# Min-plus algebraic low rank matrix approximation: a new method for revealing structure in networks

arXiv: https://arxiv.org/abs/1708.06552 · HTML: https://mlsanity.com/paper/1708.06552/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2017.

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

- [Matrix Factorization in Tropical and Mixed Tropical-Linear Algebras](https://mlsanity.com/paper/2309.13914/) (2023)

## Abstract (arXiv)

In this paper we introduce min-plus low rank matrix approximation. By using min and plus rather than plus and times as the basic operations in the matrix multiplication; min-plus low rank matrix approximation is able to detect characteristically different structures than classical low rank approximation techniques such as Principal Component Analysis (PCA). We also show how min-plus matrix algebra can be interpreted in terms of shortest paths through graphs, and consequently how min-plus low rank matrix approximation is able to find and express the predominant structure of a network.