# Paul L Bendich

- Associate Research Professor of Mathematics

**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

##### Signals, Images & Data

##### 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.

### Selected Grants

Geometric and Topological Methods for Multi-Modal Data Analysis and Fusion awarded by Air Force Office of Scientific Research (Co-Principal Investigator). 2018 to 2021

BIGDATA: F: DKA: CSD: Topological Data Analysis and Machine-Learning with Community-Accepted Features awarded by National Science Foundation (Co-Principal Investigator). 2014 to 2019

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

Tralie, CJ, Smith, A, Borggren, N, Hineman, J, Bendich, P, Zulch, P, and Harer, J. "Geometric cross-modal comparison of heterogeneous sensor data." *2018 Ieee Aerospace Conference* (March 2018).
Full Text Open Access Copy

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 1, 2016): 2644-2661.
Full Text

Bendich, P, Gasparovic, E, Harer, J, and Tralie, C. "Geometric Models for Musical Audio Data." *Proceedings of the 32st International Symposium on Computational Geometry (SOCG)* (June 2016).

Bendich, P, Marron, JS, Miller, E, Pieloch, A, and Skwerer, S. "Persistent homology analysis of brain artery trees." *Annals of Applied Statistics* 10.1 (2016): 198-218.
Open Access Copy

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

Munch, E, Turner, K, Bendich, P, Mukherjee, S, Mattingly, J, and Harer, J. "Probabilistic Fréchet means for time varying persistence diagrams." *Electronic Journal of Statistics* 9 (January 1, 2015): 1173-1204.
Full Text Open Access Copy

Bendich, P, Edelsbrunner, H, Morozov, D, and Patel, A. "Homology and robustness of level and interlevel sets." *Homology, Homotopy and Applications* 15.1 (2013): 51-72.
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Bendich, P, Cabello, S, and Edelsbrunner, H. "A point calculus for interlevel set homology." *Pattern Recognition Letters* 33.11 (August 1, 2012): 1436-1444.
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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.

## Pages

Garagić, D, Peskoe, J, Liu, F, Claffey, MS, Bendich, P, Hineman, J, Borggren, N, Harer, J, Zulch, P, and Rhodes, BJ. "Upstream fusion of multiple sensing modalities using machine learning and topological analysis: An initial exploration." June 25, 2018. Full Text

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

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

A key goal of *Together Duke* is to invest in faculty as scholars and leaders of the university’s intellectual communities. To foster collaboration around new and emerging areas of interest... read more »

For his excellent work in developing Data+ into a university model for undergraduate mentoring and research, Paul Bendich has been granted the Dean's Leadership Award. This award is given to a faculty or staff member who has made a distinctive... read more »