Paul L Bendich
- Associate Research Professor of Mathematics
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, 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. 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 (November 19, 2010): 1-10. Full Text
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. Full Text
Bendich, P, Bubenik, P, and Wagner, A. "Stabilizing the unstable output of persistent homology computations."
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."
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