Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Maximum conditional likelihood via bound maximization and the CEM algorithm
Proceedings of the 1998 conference on Advances in neural information processing systems II
IEEE Transactions on Pattern Analysis and Machine Intelligence
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Bayesian probabilistic matrix factorization using Markov chain Monte Carlo
Proceedings of the 25th international conference on Machine learning
Spectral Regularization Algorithms for Learning Large Incomplete Matrices
The Journal of Machine Learning Research
Accelerated low-rank visual recovery by random projection
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Bayesian Robust Principal Component Analysis
IEEE Transactions on Image Processing
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
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Matrix factorization underlies a large variety of computer vision applications. It is a particularly challenging problem for large-scale applications and when there exist outliers and missing data. In this paper, we propose a novel probabilistic model called Probabilistic Robust Matrix Factorization (PRMF) to solve this problem. In particular, PRMF is formulated with a Laplace error and a Gaussian prior which correspond to an ℓ1 loss and an ℓ2 regularizer, respectively. For model learning, we devise a parallelizable expectation-maximization (EM) algorithm which can potentially be applied to large-scale applications. We also propose an online extension of the algorithm for sequential data to offer further scalability. Experiments conducted on both synthetic data and some practical computer vision applications show that PRMF is comparable to other state-of-the-art robust matrix factorization methods in terms of accuracy and outperforms them particularly for large data matrices.