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.
BIGDATA: F: DKA: CSD: Topological Data Analysis and Machine-Learning with Community-Accepted Features awarded by National Science Foundation (Co-Principal Investigator). 2014 to 2018
Topological Signal Analysis for Multi-Modal Data Analysis awarded by Geometric Data Analytics, Inc. (Principal Investigator). 2016 to 2017
Bendich, P, Chin, SP, Clark, J, DeSena, J, Harer, J, Munch, E, Newman, A, Porter, D, Rouse, D, Strawn, N, and Watkins, A. "Topological and statistical behavior classifiers for tracking applications." IEEE Transactions on Aerospace and Electronic Systems 52.6 (December 1, 2016): 2644-2661. Full Text
Bendich, P, Marron, JS, Miller, E, Pieloch, A, and Skwerer, S. "Persistent Homology Analysis of Brain Artery Trees." The annals of applied statistics 10.1 (January 2016): 198-218. Open Access Copy
Bendich, P, Gasparovic, E, Harer, J, Izmailov, R, and Ness, L. "Multi-scale local shape analysis and feature selection in machine learning applications." Proceedings of the International Joint Conference on Neural Networks 2015-September (September 28, 2015). Full Text Open Access Copy
Munch, E, Turner, K, Bendich, P, Mukherjee, S, Mattingly, J, and Harer, J. "Probabilistic Fréchet means for time varying persistence diagrams." Electronic Journal of Statistics 9 (January 1, 2015): 1173-1204. Full Text Open Access Copy
Tralie, CJ, and Bendich, P. "Cover Song Identification with Timbral Shape Sequences." Proc. of Int. Symp. on Music Inf. Retrieval (2015): 38-44. Open Access Copy
Bendich, P, Wang, B, and Mukherjee, S. "Local homology transfer and stratification learning." Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (April 30, 2012): 1355-1370.
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.
Rouse, D, Watkins, A, Porter, D, Harer, J, Bendich, P, Strawn, N, Munch, E, Desena, J, Clarke, J, Gilbert, J, Chin, S, and Newman, A. "Feature-aided multiple hypothesis tracking using topological and statistical behavior classifiers." January 1, 2015. Full Text