# DFacTo: Distributed Factorization of Tensors

arXiv: https://arxiv.org/abs/1406.4519 · HTML: https://mlsanity.com/paper/1406.4519/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2014.

## Built on by (most cited first, 8 of 8)

- [Faster Robust Tensor Power Method for Arbitrary Order](https://mlsanity.com/paper/2306.00406/) (2023)
- [Nonparametric Factor Trajectory Learning for Dynamic Tensor Decomposition](https://mlsanity.com/paper/2207.02446/) (2022)
- [Factor Augmented Tensor-on-Tensor Neural Networks](https://mlsanity.com/paper/2405.19610/) (2024)
- [Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes](https://mlsanity.com/paper/2110.10082/) (2021)
- [Nonparametric Embeddings of Sparse High-Order Interaction Events](https://mlsanity.com/paper/2207.03639/) (2022)
- [Towards Sampling Data Structures for Tensor Products in Turnstile Streams](https://mlsanity.com/paper/2510.03678/) (2025)
- [Communication Efficient Generalized Tensor Factorization for Decentralized Healthcare Networks](https://mlsanity.com/paper/2109.01718/) (2021)
- [Accelerated Stochastic Gradient for Nonnegative Tensor Completion and Parallel Implementation](https://mlsanity.com/paper/2109.09534/) (2021)

## Abstract (arXiv)

We present a technique for significantly speeding up Alternating Least Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor factorization. By exploiting properties of the Khatri-Rao product, we show how to efficiently address a computationally challenging sub-step of both algorithms. Our algorithm, DFacTo, only requires two sparse matrix-vector products and is easy to parallelize. DFacTo is not only scalable but also on average 4 to 10 times faster than competing algorithms on a variety of datasets. For instance, DFacTo only takes 480 seconds on 4 machines to perform one iteration of the ALS algorithm and 1,143 seconds to perform one iteration of the GD algorithm on a 6.5 million x 2.5 million x 1.5 million dimensional tensor with 1.2 billion non-zero entries.