# Topological analysis of scalar fields with outliers

arXiv: https://arxiv.org/abs/1412.1680 · HTML: https://mlsanity.com/paper/1412.1680/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2014.

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

- [Improving Metric Dimensionality Reduction with Distributed Topology](https://mlsanity.com/paper/2106.07613/) (2021)
- [Convolutional Persistence Transforms](https://mlsanity.com/paper/2208.02107/) (2022)

## Abstract (arXiv)

Given a real-valued function f defined over a manifold M embedded in ℝd, we are interested in recovering structural information about f from the sole information of its values on a finite sample P. Existing methods provide approximation to the persistence diagram of f when geometric noise and functional noise are bounded. However, they fail in the presence of aberrant values, also called outliers, both in theory and practice. We propose a new algorithm that deals with outliers. We handle aberrant functional values with a method inspired from the k-nearest neighbors regression and the local median filtering, while the geometric outliers are handled using the distance to a measure. Combined with topological results on nested filtrations, our algorithm performs robust topological analysis of scalar fields in a wider range of noise models than handled by current methods. We provide theoretical guarantees and experimental results on the quality of our approximation of the sampled scalar field.