Topology in Real-World Machine Learning and Data Analysis

Editors

Kathryn Hess

Swiss Federal Institute of Technology Lausanne

Frédéric Chazal

Inria Saclay - Île-de-France Research Centre

Umberto Lupo

Swiss Federal Institute of Technology Lausanne

Impact

Review

29 September 2021

An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists

Frédéric Chazal

and

Bertrand Michel

132,516 views

409 citations

Original Research

11 October 2021

Minimal Cycle Representatives in Persistent Homology Using Linear Programming: An Empirical Study With User’s Guide

Lu Li

, 3 more and

Lori Ziegelmeier

5,340 views

11 citations

Hierarchical density-based spatial clustering (HDBSCAN) of six UMAP components of the imaging dataset (left panel). The orange pixels represent spectra registered from the type-1 microfossils. The green pixels represent spectra registered from the type-2 microfossils. The blue pixels represent spectra registered from the surface contamination. Black and grey pixels–spectra registered from the quartz matrix of the Gunflint chert. Right panel–the optical microscopy image of the analyzed area. Note the aligned distribution of classified spectra with the bio-lamination surface crossing the image.

Original Research

23 August 2021

On Topological Analysis of fs-LIMS Data. Implications for in Situ Planetary Mass Spectrometry

Rustam A. Lukmanov

, 7 more and

Peter Wurz

5,268 views

9 citations

Original Research

18 August 2021

Topological Data Analysis Highlights Novel Geographical Signatures of the Human Gut Microbiome

Eva Lymberopoulos

, 2 more and

Nikhil Sharma

4,197 views

4 citations

Original Research

26 April 2022

Contagion Dynamics for Manifold Learning

Barbara I. Mahler

1,778 views

0 citations

(A) Persistence Diagrams (B) Persistence Diagrams with boundaries of the support function for Tent Features (C) Persistence Diagrams with boundaries of the support for Adaptive Templates.

Review

28 July 2021

A Comparative Study of Machine Learning Methods for Persistence Diagrams

Danielle Barnes

, 1 more and

Jose A. Perea

10,336 views

22 citations

Original Research

09 July 2021

Supervised Learning Using Homology Stable Rank Kernels

Jens Agerberg

, 2 more and

Wojciech Chachólski

4,756 views

4 citations

Original Research

29 June 2021

Topological Data Analysis of C. elegans Locomotion and Behavior

Ashleigh Thomas

, 4 more and

Peter Bubenik

4,921 views

6 citations

Original Research

16 June 2021

Deep Graph Mapper: Seeing Graphs Through the Neural Lens

Cristian Bodnar

, 1 more and

Pietro Liò

5,910 views

27 citations

Precision and recall for the PredictFTs algorithm on each program indexed by the cut-off probability parameter.

Original Research

28 May 2021

Topology-Inspired Method Recovers Obfuscated Term Information From Induced Software Call-Stacks

Kelly Maggs

and

Vanessa Robins

2,746 views

0 citations

A persistence image arises as a discretisation of the density function (with appropriate weights) supported on a persistence diagram. It permits the calculation of an increasingly better-resolved sequence of images, which may be directly used as feature vectors.

Review

26 May 2021

A Survey of Topological Machine Learning Methods

Felix Hensel

, 1 more and

Bastian Rieck

59,236 views

132 citations

(Top right) An energy function for the molecule pentane. The domain is a torus, i.e., a square with periodic boundary conditions, as there are two circular degrees of freedom (dihedral angles) in the molecule. (Left) Nine different sublevel sets of energy. (Bottom right) The sublevel set persistent homology of this energy function on the torus, with 0-dimensional homology in red, 1-dimensional homology in blue, 2-dimensional homology in green. Image from Mirth et al. (2021).

Review

14 May 2021

Topology Applied to Machine Learning: From Global to Local

Henry Adams

and

Michael Moy

12,237 views

17 citations

Original Research

22 April 2021

Optimization of Spectral Wavelets for Persistence-Based Graph Classification

Ka Man Yim

and

Jacob Leygonie

5,187 views

6 citations

Pipeline for vectorizing a persistent diagram using persistent images. This figure is a modification of Figure 1 from Adams et al. (2017) which is licensed under CC BY 4.0.

Review

13 April 2021

Applications of Topological Data Analysis in Oncology

Anuraag Bukkuri

, 1 more and

Isabel K. Darcy

15,451 views

41 citations

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