Noise robustness of persistent homology on greyscale images, across filtrations and signatures

Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH...

Full description

Saved in:
Bibliographic Details
Published in:PloS one 2021-09, Vol.16 (9), p.e0257215-e0257215
Main Authors: Turkeš, Renata, Nys, Jannes, Verdonck, Tim, Latré, Steven
Format: Article
Language:English
Subjects:
Algorithms
Animals
Biology and Life Sciences
Computer and Information Sciences
Computer science
Data analysis
Datasets
Diabetic retinopathy
Diagnostic Imaging - instrumentation
Experiments
Gray scale
Handwriting
Homology
Homology (Biology)
Humans
Image classification
Image Processing, Computer-Assisted - methods
Information management
Mathematics
Methods
Models, Theoretical
Morphology
Noise
Noise measurement
Noise pollution
Noise sensitivity
Normal Distribution
Physical Sciences
Reproducibility of Results
Research and Analysis Methods
Robustness
Sensitivity and Specificity
Signatures
Stability
Theorems
Topology
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH and the main reason for practical success are the stability theorems that give theoretical results about noise robustness, since real data is typically contaminated with noise or measurement errors. However, little attention has been paid to what these stability theorems mean in practice. To gain some insight into this question, we evaluate the noise robustness of PH on the MNIST dataset of greyscale images. More precisely, we investigate to what extent PH changes under typical forms of image noise, and quantify the loss of performance in classifying the MNIST handwritten digits when noise is added to the data. The results show that the sensitivity to noise of PH is influenced by the choice of filtrations and persistence signatures (respectively the input and output of PH), and in particular, that PH features are often not robust to noise in a classification task.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0257215