen Boyd +1 more
- 01 Mar 1996
TL;DR: A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given.
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Shape and motion from image streams under orthography: a factorization method
Carlo Tomasi,Takeo Kanade +1 more
TL;DR: In this paper, the singular value decomposition (SVDC) technique is used to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively, and two of the three translation components are computed in a preprocessing stage.
•Journal Article
Spectral Regularization Algorithms for Learning Large Incomplete Matrices
TL;DR: Using the nuclear norm as a regularizer, the algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD in a sequence of regularized low-rank solutions for large-scale matrix completion problems.