#### Title

A Statistical Approach to Persistent Homology

#### Document Type

Article

#### Publication Date

2007

#### Publication Title

Homology, Homotopy and Applications

#### Abstract

Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying space. In this paper we take a statistical approach to this problem.We assume that the data is randomly sampled from an unknown probability distribution. We define two filtered complexes with which we can calculate the persistent homology of a probability distribution. Using statistical estimators for samples from certain families of distributions, we show that we can recover the persistent homology of the underlying distribution.

#### Repository Citation

Bubenik, P., & Kim, P. T. (2007). A STATISTICAL APPROACH TO PERSISTENT HOMOLOGY. Homology, Homotopy & Applications, 9(2), 337-362.

#### Original Citation

Bubenik, P., & Kim, P. T. (2007). A STATISTICAL APPROACH TO PERSISTENT HOMOLOGY. Homology, Homotopy & Applications, 9(2), 337-362.

#### Volume

9

#### Issue

2

## Comments

This research was partially funded by the Swiss National Science Foundation grant 200020-105383. This research was partially funded by NSERC grant OGP46204.