mlsanityData to 7 Oct 2026

DTM-based Filtrations

arXiv 1811.04757 ↗First posted 12 Nov 2018cs.CG math.ATcited by 16

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Abstract (arXiv)

Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the Cech or Vietoris-Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed. In this paper, we introduce and study a new family of filtrations, the DTM-filtrations, built on top of point clouds in the Euclidean space which are more robust to noise and outliers. The approach adopted in this work relies on the notion of distance-to-measure functions, and extends some previous work on the approximation of such functions.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Nov 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 4; 2023: 6; 2024: 0; 2025: 1; 2026: 5.

16 papers.

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  1. 2022RipsNet: a general architecture for fast and robust estimation of the persistent homology of point cloudscited by 20
  2. 2022On the effectiveness of persistent homologycited by 20
  3. 2023Euler Characteristic Tools For Topological Data Analysiscited by 13
  4. 2022Topological Singularity Detection at Multiple Scalescited by 11
  5. 2023Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Cloudscited by 8
  6. 2023Topological Point Cloud Clusteringcited by 5
  7. 2023Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PHcited by 3
  8. 2023Persistent Homology for High-dimensional Data Based on Spectral Methodscited by 3
  9. 2026A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classificationcited by 3
  10. 2026A Closed-Form Adaptive-Landmark Kernel for Certified Point-Cloud and Graph Classificationcited by 2
  11. 2023Differentially Private Topological Data Analysiscited by 1
  12. 2022Detection of Small Holes by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtrationcited by 0
4 more
  1. 2025Prototype Selection Using Topological Data Analysiscited by 0
  2. 2026The Topology of Multimodal Fusion: Why Current Architectures Fail at Creative Cognitioncited by 0
  3. 2026The Topological Stability Index: A Variance-Based Measure for Persistence Barcodescited by 0
  4. 2026How fine a change can moments see? A scale law for detecting distribution shift, with a kernel calibration rulecited by 0