Paul L Bendich

Paul L Bendich
  • Associate Research Professor 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

Bendich, P., et al. “A point calculus for interlevel set homology.” Pattern Recognition Letters, vol. 33, no. 11, Aug. 2012, pp. 1436–44. Scopus, doi:10.1016/j.patrec.2011.10.007. Full Text

Bendich, P., et al. “Local homology transfer and stratification learning.” Proceedings of the Annual Acm Siam Symposium on Discrete Algorithms, Jan. 2012, pp. 1355–70.

Bendich, P., et al. “Improving homology estimates with random walks.” Inverse Problems, vol. 27, no. 12, Dec. 2011. Scopus, doi:10.1088/0266-5611/27/12/124002. Full Text

Bendich, P., and J. Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics, vol. 11, no. 3, June 2011, pp. 305–36. Scopus, doi:10.1007/s10208-010-9081-1. Full Text

Bendich, P., et al. “Stratification learning through homology inference.” Aaai Fall Symposium  Technical Report, vol. FS-10-06, Dec. 2010, pp. 10–17.

Bendich, P., et al. “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, Nov. 2010, pp. 12–23. Scopus, doi:10.1007/978-3-642-15155-2_2. Full Text

Bendich, P., et al. “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, Nov. 2010, pp. 1–10. Scopus, doi:10.1007/978-3-642-15775-2_1. Full Text

Bendich, Paul, et al. “Computing robustness and persistence for images..” Ieee Transactions on Visualization and Computer Graphics, vol. 16, no. 6, Nov. 2010, pp. 1251–60. Epmc, doi:10.1109/tvcg.2010.139. Full Text

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