# Tensor completion using geodesics on Segre manifolds

arXiv: https://arxiv.org/abs/2108.00735 · HTML: https://mlsanity.com/paper/2108.00735/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 66 references that are in the map.
- First posted on arXiv 2 Aug 2021.

## Builds on (most cited first, 8 of 8)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Tensor Completion Algorithms in Big Data Analytics](https://mlsanity.com/paper/1711.10105/) (2017)
- [A Brief Introduction to Manifold Optimization](https://mlsanity.com/paper/1906.05450/) (2019)
- [Tensor Methods and Recommender Systems](https://mlsanity.com/paper/1603.06038/) (2016)
- [Tensor Completion Made Practical](https://mlsanity.com/paper/2006.03134/) (2020)
- [Geometric Optimization Methods for Adaptive Filtering](https://mlsanity.com/paper/1305.1886/) (2013)
- [Low-Rank and Sparse Enhanced Tucker Decomposition for Tensor Completion](https://mlsanity.com/paper/2010.00359/) (2020)

## Built on by (most cited first, 1 of 1)

- [Guaranteed Noisy CP Tensor Recovery via Riemannian Optimization on the Segre Manifold](https://mlsanity.com/paper/2510.00569/) (2025)

## Abstract (arXiv)

We propose a Riemannian conjugate gradient (CG) optimization method for finding low rank approximations of incomplete tensors. Our main contribution consists of an explicit expression of the geodesics on the Segre manifold. These are exploited in our algorithm to perform the retractions. We apply our method to movie rating predictions in a recommender system for the MovieLens dataset, and identification of pure fluorophores via fluorescent spectroscopy with missing data. In this last application, we recover the tensor decomposition from less than 10% of the data.