LowRankModels.jl is a julia package for modeling and fitting generalized low rank models (GLRMs). GLRMs model a data array by a low rank matrix, and include many well known models in data analysis, such as principal components analysis (PCA), matrix completion, robust PCA, nonnegative matrix factorization, k-means, and many more. For more information on GLRMs, see our paper. There is a python interface to this package, and a GLRM implementation in the H2O machine learning platform with interfaces in a variety of languages. LowRankModels.jl makes it easy to mix and match loss functions and regularizers to construct a model suitable for a particular data set. In particular, it supports: using different loss functions for different columns of the data array, which is useful when data types are heterogeneous (eg, real, boolean, and ordinal columns); fitting the model to only some of the entries in the table, which is useful for data tables with many missing (unobserved) entries; and adding offsets and scalings to the model without destroying sparsity, which is useful when the data is poorly scaled.

References in zbMATH (referenced in 19 articles , 1 standard article )

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  1. Aggarwal, Charu C.: Linear algebra and optimization for machine learning. A textbook (2020)
  2. Bossmann, Florian; Ma, Jianwei: Enhanced image approximation using shifted rank-1 reconstruction (2020)
  3. Hong, David; Kolda, Tamara G.; Duersch, Jed A.: Generalized canonical polyadic tensor decomposition (2020)
  4. Li, Xinrong; Xiu, Naihua; Zhou, Shenglong: Matrix optimization over low-rank spectral sets: stationary points and local and global minimizers (2020)
  5. Alaya, Mokhtar Z.; Klopp, Olga: Collective matrix completion (2019)
  6. Bai, Jushan; Ng, Serena: Rank regularized estimation of approximate factor models (2019)
  7. Balcan, Maria-Florina; Liang, Yingyu; Song, Zhao; Woodruff, David P.; Zhang, Hongyang: Non-convex matrix completion and related problems via strong duality (2019)
  8. Daneshmand, Amir; Sun, Ying; Scutari, Gesualdo; Facchinei, Francisco; Sadler, Brian M.: Decentralized dictionary learning over time-varying digraphs (2019)
  9. Driggs, Derek; Becker, Stephen; Aravkin, Aleksandr: Adapting regularized low-rank models for parallel architectures (2019)
  10. Gillis, Nicolas; Shitov, Yaroslav: Low-rank matrix approximation in the infinity norm (2019)
  11. Fithian, William; Mazumder, Rahul: Flexible low-rank statistical modeling with missing data and side information (2018)
  12. Liu, Lydia T.; Dobriban, Edgar; Singer, Amit: (e)PCA: high dimensional exponential family PCA (2018)
  13. Luo, Chongliang; Liang, Jian; Li, Gen; Wang, Fei; Zhang, Changshui; Dey, Dipak K.; Chen, Kun: Leveraging mixed and incomplete outcomes via reduced-rank modeling (2018)
  14. Yang, Lei; Pong, Ting Kei; Chen, Xiaojun: A nonmonotone alternating updating method for a class of matrix factorization problems (2018)
  15. Bigot, Jérémie; Deledalle, Charles; Féral, Delphine: Generalized SURE for optimal shrinkage of singular values in low-rank matrix denoising (2017)
  16. Dutta, Aritra; Li, Xin: On a problem of weighted low-rank approximation of matrices (2017)
  17. Fithian, William; Josse, Julie: Multiple correspondence analysis and the multilogit bilinear model (2017)
  18. Josse, Julie; Wager, Stefan: Bootstrap-based regularization for low-rank matrix estimation (2016)
  19. Udell, Madeleine; Horn, Corinne; Zadeh, Reza; Boyd, Stephen: Generalized low rank models (2016)