Paul L Bendich

  • Assistant Research Professor in the Department of Mathematics
  • Assistant Director of Curricular Engagement of the Information Initiative at Duke
External address: 121 Physcis Bldg, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2811

Research Areas and Keywords

Computational Mathematics
topological data analysis, data science
Signals, Images & Data
topological data analysis, machine learning, applied topology, data science
Topology
topological data analysis, applied topology

I work in computational topology, which for me means adapting and using tools from algebraic topology in order to study noisy and high-dimensional datasets arising from a variety of scientific applications. My thesis research involved the analysis of datasets for which the number of degrees of freedom varies across the parameter space. The main tools are local homology and intersection homology, suitably redefined in this fuzzy multi-scale context. I am also working on building connections between computational topology and various statistical data analysis algorithms, such as clustering or manifold learning, as well as building connections between computational topology and diffusion geometry.

Education & Training
  • Ph.D., Duke University 2008

Selected Grants

BIGDATA: F: DKA: CSD: Topological Data Analysis and Machine-Learning with Community-Accepted Features awarded by National Science Foundation (Co-Principal Investigator). 2014 to 2018

Topological Signal Analysis for Multi-Modal Data Analysis awarded by Geometric Data Analytics, Inc. (Principal Investigator). 2016 to 2017

Bendich, P, Chin, SP, Clark, J, Desena, J, Harer, J, Munch, E, Newman, A, Porter, D, Rouse, D, Strawn, N, and Watkins, A. "Topological and statistical behavior classifiers for tracking applications." IEEE Transactions on Aerospace and Electronic Systems 52.6 (December 2016): 2644-2661. Full Text

Tralie, CJ, and Bendich, P. "Cover Song Identification with Timbral Shape Sequences." 16th International Society for Music Information Retrieval (ISMIR) (October 1, 2015): 38-44. Open Access Copy

Bendich, P, Gasparovic, E, Harer, J, Izmailov, R, and Ness, L. "Multi-scale local shape analysis and feature selection in machine learning applications." Proceedings of the International Joint Conference on Neural Networks 2015-September (September 28, 2015). Full Text Open Access Copy

Bendich, P, Wang, B, and Mukherjee, S. "Local homology transfer and stratification learning." Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (April 30, 2012): 1355-1370.

Bendich, P, Cabello, S, and Edelsbrunner, H. "A point calculus for interlevel set homology." Pattern Recognition Letters 33.11 (2012): 1436-1444. Full Text

Bendich, P, and Harer, J. "Persistent Intersection Homology." Foundations of Computational Mathematics 11.3 (2011): 305-336. Full Text

Bendich, P, Galkovskyi, T, and Harer, J. "Improving homology estimates with random walks." Inverse Problems 27.12 (2011). Full Text

Bendich, P, Mukherjee, S, and Wang, B. "Stratification learning through homology inference." AAAI Fall Symposium - Technical Report FS-10-06 (December 1, 2010): 10-17.

Bendich, P, Edelsbrunner, H, and Kerber, M. "Computing robustness and persistence for images." IEEE transactions on visualization and computer graphics 16.6 (November 2010): 1251-1260. Full Text

Bendich, P, Edelsbrunner, H, Kerber, M, and 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) 6281 LNCS (2010): 12-23. Full Text

Pages

Bendich, P, Gasparovic, E, Harer, J, and Tralie, C. "Geometric models for musical audio data." June 1, 2016. Full Text

Rouse, D, Watkins, A, Porter, D, Harer, J, Bendich, P, Strawn, N, Munch, E, Desena, J, Clarke, J, Gilbert, J, Chin, S, and Newman, A. "Feature-aided multiple hypothesis tracking using topological and statistical behavior classifiers." January 1, 2015. Full Text