# 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

##### 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.

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 1, 2016): 2644-2661.
Full Text

Bendich, P, Marron, JS, Miller, E, Pieloch, A, and Skwerer, S. "Persistent Homology Analysis of Brain Artery Trees." *The annals of applied statistics* 10.1 (January 2016): 198-218.
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

Tralie, CJ, and Bendich, P. "Cover Song Identification with Timbral Shape Sequences." *Proc. of Int. Symp. on Music Inf. Retrieval* (2015): 38-44.
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.
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Bendich, P, and Harer, J. "Persistent Intersection Homology." *Foundations of Computational Mathematics* 11.3 (2011): 305-336.
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Bendich, P, Galkovskyi, T, and Harer, J. "Improving homology estimates with random walks." *Inverse Problems* 27.12 (2011).
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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.

## 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