DeepAI AI Chat
Log In Sign Up

A Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science

by   Lander Ver Hoef, et al.

Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is particularly useful for the analysis of imagery, namely persistent homology. We briefly discuss the theoretical background but focus primarily on understanding the output of this tool and discussing what information it can glean. To this end, we frame our discussion around a guiding example of classifying satellite images from the Sugar, Fish, Flower, and Gravel Dataset produced for the study of mesocale organization of clouds by Rasp et. al. in 2020 (arXiv:1906:01906). We demonstrate how persistent homology and its vectorization, persistence landscapes, can be used in a workflow with a simple machine learning algorithm to obtain good results, and explore in detail how we can explain this behavior in terms of image-level features. One of the core strengths of persistent homology is how interpretable it can be, so throughout this paper we discuss not just the patterns we find, but why those results are to be expected given what we know about the theory of persistent homology. Our goal is that a reader of this paper will leave with a better understanding of TDA and persistent homology, be able to identify problems and datasets of their own for which persistent homology could be helpful, and gain an understanding of results they obtain from applying the included GitHub example code.


page 6

page 8

page 13

page 16

page 19

page 20

page 21

page 25


Discussion of 'Event History and Topological Data Analysis'

Garside et al. use event history methods to analyze topological data. We...

Using Persistent Homology to Quantify a Diurnal Cycle in Hurricane Felix

The diurnal cycle of tropical cyclones (TCs) is a daily cycle in clouds ...

On topological data analysis for SHM; an introduction to persistent homology

This paper aims to discuss a method of quantifying the 'shape' of data, ...

Topological Data Analysis of Spatial Systems

In this chapter, we discuss applications of topological data analysis (T...

Efficient Approximation of Multiparameter Persistence Modules

Topological Data Analysis is a growing area of data science, which aims ...

Topology Applied to Machine Learning: From Global to Local

Through the use of examples, we explain one way in which applied topolog...

The Impact of Changes in Resolution on the Persistent Homology of Images

Digital images enable quantitative analysis of material properties at mi...