softImpute

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 16 articles , 2 standard articles )

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  1. 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)
  2. Huan, Guoqiang; Li, Ying; Song, Zhanjie: A novel robust principal component analysis method for image and video processing. (2016)
  3. Josse, Julie; Sardy, Sylvain: Adaptive shrinkage of singular values (2016)
  4. Sun, Tingni; Zhang, Cun-Hui: A graphical approach to the analysis of matrix completion (2016)
  5. Zhang, Yan-Qing; Tian, Guo-Liang; Tang, Nian-Sheng: Latent variable selection in structural equation models (2016)
  6. Zhou, Yunkai; Wang, Zheng; Zhou, Aihui: Accelerating large partial EVD/SVD calculations by filtered block Davidson methods (2016)
  7. Cai, Yun; Li, Song: Convergence analysis of projected gradient descent for Schatten-$p$ nonconvex matrix recovery (2015)
  8. Hastie, Trevor; Mazumder, Rahul; Lee, Jason D.; Zadeh, Reza: Matrix completion and low-rank SVD via fast alternating least squares (2015)
  9. Tibshirani, Ryan J.: A general framework for fast stagewise algorithms (2015)
  10. Verbanck, Marie; Josse, Julie; Husson, François: Regularised PCA to denoise and visualise data (2015)
  11. Lin, Junhong; Li, Song: Convergence of projected Landweber iteration for matrix rank minimization (2014)
  12. Liu, Lu; Huang, Wei; Chen, Di-Rong: Exact minimum rank approximation via Schatten $p$-norm minimization (2014)
  13. Mishra, Bamdev; Meyer, Gilles; Bonnabel, Silvère; Sepulchre, Rodolphe: Fixed-rank matrix factorizations and Riemannian low-rank optimization (2014)
  14. Taylor, Jonathan: The geometry of least squares in the 21st century (2013)
  15. Ghazanfar, Mustansar Ali; Prügel-Bennett, Adam; Szedmak, Sandor: Kernel-mapping recommender system algorithms (2012)
  16. Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert: Spectral regularization algorithms for learning large incomplete matrices (2010)