Papers on Topology + Learning.

A biased list of papar on the application of topology in machine learning. Feel free to suggest related paper. I will add them gradually.

Content

1. Survey Papers/Books
2. Persistence Diagram for ML
   1. Vector method
   2. Kernel method
   3. Others
3. Applications
   1. Graph Classification
   2. Neural Network
   3. Natural Language Processing
   4. Vision

Survey Papers

1. Computational topology: an introduction Herbert Edelsbrunner and John Harer book

2. Persistence Theory: From Quiver Representations to Data Analysis Steve Y. Oudot book

3. Topology and data Gunnar Carlsson paper

4. Elementary Applied Topology Robert Ghrist book

5. A roadmap for the computation of persistent homology Nina Otter, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, Heather A. Harrington paper

Persistence Diagram for ML

Vector method

1. A persistence landscapes toolbox for topological statistics Peter Bubenik, Pawel Dlotko paper
2. Stable topological signatures for points on 3D shapes Mathieu Carrière, Steve Yann Oudot, Maks Ovsjanikov Computer Graphics Forum 2015 paper
3. Stochastic Convergence of Persistence Landscapes and Silhouettes Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman SoCG 2014 paper
4. Persistence Images: A Stable Vector Representation of Persistent Homology Henry Adams, Sofya Chepushtanova, Tegan Emerson, Eric Hanson, Michael Kirby, Francis Motta, Rachel Neville, Chris Peterson, Patrick Shipman, and Lori Ziegelmeier JMLR 2017 paper

Kernel method

1. Sliced wasserstein kernel for persistence diagrams Mathieu Carriere and Marco Cuturi and Steve Oudot ICML 2017 paper

2. Persistence weighted Gaussian kernel for topological data analysis Genki Kusano, Yasuaki Hiraoka and Kenji Fukumizu ICML 2016 paper

3. A stable multi-scale kernel for topological machine learning Jan Reininghaus, Stefan Huber, Ulrich Bauer, Roland Kwitt CVPR 2015 paper

4. Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams Tam Le, Makoto Yamada NeurIPS 2018 paper

5. On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spaces

Mathieu Carriere, Ulrich Bauer SoCG 2019 paper

1. Learning metrics for persistence-based summaries and applications for graph classification Qi Zhao, Yusu Wang NeurIPS 2019 paper

Others

1. PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures Mathieu Carrière, Frédéric Chazal, Yuichi Ike, Théo Lacombe, Martin Royer, Yuhei Umeda AISTATS 2010 paper

2. Understanding the Power of Persistence Pairing via Permutation Test Chen Cai, Yusu Wang Arxiv 2020 paper

Applications

Graph Classification

1. Deep Learning with Topological Signatures Christoph Hofer, Roland Kwitt, Marc Niethammer, Andreas Uhl NeurIPS 2018 paper

2. A Persistent Weisfeiler-Lehman Procedure for Graph Classification Bastian Rieck, Christian Bock, Karsten Borgwardt ICML 2019 paper

Neural Network

1. A Topology Layer for Machine Learning Rickard Brüel-Gabrielsson, Bradley J. Nelson, Anjan Dwaraknath, Primoz Skraba, Leonidas J. Guibas, Gunnar Carlsson Arxiv 2019 paper

2. Topological Autoencoders Michael Moor, Max Horn, Bastian Rieck, Karsten Borgwardt Arxiv 2019 paper

3. Characterizing the Shape of Activation Space in Deep Neural Networks Thomas Gebhart, Paul Schrater, Alan Hylton Arxiv 2019 paper

4. Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology Bastian Rieck, Matteo Togninalli, Christian Bock, Michael Moor, Max Horn, Thomas Gumbsch, Karsten Borgwardt ICLR 2019 paper

5. Empirical study of the topology and geometry of deep networks Alhussein Fawzi ; Seyed-Mohsen Moosavi-Dezfooli ; Pascal Frossard; Stefano Soatto CVPR 2018 paper

6. Topology and Geometry of Half-Rectified Network Optimization C. Daniel Freeman, Joan Bruna ICLR 2017 paper

7. Topological Data Analysis of Decision Boundaries with Application to Model Selection Karthikeyan Natesan Ramamurthy, Kush R. Varshney, Krishnan Mody ICML 2019 paper

8. A Topological Regularizer for Classifiers via Persistent Homology Chao Chen, Xiuyan Ni, Qinxun Bai, Yusu Wang AISTATS 2019 paper

9. Connectivity-Optimized Representation Learning via Persistent Homology Christoph Hofer, Roland Kwitt, Marc Niethammer, Mandar Dixit ICML 2019 paper

10. Topology of deep neural networks Gregory Naitzat, Andrey Zhitnikov, Lek-Heng Lim paper

Natural Language Processing

1. Does the Geometry of Word Embeddings Help Document Classification? A Case Study on Persistent Homology Based Representations Paul Michel, Abhilasha Ravichander, Shruti Rijhwani paper

Vision

1. Topology-Preserving Deep Image Segmentation Xiaoling Hu, Li Fuxin, Dimitris Samaras, Chao Chen NeurIPS 2019 paper

Event

1. AI Institute “Geometry of Deep Learning” 2019 Link