# Generalized Low Rank Models

arXiv: https://arxiv.org/abs/1410.0342 · HTML: https://mlsanity.com/paper/1410.0342/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2014.

## Built on by (most cited first, 30 of 55)

- [Is Attention Better Than Matrix Decomposition?](https://mlsanity.com/paper/2109.04553/) (2021)
- [Multi-Task Dense Prediction via Mixture of Low-Rank Experts](https://mlsanity.com/paper/2403.17749/) (2024)
- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Fair and efficient contribution valuation for vertical federated learning](https://mlsanity.com/paper/2201.02658/) (2022)
- [Tensor and Matrix Low-Rank Value-Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/2201.09736/) (2022)
- [Controlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learning](https://mlsanity.com/paper/2112.00423/) (2021)
- [Low-rank State-action Value-function Approximation](https://mlsanity.com/paper/2104.08805/) (2021)
- [Efficient Low-Rank Matrix Estimation, Experimental Design, and Arm-Set-Dependent Low-Rank Bandits](https://mlsanity.com/paper/2402.11156/) (2024)
- [Graph-based Neural Acceleration for Nonnegative Matrix Factorization](https://mlsanity.com/paper/2202.00264/) (2022)
- [Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing](https://mlsanity.com/paper/2309.08634/) (2023)
- [Federated PCA on Grassmann Manifold for Anomaly Detection in IoT Networks](https://mlsanity.com/paper/2212.12121/) (2022)
- [High-dimensional analysis of ridge regression for non-identically distributed data with a variance profile](https://mlsanity.com/paper/2403.20200/) (2024)
- [Unsupervised EHR-based Phenotyping via Matrix and Tensor Decompositions](https://mlsanity.com/paper/2209.00322/) (2022)
- [Sparse PCA With Multiple Components](https://mlsanity.com/paper/2209.14790/) (2022)
- [Dual Simplex Volume Maximization for Simplex-Structured Matrix Factorization](https://mlsanity.com/paper/2403.20197/) (2024)
- [An Accelerated Alternating Partial Bregman Algorithm for ReLU-based Matrix Decomposition](https://mlsanity.com/paper/2503.02386/) (2025)
- [A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization](https://mlsanity.com/paper/2102.05433/) (2021)
- [Signal Decomposition Using Masked Proximal Operators](https://mlsanity.com/paper/2202.09338/) (2022)
- [Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Software](https://mlsanity.com/paper/2402.06019/) (2024)
- [Federated PCA on Grassmann Manifold for IoT Anomaly Detection](https://mlsanity.com/paper/2407.07421/) (2024)
- [Multilinear Tensor Low-Rank Approximation for Policy-Gradient Methods in Reinforcement Learning](https://mlsanity.com/paper/2501.04879/) (2025)
- [AI Evaluation Should Require Standardized Item-Level Data Releases](https://mlsanity.com/paper/2604.03244/) (2026)
- [Weighted Low-Rank Matrix Approximation: Acceleration and Applications](https://mlsanity.com/paper/2109.11057/) (2021)
- [Archetypal Analysis++: Rethinking the Initialization Strategy](https://mlsanity.com/paper/2301.13748/) (2023)
- [RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imaging](https://mlsanity.com/paper/2304.03483/) (2023)
- [Disjunctive Branch-and-Bound for Certifiably Optimal Low-Rank Matrix Completion](https://mlsanity.com/paper/2305.12292/) (2023)
- [Factor Fitting, Rank Allocation, and Partitioning in Multilevel Low Rank Matrices](https://mlsanity.com/paper/2310.19214/) (2023)
- [Mixed Matrix Completion in Complex Survey Sampling under Heterogeneous Missingness](https://mlsanity.com/paper/2402.03954/) (2024)
- [Privacy-Preserving Distributed Nonnegative Matrix Factorization](https://mlsanity.com/paper/2403.18326/) (2024)
- [Matrix Low-Rank Trust Region Policy Optimization](https://mlsanity.com/paper/2405.17625/) (2024)

## 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.