# Block-Randomized Stochastic Proximal Gradient for Low-Rank Tensor Factorization

arXiv: https://arxiv.org/abs/1901.05529 · HTML: https://mlsanity.com/paper/1901.05529/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2019.

## Built on by (most cited first, 12 of 12)

- [Deep Spectrum Cartography: Completing Radio Map Tensors Using Learned Neural Models](https://mlsanity.com/paper/2105.00177/) (2021)
- [Cyclic Block Coordinate Descent With Variance Reduction for Composite Nonconvex Optimization](https://mlsanity.com/paper/2212.05088/) (2022)
- [Crowdsourcing via Annotator Co-occurrence Imputation and Provable Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2106.07193/) (2021)
- [Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing](https://mlsanity.com/paper/2205.03798/) (2022)
- [Quantized Radio Map Estimation Using Tensor and Deep Generative Models](https://mlsanity.com/paper/2303.01770/) (2023)
- [Stochastic Mirror Descent for Low-Rank Tensor Decomposition Under Non-Euclidean Losses](https://mlsanity.com/paper/2104.14562/) (2021)
- [Under-Counted Tensor Completion with Neural Incorporation of Attributes](https://mlsanity.com/paper/2306.03273/) (2023)
- [Communication Efficient Generalized Tensor Factorization for Decentralized Healthcare Networks](https://mlsanity.com/paper/2109.01718/) (2021)
- [Communication-Efficient Federated Linear and Deep Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/2109.12400/) (2021)
- [An Accelerated Stochastic Gradient for Canonical Polyadic Decomposition](https://mlsanity.com/paper/2109.13964/) (2021)
- [Scalable and Robust Tensor Ring Decomposition for Large-scale Data](https://mlsanity.com/paper/2305.09044/) (2023)
- [Accelerating Large-Scale Regularized High-Order Tensor Recovery](https://mlsanity.com/paper/2506.09594/) (2025)

## Abstract (arXiv)

This work considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in applications such as medical imaging, computer vision, and remote sensing. Stochastic optimization is known for its low memory cost and per-iteration complexity when handling dense data. However, exisiting stochastic CPD algorithms are not flexible enough to incorporate a variety of constraints/regularizations that are of interest in signal and data analytics. Convergence properties of many such algorithms are also unclear. In this work, we propose a stochastic optimization framework for large-scale CPD with constraints/regularizations. The framework works under a doubly randomized fashion, and can be regarded as a judicious combination of randomized block coordinate descent (BCD) and stochastic proximal gradient (SPG). The algorithm enjoys lightweight updates and small memory footprint. In addition, this framework entails considerable flexibility---many frequently used regularizers and constraints can be readily handled under the proposed scheme. The approach is also supported by convergence analysis. Numerical results on large-scale dense tensors are employed to showcase the effectiveness of the proposed approach.