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