# 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.

Bendich, P, Galkovskyi, T, and Harer, J. "Improving homology estimates with random walks." *Inverse Problems* 27.12 (December 1, 2011).
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Bendich, P, and Harer, J. "Persistent Intersection Homology." *Foundations of Computational Mathematics* 11.3 (June 1, 2011): 305-336.
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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.

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 (November 22, 2010): 12-23.
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Bendich, P, Edelsbrunner, H, Morozov, D, and Patel, A. "The robustness of level sets." *Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)* 6346 LNCS.PART 1 (November 19, 2010): 1-10.
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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.
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Bendich, P, Gasparovic, E, Tralie, CJ, and Harer, J. "Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology."

Bendich, P, Mukherjee, S, and Wang, B. "Towards Stratification Learning through Homology Inference."

Bendich, P, Bubenik, P, and Wagner, A. "Stabilizing the unstable output of persistent homology computations.".