ArticlePloS one2021
Noise robustness of persistent homology on greyscale images, across filtrations and signatures.
Article in PloS one, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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Who cites it
4 citing papers in PubMed.
- Uncertainty-aware Topological Persistence Guided Knowledge Distillation on Wearable Sensor Data.IEEE internet of things journal · 2024Article
- Three-dimensional topology-based analysis segments volumetric and spatiotemporal fluorescence microscopy.Biological imaging · 2024Article
- Article
- Constrained Adaptive Distillation Based on Topological Persistence for Wearable Sensor Data.IEEE transactions on instrumentation and measurement · 2023Article
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4 authors.
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Abstract
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.
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