# Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries

arXiv: https://arxiv.org/abs/1710.02261 · HTML: https://mlsanity.com/paper/1710.02261/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2017.

## Built on by (most cited first, 14 of 14)

- [CGC: Contrastive Graph Clustering for Community Detection and Tracking](https://mlsanity.com/paper/2204.08504/) (2022)
- [Fast and Accurate Randomized Algorithms for Low-rank Tensor Decompositions](https://mlsanity.com/paper/2104.01101/) (2021)
- [Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data](https://mlsanity.com/paper/2311.04829/) (2023)
- [Influence-guided Data Augmentation for Neural Tensor Completion](https://mlsanity.com/paper/2108.10248/) (2021)
- [Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes](https://mlsanity.com/paper/2110.10082/) (2021)
- [Streaming Factor Trajectory Learning for Temporal Tensor Decomposition](https://mlsanity.com/paper/2310.17021/) (2023)
- [A rank-adaptive higher-order orthogonal iteration algorithm for truncated Tucker decomposition](https://mlsanity.com/paper/2110.12564/) (2021)
- [Bayesian Robust Tensor Ring Model for Incomplete Multiway Data](https://mlsanity.com/paper/2202.13321/) (2022)
- [Scalable Bayesian Tensor Ring Factorization for Multiway Data Analysis](https://mlsanity.com/paper/2412.03321/) (2024)
- [Efficient Decision Trees for Tensor Regressions](https://mlsanity.com/paper/2408.01926/) (2024)
- [MLCTR: A Fast Scalable Coupled Tensor Completion Based on Multi-Layer Non-Linear Matrix Factorization](https://mlsanity.com/paper/2109.01773/) (2021)
- [Sample Efficient Learning of Factored Embeddings of Tensor Fields](https://mlsanity.com/paper/2209.00372/) (2022)
- [Tensor Convolutional Network for Higher-Order Interaction Prediction in Sparse Tensors](https://mlsanity.com/paper/2503.11786/) (2025)
- [Dual-Attention Convolution Experts for Sparse Tensor Completion](https://mlsanity.com/paper/2606.21427/) (2026)

## Abstract (arXiv)

Given sparse multi-dimensional data (e.g., (user, movie, time; rating) for movie recommendations), how can we discover latent concepts/relations and predict missing values? Tucker factorization has been widely used to solve such problems with multi-dimensional data, which are modeled as tensors. However, most Tucker factorization algorithms regard and estimate missing entries as zeros, which triggers a highly inaccurate decomposition. Moreover, few methods focusing on an accuracy exhibit limited scalability since they require huge memory and heavy computational costs while updating factor matrices. In this paper, we propose P-Tucker, a scalable Tucker factorization method for sparse tensors. P-Tucker performs alternating least squares with a row-wise update rule in a fully parallel way, which significantly reduces memory requirements for updating factor matrices. Furthermore, we offer two variants of P-Tucker: a caching algorithm P-Tucker-Cache and an approximation algorithm P-Tucker-Approx, both of which accelerate the update process. Experimental results show that P-Tucker exhibits 1.7-14.1x speed-up and 1.4-4.8x less error compared to the state-of-the-art. In addition, P-Tucker scales near linearly with the number of observable entries in a tensor and number of threads. Thanks to P-Tucker, we successfully discover hidden concepts and relations in a large-scale real-world tensor, while existing methods cannot reveal latent features due to their limited scalability or low accuracy.