# DTM-based Filtrations

arXiv: https://arxiv.org/abs/1811.04757 · HTML: https://mlsanity.com/paper/1811.04757/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2018.

## Built on by (most cited first, 16 of 16)

- [RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds](https://mlsanity.com/paper/2202.01725/) (2022)
- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [Euler Characteristic Tools For Topological Data Analysis](https://mlsanity.com/paper/2303.14040/) (2023)
- [Topological Singularity Detection at Multiple Scales](https://mlsanity.com/paper/2210.00069/) (2022)
- [Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds](https://mlsanity.com/paper/2307.09259/) (2023)
- [Topological Point Cloud Clustering](https://mlsanity.com/paper/2303.16716/) (2023)
- [A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification](https://mlsanity.com/paper/2605.02836/) (2026)
- [Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PH](https://mlsanity.com/paper/2310.16437/) (2023)
- [Persistent Homology for High-dimensional Data Based on Spectral Methods](https://mlsanity.com/paper/2311.03087/) (2023)
- [A Closed-Form Adaptive-Landmark Kernel for Certified Point-Cloud and Graph Classification](https://mlsanity.com/paper/2605.04046/) (2026)
- [Differentially Private Topological Data Analysis](https://mlsanity.com/paper/2305.03609/) (2023)
- [Detection of Small Holes by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtration](https://mlsanity.com/paper/2204.07821/) (2022)
- [Prototype Selection Using Topological Data Analysis](https://mlsanity.com/paper/2511.04873/) (2025)
- [The Topology of Multimodal Fusion: Why Current Architectures Fail at Creative Cognition](https://mlsanity.com/paper/2604.04465/) (2026)
- [The Topological Stability Index: A Variance-Based Measure for Persistence Barcodes](https://mlsanity.com/paper/2605.29839/) (2026)
- [How fine a change can moments see? A scale law for detecting distribution shift, with a kernel calibration rule](https://mlsanity.com/paper/2608.01268/) (2026)

## 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.