Paul L Bendich
- Assistant Research Professor in the Department 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, 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 (2010): 12-23. Full Text
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 (2010): 1-10. Full Text
Bendich, P, Edelsbrunner, H, Morozov, D, and Patel, A. "Homology and Robustness of Level and Interlevel Sets."
Bendich, P, Mukherjee, S, and Wang, B. "Towards Stratification Learning through Homology Inference."
Munch, E, Turner, K, Bendich, P, Mukherjee, S, Mattingly, J, and Harer, J. "Probabilistic Fréchet Means for Time Varying Persistence Diagrams." Full Text Open Access Copy