# Topological Data Analysis for Object Data

arXiv: https://arxiv.org/abs/1804.10255 · HTML: https://mlsanity.com/paper/1804.10255/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2018.

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

- [Visualizing Topological Importance: A Class-Driven Approach](https://mlsanity.com/paper/2309.13185/) (2023)
- [Topological data analysis of human vowels: Persistent homologies across representation spaces](https://mlsanity.com/paper/2310.06508/) (2023)

## Abstract (arXiv)

Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes to vectorize object data and perform statistical analysis. We apply to this pipeline to some biological images that were previously shown to be challenging to study using shape theory. Surprisingly, the most persistent features are shown to be "topological noise" and the statistical analysis depends on the less persistent features which we refer to as the "geometric signal". We also describe the first steps to a new approach to using topology for object data analysis, which applies topology to distributions on object spaces.