Math @ Duke
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Papers Published
- with David Cohen-Steiner, Herbert Edelsbrunner, John Harer, and Dmitriy Morozov, Inferring Local Homology from Sampled Stratified Spaces,
In Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, pages 536-546, 2007.
(2007)
- Bendich, P; Mukherjee, S; Wang, B, Stratification learning through homology inference, vol. FS-10-06
(January, 2010),
pp. 10-17, ISBN 9781577354888 [abs]
- Bendich, P; Mukherjee, S; Wang, B, Towards Stratification Learning through Homology Inference
(August, 2010) [1008.3572v1] [abs]
- with Bendich, P; Edelsbrunner, H; Kerber, M, Computing robustness and persistence for images.,
IEEE transactions on visualization and computer graphics, vol. 16 no. 6
(November, 2010),
pp. 1251-1260, ISSN 1077-2626 [doi] [abs]
- with Bendich, P; Edelsbrunner, H; Morozov, D; Patel, A, The robustness of level sets,
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6346 LNCS no. PART 1
(November, 2010),
pp. 1-10, Springer Berlin Heidelberg, ISSN 0302-9743 [doi] [abs]
- with Bendich, P; Edelsbrunner, H; Kerber, M; Patel, A, Persistent homology under non-uniform error,
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6281 LNCS
(November, 2010),
pp. 12-23, Springer Berlin Heidelberg, ISSN 0302-9743, ISBN 9783642151545 [doi] [abs]
- with Bendich, P; Harer, J, Persistent Intersection Homology,
Foundations of Computational Mathematics, vol. 11 no. 3
(June, 2011),
pp. 305-336, Springer Nature, ISSN 1615-3375 [doi] [abs]
- with Bendich, P; Galkovskyi, T; Harer, J, Improving homology estimates with random walks,
Inverse Problems, vol. 27 no. 12
(December, 2011),
pp. 124002-124002, IOP Publishing, ISSN 0266-5611 [doi] [abs]
- with Bendich, P; Wang, B; Mukherjee, S, Local homology transfer and stratification learning,
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
(January, 2012),
pp. 1355-1370, ISBN 9781611972108 [doi] [abs]
- with Bendich, P; Cabello, S; Edelsbrunner, H, A point calculus for interlevel set homology,
Pattern Recognition Letters, vol. 33 no. 11
(August, 2012),
pp. 1436-1444, Elsevier BV, ISSN 0167-8655 [doi] [abs]
- Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel, Homology and Robustness of Level and Interlevel Sets, edited by Gunnar Carlsson,
Homology, Homotopy, and Applications, vol. 15 no. 1
(March, 2013),
pp. 51-72 [abs]
- Bendich, P; Edelsbrunner, H; Morozov, D; Patel, A, Homology and robustness of level and interlevel sets,
Homology, Homotopy and Applications, vol. 15 no. 1
(April, 2013),
pp. 51-72, International Press of Boston [1102.3389v1], [doi] [abs]
- Christopher J Tralie and Paul Bendich, Cover Song Identification with Timbral Shape,
Proceedings of the 16th International Society for Music Information Retrieval
(2015),
pp. 38-44 [1507.05143] [abs]
- Liz Munch, Paul Bendich, Kate Turner, Sayan Mukherjee, Jonathan Mattingly, and John Harer, Probabalistic Frechet Means and Statistics on Vineyards,
Electronic Journal of Statistics, vol. 9
(2015),
pp. 1173-1204 [6530] [abs] [author's comments]
- Munch, E; Turner, K; Bendich, P; Mukherjee, S; Mattingly, J; Harer, J, Probabilistic Fréchet means for time varying persistence diagrams,
Electronic Journal of Statistics, vol. 9 no. 1
(January, 2015),
pp. 1173-1204, Institute of Mathematical Statistics [1307.6530v3], [doi] [abs]
- Rouse, D; Watkins, A; Porter, D; Harer, J; Bendich, P; Strawn, N; Munch, E; Desena, J; Clarke, J; Gilbert, J; Chin, S; Newman, A, Feature-aided multiple hypothesis tracking using topological and statistical behavior classifiers,
Proceedings of SPIE - The International Society for Optical Engineering, vol. 9474
(January, 2015), SPIE, ISBN 9781628415902 [doi] [abs]
- Bendich, P; Gasparovic, E; Harer, J; Izmailov, R; Ness, L, Multi-scale local shape analysis and feature selection in machine learning applications,
Proceedings of the International Joint Conference on Neural Networks, vol. 2015-September
(September, 2015),
pp. 1-8, IEEE, ISBN 9781479919604 [arXiv:1410.3169], [repository], [doi] [abs]
- Tralie, CJ; Bendich, P, Cover Song Identification with Timbral Shape Sequences,
16th International Society for Music Information Retrieval (ISMIR)
(October, 2015),
pp. 38-44 [1507.05143v1] [abs]
- Bendich, P; Marron, JS; Miller, E; Pieloch, A; Skwerer, S, Persistent homology analysis of brain artery trees,
Annals of Applied Statistics, vol. 10 no. 1
(2016),
pp. 198-218, ISSN 1932-6157 (to appear.) [repository], [doi] [abs]
- Bendich, P; Gasparovic, E; Harer, J; Tralie, C, Geometric Models for Musical Audio Data,
Proceedings of the 32st International Symposium on Computational Geometry (SOCG)
(June, 2016)
- Bendich, P; Gasparovic, E; Harer, J; Tralie, C, Geometric models for musical audio data,
Leibniz International Proceedings in Informatics, LIPIcs, vol. 51
(June, 2016),
pp. 65.1-65.5, ISBN 9783959770095 [doi] [abs]
- Bendich, P; Chin, SP; Clark, J; DeSena, J; Harer, J; Munch, E; Newman, A; Porter, D; Rouse, D; Strawn, N; Watkins, A, Topological and statistical behavior classifiers for tracking applications,
IEEE Transactions on Aerospace and Electronic Systems, vol. 52 no. 6
(December, 2016),
pp. 2644-2661, Institute of Electrical and Electronics Engineers (IEEE) [doi] [abs]
- Bendich, P; Gasparovic, E; Harer, J; Tralie, CJ, Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology, vol. 13
(January, 2018),
pp. 93-114 [doi] [abs]
- Tralie, CJ; Smith, A; Borggren, N; Hineman, J; Bendich, P; Zulch, P; Harer, J, Geometric Cross-Modal Comparison of Heterogeneous Sensor Data,
Proceedings of the 39th IEEE Aerospace Conference, vol. 2018-March
(March, 2018),
pp. 1-10, IEEE, ISBN 9781538620144 [doi] [abs]
- Garagić, D; Peskoe, J; Liu, F; Claffey, MS; Bendich, P; Hineman, J; Borggren, N; Harer, J; Zulch, P; Rhodes, BJ, Upstream fusion of multiple sensing modalities using machine learning and topological analysis: An initial exploration,
IEEE Aerospace Conference Proceedings, vol. 2018-March
(June, 2018),
pp. 1-8, IEEE, ISBN 9781538620144 [doi] [abs]
- Bendich, P, Topology, geometry, and machine-learning for tracking and sensor fusion,
Proceedings of SPIE - The International Society for Optical Engineering, vol. 11017
(January, 2019),
pp. lxxxiii-cii, ISBN 9781510627017
- Tralie, CJ; Bendich, P; Harer, J, Multi-Scale Geometric Summaries for Similarity-Based Sensor Fusion,
IEEE Aerospace Conference Proceedings, vol. 2019-March
(March, 2019), ISBN 9781538668542 [doi] [abs]
- Bendich, P; Bubenik, P; Wagner, A, Stabilizing the unstable output of persistent homology computations,
Journal of Applied and Computational Topology
(November, 2019),
pp. 1-30, Springer [abs]
- Blasch, E; Grewe, LL; Waltz, EL; Bendich, P; Pavlovic, V; Kadar, I; Chong, CY, Machine learning in/with information fusion for infrastructure understanding, panel summary,
Proceedings of SPIE - The International Society for Optical Engineering, vol. 11423
(January, 2020), ISBN 9781510636231 [doi] [abs]
- Yao, L; Bendich, P, Graph Spectral Embedding for Parsimonious Transmission of Multivariate Time Series,
IEEE Aerospace Conference Proceedings
(March, 2020), ISBN 9781728127347 [doi] [abs]
- Solomon, E; Bendich, P, Geometric fusion via joint delay embeddings,
Proceedings of 2020 23rd International Conference on Information Fusion, FUSION 2020
(July, 2020) [doi] [abs]
- Solomon, E; Wagner, A; Bendich, P, A Fast and Robust Method for Global Topological Functional Optimization,
24TH INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS (AISTATS), vol. 130
(2021),
pp. 109-+ [abs]
- Solomon, E; Wagner, A; Bendich, P, A Fast and Robust Method for Global Topological Functional Optimization,
Proceedings of Machine Learning Research, vol. 130
(January, 2021),
pp. 109-117 [abs]
- Smith, AD; Bendich, P; Harer, J, PERSISTENT OBSTRUCTION THEORY FOR A MODEL CATEGORY OF MEASURES WITH APPLICATIONS TO DATA MERGING,
Transactions of the American Mathematical Society Series B, vol. 8 no. 1
(February, 2021),
pp. 1-38, American Mathematical Society (AMS) [doi] [abs]
- Solomon, E; Wagner, A; Bendich, P, From Geometry to Topology: Inverse Theorems for Distributed Persistence,
Leibniz International Proceedings in Informatics, LIPIcs, vol. 224
(June, 2022), ISBN 9783959772273 [doi] [abs]
- Voisin, S; Hineman, J; Polly, JB; Koplik, G; Ball, K; Bendich, P; D‘Addezio, J; Jacobs, GA; Özgökmen, T, Topological Feature Tracking for Submesoscale Eddies,
Geophysical Research Letters, vol. 49 no. 20
(October, 2022) [doi] [abs]
- Koplik, G; Borggren, N; Voisin, S; Angeloro, G; Hineman, J; Johnson, T; Bendich, P, Topological Simplification of Signals for Inference and Approximate Reconstruction,
IEEE Aerospace Conference Proceedings, vol. 2023-March
(January, 2023), ISBN 9781665490320 [doi] [abs]
- Solomon, E; Wagner, A; Bendich, P, FROM GEOMETRY TO TOPOLOGY: INVERSE THEOREMS FOR DISTRIBUTED PERSISTENCE,
Journal of Computational Geometry, vol. 14 no. 2 Special Issue
(January, 2023),
pp. 172-196 [doi] [abs]
- Solomon, YE; Bendich, P, Convolutional persistence transforms,
Journal of Applied and Computational Topology
(January, 2024) [doi] [abs]
Papers Submitted
- Paul Bendich and Peter Bubenik, Stabilizing the output of persistent homology computations,
Proc. 2016 Symposium on Computational Geometry
(2015) [1512.01700]
- Paul Bendich, Ellen Gasparovic, John Harer, and Christopher J. Tralie, Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology
(2016) [1602.06245]
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dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
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