English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Topological data analysis is a recent and fast growing field that approachesthe analysis of datasets using techniques from (algebraic) topology. Its maintool, persistent homology (PH), has seen a notable increase in applications inthe last decade. Often cited as the most favourable property of PH and the mainreason for practical success are the stability theorems that give theoreticalresults about noise robustness, since real data is typically contaminated withnoise or measurement errors. However, little attention has been paid to whatthese stability theorems mean in practice. To gain some insight into thisquestion, we evaluate the noise robustness of PH on the MNIST dataset ofgreyscale images. More precisely, we investigate to what extent PH changesunder typical forms of image noise, and quantify the loss of performance inclassifying the MNIST handwritten digits when noise is added to the data. Theresults show that the sensitivity to noise of PH is influenced by the choice offiltrations and persistence signatures (respectively the input and output ofPH), and in particular, that PH features are often not robust to noise in aclassification task.

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