# A rank-adaptive higher-order orthogonal iteration algorithm for truncated Tucker decomposition

arXiv: https://arxiv.org/abs/2110.12564 · HTML: https://mlsanity.com/paper/2110.12564/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 34 references that are in the map.
- First posted on arXiv 25 Oct 2021.

## Builds on (most cited first, 4 of 4)

- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries](https://mlsanity.com/paper/1710.02261/) (2017)
- [Fast and Accurate Randomized Algorithms for Low-rank Tensor Decompositions](https://mlsanity.com/paper/2104.01101/) (2021)
- [Parallel Tensor Compression for Large-Scale Scientific Data](https://mlsanity.com/paper/1510.06689/) (2015)

## Built on by (most cited first, 2 of 2)

- [Approximately Optimal Core Shapes for Tensor Decompositions](https://mlsanity.com/paper/2302.03886/) (2023)
- [Subquadratic Kronecker Regression with Applications to Tensor Decomposition](https://mlsanity.com/paper/2209.04876/) (2022)

## Abstract (arXiv)

We propose a novel rank-adaptive higher-order orthogonal iteration (HOOI) algorithm to compute the truncated Tucker decomposition of higher-order tensors with a given error tolerance, and prove that the method is locally optimal and monotonically convergent. A series of numerical experiments related to both synthetic and real-world tensors are carried out to show that the proposed rank-adaptive HOOI algorithm is advantageous in terms of both accuracy and efficiency. Some further analysis on the HOOI algorithm and the classical alternating least squares method are presented to further understand why rank adaptivity can be introduced into the HOOI algorithm and how it works.