Implications of Data Topology for Deep Generative Models

Yinzhu Jin, Rory McDaniel, N. Joseph Tatro, Michael J. Catanzaro, Abraham D. Smith, Paul Bendich, Matthew B. Dwyer, and P. Thomas Fletcher
Frontiers in Computer Science, Volume 6, 2024.

Convolutional Persistence Transforms

Elchanan Solomon and Paul Bendich
Journal of Applied and Computational Topology, to appear, 2024.

Topological Decompositions Enhance Efficiency of Reinforcement Learning

Michael J. Catanzaro, Aaron Dharna, Jay Hineman, James B. Polly, Kevin McGoff, Abraham D. Smith, and Paul Bendich
Proceedings of the 44th IEEE Aerospace, to appear, 2024.

Topological Parallax: a Geometric Specification for Deep Perception Models

Abraham D. Smith, Michael J. Catanzaro, Gabrielle Angeloro, Nirav Patel, and Paul Bendich
Proceedings of the 37th Conference on Neural Information Processing Systems (NeurIPS), to appear, 2023.

Topological Simplification of Signals for Inference and Approximate Reconstruction

Gary Koplik, Nathan Borggren, Sam Voisin, Gabrielle Angeloro, Jay Hineman, Tessa Johnson, and Paul Bendich
Proceedings of the 43rd IEEE Aerospace Conference, to appear, 2023.

Topological Feature Tracking for Submesoscale Eddies

Sam Voisin, Jay Hineman, James Bruce Polly, Gary Koplik, Ken Ball, Paul Bendich, Joseph D`Addezio ,Gregg A Jacobs, and Tamay Ozgokmen.
Geophysical Research Letters, to appear .

From Geometry to Topology: Inverse Theorems for Distributed Persistence

Elchanan Solomon, Alexander Wagner, and Paul Bendich.
Proceedings of the 38th International Symposium on Computational Geometry 61:1-61:16, 2022. .

A Fast and Robust Method for Global Topological Functional Optimization

Elchanan Solomon, Alexander Wagner, and Paul Bendich.
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:109-117, 2021. .

Persistent Obstruction Theory for a Model Category of Measures with Applications to Data Merging

Abraham Smith, Paul Bendich, and John Harer.
Transactions of the American Mathematical Society Series B, 1-38, 2021.

Geometric Fusion via Joint Delay Embeddings

Elchanan Solomon and Paul Bendich.
Proceedings of the 23rd Int. Conf. on Inf. Fusion, 2020 (Best Paper Award, 3rd Runner-up)

Graph Spectral Embedding for Parsimonious Transmission of Multivariate Time Series

Lihan Yao and Paul Bendich.
Proceedings of the 41st IEEE Aerospace Conference, 2020 (Best Paper Award, Remote Sensing Track)

Stabilizing the Unstable Output of Persistent Homology Computations

Paul Bendich, Peter Bubenik, and Alex Wagner.
Journal of Applied and Computational Topology, pp 1-30, 2019.

Multi-scale Geometric Summaries for Similarity-based Sensor Fusion

Christopher J. Tralie, Paul Bendich, and John Harer.
Proceedings of the 40th IEEE Aerospace Conference, 2019.

Topology and Geometry for Tracking and Sensor Fusion (Invited Position Paper)

Paul Bendich.
Proceedings of the SPIE Conference on Signal Processing, Sensor/Information Fusion, and Target Recognition XXVIII, 2019.

Geometric Cross-modal Comparision of Heterogeneous Sensor Data

Christopher J. Tralie, Abraham Smith, Nathan Borggren, Jay Hineman, Paul Bendich, Peter Zulch, and John Harer.
Proceedings of the 39th IEEE Aerospace Conference, 2018.

Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology

Paul Bendich, Ellen Gasparovic , Christopher J. Tralie and John Harer,
in Research in Computational Topology, AWM-IMA Springer Series, vol. 13, pages 93-114..

Topological and Statistical Behavior Classifiers for Tracking Applications

Paul Bendich, Sang Chin ,Jesse Clarke, Jonathan DeSena, John Harer, Liz Munch , Andrew Newman , David Porter, David Rouse, Nate Strawn, and Adam Watkins.
IEEE Transactions on Aerospace and Electronic Systems, 52(6): 2644-2661, 2016.

Persistent Homology Analysis of Brain Artery Trees

Paul Bendich, J.S.Marron ,Ezra Miller, Alex Pieloch, and Sean Skwerer.
Annals of Applied Statistics, 10(1): 198-218, 2016.

Cover Song Identification with Timbral Shape Sequences

Christopher J. Tralie and Paul Bendich.
Proceedings of the Int. Symp. on Music Information Retrieval, pp 38-44, 2015

Probabilistic Frechet Means for Time-Varying Persistence Diagrams

Liz Munch ,Kate Turner, Paul Bendich, Sayan Mukherjee, Jonathan Mattingly, and John Harer,
Electronic Journal of Statistics , Volume 9, pages 1173-1204.

Multi-scale Local Shape Analysis and Feature Selection for Machine Learning Applications

Paul Bendich, Ellen Gasparovic , John Harer, Rauf Ismailov, and Linda Ness.
to appear in the 2015 proceedings of the International Joint Conference on Neural Networks.

Homology and Robustness of Level and Interlevel Sets

Paul Bendich, Herbert Edelsbrunner, Dmitrity Morozov, and Amit Patel
Homology, Homotopy, and Applications, Volume 15, Issue 1, pages 15-72, 2013.

A Point Calculus for Interlevel set Homology

Paul Bendich, Sergio Cabello , and Herbert Edelsbrunner
Pattern Recognition Letters, Volume 33, Issue 11, pages 1436-1444, 2012.

Local Homology Transfer and Stratification Learning

Paul Bendich, Bei Wang , and Sayan Mukherjee
Proc. 24th Sympos. on Discrete Algorithms, pages 1355-1370, 2012. Full version here.

Impoving Homology Estimates with Random Walks

Paul Bendich, Taras Galkovskyi , and John Harer
Inverse Problems 27 (2011) 124002.

Persistent Intersection Homology

Paul Bendich and John Harer
Foundations of Computational Mathematics, 11 (2011), no. 3, 305-336.

Computing Robustness and Persistence for Images

Paul Bendich, Herbert Edelsbrunner, and Michael Kerber
IEEE Trans. Visual. and Comput. Graphics, 2010, pp. 1251-1260

Persistent Homology under Non-Uniform Error

Paul Bendich, Herbert Edelsbrunner, Michael Kerber, and Amit Patel
Proc. 35th Internat. Sympos. on Math. Found, of Comput, Science, 2010, pp. 12-23.

The Robustness of Level Sets

Paul Bendich, Herbert Edelsbrunner, Dmitrity Morozov, and Amit Patel
Proc. 18th Europ. Sympos. Algorithms, 2010, pp. 1-10

Inferring Local Homology from Sampled Stratified Spaces

With David Cohen-Steiner, Herbert Edelsbrunner, John Harer, and Dmitrity Morozov
Proc. 48th Sympos. on Found. of Comput. Science, 2007, pp. 536-546.

Analyzing Stratified Spaces Using Persistent Versions of Intersection and Local Homology

Ph.D. Thesis, Duke University, August 2008.