softImpute: Matrix Completion via Iterative Soft-Thresholded SVD. Iterative methods for matrix completion that use nuclear-norm regularization. There are two main approaches.The one approach uses iterative soft-thresholded svds to impute the missing values. The second approach uses alternating least squares. Both have an ”EM” flavor, in that at each iteration the matrix is completed with the current estimate. For large matrices there is a special sparse-matrix class named ”Incomplete” that efficiently handles all computations. The package includes procedures for centering and scaling rows, columns or both, and for computing low-rank SVDs on large sparse centered matrices (i.e. principal components)

References in zbMATH (referenced in 29 articles , 2 standard articles )

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  1. O’Rourke, Sean; Vu, Van; Wang, Ke: Random perturbation of low rank matrices: improving classical bounds (2018)
  2. Shabat, Gil; Shmueli, Yaniv; Aizenbud, Yariv; Averbuch, Amir: Randomized LU decomposition (2018)
  3. Bouwmans, Thierry; Sobral, Andrews; Javed, Sajid; Jung, Soon Ki; Zahzah, El-Hadi: Decomposition into low-rank plus additive matrices for background/foreground separation: a review for a comparative evaluation with a large-scale dataset (2017)
  4. Chi, Eric C.; Allen, Genevera I.; Baraniuk, Richard G.: Convex biclustering (2017)
  5. Durante, Daniele: A note on the multiplicative gamma process (2017)
  6. Eghbali, Reza; Fazel, Maryam: Decomposable norm minimization with proximal-gradient homotopy algorithm (2017)
  7. Freund, Robert M.; Grigas, Paul; Mazumder, Rahul: An extended Frank-Wolfe method with “in-face” directions, and its application to low-rank matrix completion (2017)
  8. Huan, Guoqiang; Li, Ying; Song, Zhanjie: A novel robust principal component analysis method for image and video processing. (2016)
  9. Josse, Julie; Sardy, Sylvain: Adaptive shrinkage of singular values (2016)
  10. Julie Josse; François Husson: missMDA: A Package for Handling Missing Values in Multivariate Data Analysis (2016)
  11. Julie Josse, Sylvain Sardy, Stefan Wager: denoiseR: A Package for Low Rank Matrix Estimation (2016) arXiv
  12. Sun, Tingni; Zhang, Cun-Hui: A graphical approach to the analysis of matrix completion (2016)
  13. Taylor, Jonathan E.; Loftus, Joshua R.; Tibshirani, Ryan J.: Inference in adaptive regression via the Kac-Rice formula (2016)
  14. Zhang, Yan-Qing; Tian, Guo-Liang; Tang, Nian-Sheng: Latent variable selection in structural equation models (2016)
  15. Zhou, Yunkai; Wang, Zheng; Zhou, Aihui: Accelerating large partial EVD/SVD calculations by filtered block Davidson methods (2016)
  16. Cai, Yun; Li, Song: Convergence analysis of projected gradient descent for Schatten-$p$ nonconvex matrix recovery (2015)
  17. Chatterjee, Sourav: Matrix estimation by universal singular value thresholding (2015)
  18. Hastie, Trevor; Mazumder, Rahul; Lee, Jason D.; Zadeh, Reza: Matrix completion and low-rank SVD via fast alternating least squares (2015)
  19. Klopp, Olga: Matrix completion by singular value thresholding: sharp bounds (2015)
  20. Klopp, Olga; Lafond, Jean; Moulines, Éric; Salmon, Joseph: Adaptive multinomial matrix completion (2015)

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