Reading List
Suggested papers
Manifold Learning
- Niyogi, Smale, Weinberger: Finding the Homology of Submanifolds with High Confidence from Random Samples
- Tenenbaum, de Silva, Langford: A Global Geometric Framework for Nonlinear Dimensionality Reduction
Graph Learning
- Eldridge, Belkin, Wang: Beyond Hartigan Consistency: Merge Distortion Metric for Hierarchical Clustering
- Eldridge, Belkin, Wang: Graphons, mergeons, and so on!
- Parthasarathy, Sivakoff, Tian, Wang: A Quest to Unravel the Metric Structure Behind Perturbed Networks
## Topological Data Analysis
Surveys
- Gunnar Carlsson: Topology and Data
- Robert Ghrist: Barcodes: the persistent topology of data
- Mikael Vejdemo-Johansson: Sketches of a Platypus
- Herbert Edelsbrunner, John Harer: Persistent homology - a survey
Algorithmics
- Edelsbrunner, Letscher, Zomorodian: Topological persistence and simplification
- Afra Zomorodian: Fast construction of the Vietoris-Rips complex
- de Silva, Morozov, Vejdemo-Johansson: Persistent cohomology and circular coordinates
- de Silva, Morozov, Vejdemo-Johansson: Dualities in persistent (co)homology
- Chao Chen, Michael Kerber: Persistent homology computation with a twist
- Bauer, Kerber, Reininghaus: Clear and compress: computing persistent homology in chunks
- Milosavljevic, Morozov, Skraba: Zigzag persistent homology in matrix multiplication time
- Boissonat, Dey, Maria: The compressed annotation matrix: an efficient data structure for computing persistent cohomology
Types of Persistent Homology
- Afra Zomorodian, Gunnar Carlsson: Computing persistent homology
- Gunnar Carlsson, Vin de Silva: Zigzag persistence
- Gunnar Carlsson, Afra Zomorodian: The theory of multidimensional persistence
- Carlsson, Singh, Zomorodian: Computing multidimensional persistence
- Burghelea, Dey: Topological persistence for circle-valued maps
- Chambers, Letscher: Persistent homology over directed acyclic graphs
- Bubenik, Scott: Categorification of persistent homology
- Dey, Fan, Wang: Computing Topological Persistence for Simplicial Maps
Mapper
- Lum, Singh, Lehman, Ishkanov, Vejdemo-Johansson, Alagappan, Carlsson, Carlsson: Extracting insights from the shape of complex data using topology ### Stability
For Persistent Homology
- Cohen-Steiner, Edelsbrunner, Harer: Stability of Persistence Diagrams
- Chazal, Cohen-Steiner, Glisse: Proximity of persistence modules and their diagrams
- Chazal, de Silva, Glisse, Oudot: The structure and stability of persistence modules
- Bauer, Lesnick: Induced Matchings and the Algebraic Stability of Persistence Barcodes
For Mapper and Reeb Graphs
- Carrière, Oudot: Structure and Stability of the 1-Dimensional Mapper
- Carrière, Oudot: Local Equivalence and Intrinsic Metrics between Reeb Graphs
- Munch, Wang: Convergence between Categorical Representations of Reeb Space and Mapper
Statistics
- Bubenik: Statistical topological data analysis using persistence landscapes
- Turner, Mileyko, Mukherjee, Harer: Fréchet means for distributions of persistence diagrams
- Munch, Turner, Bendich: Probabilistic Fréchet means for time varying persistence diagrams
- Møller: The accumulated persistence function, a new useful functional summary statistic for topological data analysis, with a view to brain artery trees and spatial point process applications