# Sheaves: A Topological Approach to Big Data

arXiv: https://arxiv.org/abs/1901.01341 · HTML: https://mlsanity.com/paper/1901.01341/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2019.

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

- [Disentangling Hyperedges through the Lens of Category Theory](https://mlsanity.com/paper/2510.16289/) (2025)

## Abstract (arXiv)

This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that the data can be presented in terms of pair-wise relationships between objects/events. This assumption is used to mine for patterns in the dataset, defining a reduced graph or dataset that boils-down or concentrates information into a more compact form. The resulting extracted structure or set of patterns are manifestly symbolic in nature, as they capture and encode the graph structure of the dataset in terms of a (generative) grammar. This structure is identified as having the formal mathematical structure of a sheaf. In essence, this paper introduces the basic concepts of sheaf theory into the domain of graphical datasets.