# Structured low-rank matrix learning: algorithms and applications

arXiv: https://arxiv.org/abs/1704.07352 · HTML: https://mlsanity.com/paper/1704.07352/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2017.

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

- [Early Recognition of Parkinson's Disease Through Acoustic Analysis and Machine Learning](https://mlsanity.com/paper/2407.16091/) (2024)

## Abstract (arXiv)

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the low-rank and the structural constraints onto separate factors. We formulate the optimization problem on the Riemannian spectrahedron manifold, where the Riemannian framework allows to develop computationally efficient conjugate gradient and trust-region algorithms. Experiments on problems such as standard/robust/non-negative matrix completion, Hankel matrix learning and multi-task learning demonstrate the efficacy of our approach. A shorter version of this work has been published in ICML'18.