Paul L Bendich
- Associate Research Professor of Mathematics
- Assistant Director of Curricular Engagement of the Information Initiative at Duke
Research Areas and Keywords
Signals, Images & Data
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., 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. “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
Bendich, Paul, et al. Stabilizing the unstable output of persistent homology computations.
Bendich, Paul, et al. Towards Stratification Learning through Homology Inference.