mlsanityData to 7 Oct 2026

Generalized Low Rank Models

arXiv 1410.0342 ↗First posted 1 Oct 2014stat.ML cs.LG math.OCcited by 55

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Abstract (arXiv)

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, k-means, k-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.

Key facts. Cited by 55 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Oct 2014.

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Citing papers per year: 2021: 6; 2022: 9; 2023: 6; 2024: 14; 2025: 11; 2026: 9.

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  1. 2021Is Attention Better Than Matrix Decomposition?cited by 75
  2. 2024Multi-Task Dense Prediction via Mixture of Low-Rank Expertscited by 58
  3. 2022Machine Learning in Aerodynamic Shape Optimizationcited by 39
  4. 2022Fair and efficient contribution valuation for vertical federated learningcited by 18
  5. 2022Tensor and Matrix Low-Rank Value-Function Approximation in Reinforcement Learningcited by 16
  6. 2021Controlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learningcited by 13
  7. 2021Low-rank State-action Value-function Approximationcited by 10
  8. 2022Graph-based Neural Acceleration for Nonnegative Matrix Factorizationcited by 9
  9. 2024Efficient Low-Rank Matrix Estimation, Experimental Design, and Arm-Set-Dependent Low-Rank Banditscited by 9
  10. 2023Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricingcited by 8
  11. 2022Federated PCA on Grassmann Manifold for Anomaly Detection in IoT Networkscited by 5
  12. 2022Unsupervised EHR-based Phenotyping via Matrix and Tensor Decompositionscited by 4
38 more
  1. 2022Sparse PCA With Multiple Componentscited by 4
  2. 2024Dual Simplex Volume Maximization for Simplex-Structured Matrix Factorizationcited by 4
  3. 2024High-dimensional analysis of ridge regression for non-identically distributed data with a variance profilecited by 4
  4. 2025An Accelerated Alternating Partial Bregman Algorithm for ReLU-based Matrix Decompositioncited by 4
  5. 2021A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimizationcited by 3
  6. 2022Signal Decomposition Using Masked Proximal Operatorscited by 3
  7. 2024Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Softwarecited by 3
  8. 2024Federated PCA on Grassmann Manifold for IoT Anomaly Detectioncited by 3
  9. 2025Multilinear Tensor Low-Rank Approximation for Policy-Gradient Methods in Reinforcement Learningcited by 3
  10. 2021Weighted Low-Rank Matrix Approximation: Acceleration and Applicationscited by 2
  11. 2023Archetypal Analysis++: Rethinking the Initialization Strategycited by 2
  12. 2023RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imagingcited by 2
  13. 2023Disjunctive Branch-and-Bound for Certifiably Optimal Low-Rank Matrix Completioncited by 2
  14. 2023Factor Fitting, Rank Allocation, and Partitioning in Multilevel Low Rank Matricescited by 2
  15. 2024Mixed Matrix Completion in Complex Survey Sampling under Heterogeneous Missingnesscited by 2
  16. 2024Privacy-Preserving Distributed Nonnegative Matrix Factorizationcited by 2
  17. 2024Matrix Low-Rank Trust Region Policy Optimizationcited by 2
  18. 2024Matrix Low-Rank Approximation For Policy Gradient Methodscited by 2
  19. 2024Learning Counterfactual Distributions via Kernel Nearest Neighborscited by 2
  20. 2025Disciplined Biconvex Programmingcited by 2
  21. 2026Manifold-based Algorithms for the Hadamard Decompositioncited by 2
  22. 2021Low Rank Forecastingcited by 1
  23. 2023Algorithms for Boolean Matrix Factorization using Integer Programmingcited by 1
  24. 2024Parameter inference from a non-stationary unknown processcited by 1
  25. 2025An Efficient Alternating Algorithm for ReLU-based Symmetric Matrix Decompositioncited by 1
  26. 2026AI Evaluation Should Require Standardized Item-Level Data Releasescited by 1
  27. 2022Asymptotics of ℓ2 Regularized Network Embeddingscited by 0
  28. 2024Tailed Low-Rank Matrix Factorization for Similarity Matrix Completioncited by 0
  29. 2024Stochastic gradient descent estimation of generalized matrix factorization models with application to single-cell RNA sequencing datacited by 0
  30. 2025Transforming Vision Transformer: Towards Efficient Multi-Task Asynchronous Learningcited by 0
  31. 2025Integration of TinyML and LargeML: A Survey of 6G and Beyondcited by 0
  32. 2025Supervised Coupled Matrix-Tensor Factorization (SCMTF) for Computational Phenotyping of Patient Reported Outcomes in Ulcerative Colitiscited by 0
  33. 2025Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Conditioncited by 0
  34. 2025Multilingual Lexical Feature Analysis of Spoken Language for Predicting Major Depression Symptom Severitycited by 0
  35. 2025Algorithms for Boolean Matrix Factorization using Integer Programming and Heuristicscited by 0
  36. 2025Low-rank MMSE filters, Kronecker-product representation, and regularization: a new perspectivecited by 0
  37. 2026Fast and Effective Computation of Generalized Symmetric Matrix Factorizationcited by 0
  38. 2026LAPLEX: The FFT of Learnable Laplace Kernelscited by 0

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